sandwich/0000755000176200001440000000000014535611613012057 5ustar liggesuserssandwich/NAMESPACE0000644000176200001440000000362014277043203013274 0ustar liggesusersimport("stats", "zoo") importFrom("utils", "combn") export( ## core ingredients "sandwich", "bread", "meat", ## OPG estimator "vcovOPG", ## HC estimators "vcovHC", "vcovHC.default", "meatHC", ## clustered estimators "vcovCL", "meatCL", ## HAC estimators "vcovHAC", "vcovHAC.default", "meatHAC", "kernHAC", "NeweyWest", "weave", ## panel estimators "vcovPL", "meatPL", ## panel corrected estimators "vcovPC", "meatPC", ## clustered bootstrap (and jackknife) estimator "vcovBS", "vcovBS.default", "vcovBS.lm", ".vcovBSenv", "vcovJK", ## weights/bandwidths for HAC estimators "weightsLumley", "weightsAndrews", "bwAndrews", "bwNeweyWest", ## new estfun generic "estfun", ## auxiliary functions "kweights", "lrvar", "isoacf", "pava.blocks" ) ## methods for extracting bread matrix S3method("bread", "default") S3method("bread", "lm") S3method("bread", "mlm") S3method("bread", "glm") S3method("bread", "survreg") S3method("bread", "coxph") S3method("bread", "nls") S3method("bread", "rlm") S3method("bread", "clm") S3method("bread", "polr") S3method("bread", "gam") S3method("bread", "hurdle") S3method("bread", "zeroinfl") S3method("bread", "mlogit") ## methods for empirical estimating functions S3method("estfun", "lm") S3method("estfun", "glm") S3method("estfun", "mlm") S3method("estfun", "survreg") S3method("estfun", "coxph") S3method("estfun", "nls") S3method("estfun", "rlm") S3method("estfun", "clm") S3method("estfun", "polr") S3method("estfun", "hurdle") S3method("estfun", "zeroinfl") S3method("estfun", "mlogit") ## methods for vcov* S3method("vcovHC", "default") S3method("vcovHC", "mlm") S3method("vcovHAC", "default") S3method("vcovBS", "default") S3method("vcovBS", "lm") S3method("vcovBS", "glm") S3method("vcovJK", "default") sandwich/README.md0000644000176200001440000000272514272074171013344 0ustar liggesusers ## Robust Covariance Matrix Estimators Model-robust standard error estimators for cross-sectional, time series, clustered, panel, and longitudinal data. Modular object-oriented implementation with support for many model objects, including: `lm`, `glm`, `fixest`, `survreg`, `coxph`, `mlogit`, `polr`, `hurdle`, `zeroinfl`, and beyond. **Sandwich covariances for general parametric models:** Central limit theorem and sandwich estimator **Object-oriented implementation in R:** ``` r library("sandwich") library("lmtest") data("PetersenCL", package = "sandwich") m <- lm(y ~ x, data = PetersenCL) coeftest(m, vcov = sandwich) ``` ## t test of coefficients: ## ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 0.0297 0.0284 1.05 0.3 ## x 1.0348 0.0284 36.45 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` r coeftest(m, vcov = vcovCL, cluster = ~ firm) ``` ## t test of coefficients: ## ## Estimate Std. 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In case two variables are specified, the second variable is assumed to provide the time ordering (instead of using the argument \code{order.by}). By default (\code{cluster = NULL}), either \code{attr(x, "cluster")} is used (if any) or otherwise every observation is assumed to be its own cluster.} \item{order.by}{a variable, list/data.frame, or formula indicating the aggregation within time periods. By default \code{attr(x, "order.by")} is used (if any) or specified through the second variable in \code{cluster} (see above). If neither is available, observations within clusters are assumed to be ordered.} \item{kernel}{a character specifying the kernel used. All kernels described in Andrews (1991) are supported, see \code{\link{kweights}}.} \item{lag}{character or numeric, indicating the lag length used. Three rules of thumb (\code{"max"} or equivalently \code{"P2009"}, \code{"NW1987"}, or \code{"NW1994"}) can be specified, or a numeric number of lags can be specified directly. By default, \code{"NW1987"} is used.} \item{bw}{numeric. The bandwidth of the kernel which by default corresponds to \code{lag + 1}. Only one of \code{lag} and \code{bw} should be used.} \item{sandwich}{logical. Should the sandwich estimator be computed? If set to \code{FALSE} only the meat matrix is returned.} \item{fix}{logical. Should the covariance matrix be fixed to be positive semi-definite in case it is not?} \item{adjust}{logical. Should a finite sample adjustment be made? This amounts to multiplication with \eqn{n/(n - k)} where \eqn{n} is the number of observations and \eqn{k} is the number of estimated parameters.} \item{aggregate}{logical. Should the \code{estfun} be aggregated within each time period (yielding Driscoll and Kraay 1998) or not (restricting cross-sectional and cross-serial correlation to zero, yielding panel Newey-West)?} \item{\dots}{arguments passed to the \code{metaPL} or \code{estfun} function, respectively.} } \details{ \code{vcovPL} is a function for estimating the Newey-West (1987) and Driscoll and Kraay (1998) covariance matrix. Driscoll and Kraay (1998) apply a Newey-West type correction to the sequence of cross-sectional averages of the moment conditions (see Hoechle (2007)). For large \eqn{T} (and regardless of the length of the cross-sectional dimension), the Driscoll and Kraay (1998) standard errors are robust to general forms of cross-sectional and serial correlation (Hoechle (2007)). The Newey-West (1987) covariance matrix restricts the Driscoll and Kraay (1998) covariance matrix to no cross-sectional correlation. The function \code{meatPL} is the work horse for estimating the meat of Newey-West (1987) and Driscoll and Kraay (1998) covariance matrix estimators. \code{vcovPL} is a wrapper calling \code{\link{sandwich}} and \code{\link{bread}} (Zeileis 2006). Default lag length is the \code{"NW1987"}. For \code{lag = "NW1987"}, the lag length is chosen from the heuristic \eqn{floor[T^{(1/4)}]}. More details on lag length selection in Hoechle (2007). For \code{lag = "NW1994"}, the lag length is taken from the first step of Newey and West's (1994) plug-in procedure. The \code{cluster}/\code{order.by} specification can be made in a number of ways: Either both can be a single variable or \code{cluster} can be a \code{list}/\code{data.frame} of two variables. If \code{\link[stats]{expand.model.frame}} works for the model object \code{x}, the \code{cluster} (and potentially additionally \code{order.by}) can also be a \code{formula}. By default (\code{cluster = NULL, order.by = NULL}), \code{attr(x, "cluster")} and \code{attr(x, "order.by")} are checked and used if available. If not, every observation is assumed to be its own cluster, and observations within clusters are assumed to be ordered accordingly. If the number of observations in the model \code{x} is smaller than in the original \code{data} due to \code{NA} processing, then the same \code{NA} processing can be applied to \code{cluster} if necessary (and \code{x$na.action} being available). } \value{ A matrix containing the covariance matrix estimate. } \references{ Andrews DWK (1991). \dQuote{Heteroscedasticity and Autocorrelation Consistent Covariance Matrix Estimation}, \emph{Econometrica}, 817--858. Driscoll JC & Kraay AC (1998). \dQuote{Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data}, \emph{The Review of Economics and Statistics}, \bold{80}(4), 549--560. Hoechle D (2007). \dQuote{Robust Standard Errors for Panel Regressions with Cross-Sectional Dependence}, \emph{Stata Journal}, \bold{7}(3), 281--312. Newey WK & West KD (1987). \dQuote{Hypothesis Testing with Efficient Method of Moments Estimation}, \emph{International Economic Review}, 777-787. Newey WK & West KD (1994). \dQuote{Automatic Lag Selection in Covariance Matrix Estimation}, \emph{The Review of Economic Studies}, \bold{61}(4), 631--653. White H (1980). \dQuote{A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity}, \emph{Econometrica}, 817--838. \doi{10.2307/1912934} Zeileis A (2004). \dQuote{Econometric Computing with HC and HAC Covariance Matrix Estimator}, \emph{Journal of Statistical Software}, \bold{11}(10), 1--17. \doi{10.18637/jss.v011.i10} Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators}, \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} Zeileis A, Köll S, Graham N (2020). \dQuote{Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.} \emph{Journal of Statistical Software}, \bold{95}(1), 1--36. \doi{10.18637/jss.v095.i01} } \seealso{\code{\link{vcovCL}}, \code{\link{vcovPC}}} \examples{ ## Petersen's data data("PetersenCL", package = "sandwich") m <- lm(y ~ x, data = PetersenCL) ## Driscoll and Kraay standard errors ## lag length set to: T - 1 (maximum lag length) ## as proposed by Petersen (2009) sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "max", adjust = FALSE))) ## lag length set to: floor(4 * (T / 100)^(2/9)) ## rule of thumb proposed by Hoechle (2007) based on Newey & West (1994) sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1994"))) ## lag length set to: floor(T^(1/4)) ## rule of thumb based on Newey & West (1987) sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1987"))) ## the following specifications of cluster/order.by are equivalent vcovPL(m, cluster = ~ firm + year) vcovPL(m, cluster = PetersenCL[, c("firm", "year")]) vcovPL(m, cluster = ~ firm, order.by = ~ year) vcovPL(m, cluster = PetersenCL$firm, order.by = PetersenCL$year) ## these are also the same when observations within each ## cluster are already ordered vcovPL(m, cluster = ~ firm) vcovPL(m, cluster = PetersenCL$firm) } \keyword{regression} sandwich/man/weightsAndrews.Rd0000644000176200001440000001502414125157660016123 0ustar liggesusers\name{weightsAndrews} \alias{weightsAndrews} \alias{bwAndrews} \alias{kernHAC} \title{Kernel-based HAC Covariance Matrix Estimation} \description{ A set of functions implementing a class of kernel-based heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimators as introduced by Andrews (1991). } \usage{ kernHAC(x, order.by = NULL, prewhite = 1, bw = bwAndrews, kernel = c("Quadratic Spectral", "Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)", "ARMA(1,1)"), adjust = TRUE, diagnostics = FALSE, sandwich = TRUE, ar.method = "ols", tol = 1e-7, data = list(), verbose = FALSE, \dots) weightsAndrews(x, order.by = NULL, bw = bwAndrews, kernel = c("Quadratic Spectral", "Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), prewhite = 1, ar.method = "ols", tol = 1e-7, data = list(), verbose = FALSE, \dots) bwAndrews(x, order.by = NULL, kernel = c("Quadratic Spectral", "Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)", "ARMA(1,1)"), weights = NULL, prewhite = 1, ar.method = "ols", data = list(), \dots) } \arguments{ \item{x}{a fitted model object. For \code{bwAndrews} it can also be a score matrix (as returned by \code{estfun}) directly.} \item{order.by}{Either a vector \code{z} or a formula with a single explanatory variable like \code{~ z}. The observations in the model are ordered by the size of \code{z}. If set to \code{NULL} (the default) the observations are assumed to be ordered (e.g., a time series).} \item{prewhite}{logical or integer. Should the estimating functions be prewhitened? If \code{TRUE} or greater than 0 a VAR model of order \code{as.integer(prewhite)} is fitted via \code{ar} with method \code{"ols"} and \code{demean = FALSE}. The default is to use VAR(1) prewhitening.} \item{bw}{numeric or a function. The bandwidth of the kernel (corresponds to the truncation lag). If set to to a function (the default is \code{bwAndrews}) it is adaptively chosen.} \item{kernel}{a character specifying the kernel used. All kernels used are described in Andrews (1991).} \item{approx}{a character specifying the approximation method if the bandwidth \code{bw} has to be chosen by \code{bwAndrews}.} \item{adjust}{logical. Should a finite sample adjustment be made? This amounts to multiplication with \eqn{n/(n-k)} where \eqn{n} is the number of observations and \eqn{k} the number of estimated parameters.} \item{diagnostics}{logical. Should additional model diagnostics be returned? See \code{\link{vcovHAC}} for details.} \item{sandwich}{logical. Should the sandwich estimator be computed? If set to \code{FALSE} only the middle matrix is returned.} \item{ar.method}{character. The \code{method} argument passed to \code{\link{ar}} for prewhitening (only, not for bandwidth selection).} \item{tol}{numeric. Weights that exceed \code{tol} are used for computing the covariance matrix, all other weights are treated as 0.} \item{data}{an optional data frame containing the variables in the \code{order.by} model. By default the variables are taken from the environment which the function is called from.} \item{verbose}{logical. Should the bandwidth parameter used be printed?} \item{\dots}{further arguments passed to \code{bwAndrews}.} \item{weights}{numeric. A vector of weights used for weighting the estimated coefficients of the approximation model (as specified by \code{approx}). By default all weights are 1 except that for the intercept term (if there is more than one variable).} } \details{\code{kernHAC} is a convenience interface to \code{\link{vcovHAC}} using \code{weightsAndrews}: first a weights function is defined and then \code{vcovHAC} is called. The kernel weights underlying \code{weightsAndrews} are directly accessible via the function \code{\link{kweights}} and require the specification of the bandwidth parameter \code{bw}. If this is not specified it can be chosen adaptively by the function \code{bwAndrews} (except for the \code{"Truncated"} kernel). The automatic bandwidth selection is based on an approximation of the estimating functions by either AR(1) or ARMA(1,1) processes. To aggregate the estimated parameters from these approximations a weighted sum is used. The \code{weights} in this aggregation are by default all equal to 1 except that corresponding to the intercept term which is set to 0 (unless there is no other variable in the model) making the covariance matrix scale invariant. Further details can be found in Andrews (1991). The estimator of Newey & West (1987) is a special case of the class of estimators introduced by Andrews (1991). It can be obtained using the \code{"Bartlett"} kernel and setting \code{bw} to \code{lag + 1}. A convenience interface is provided in \code{\link{NeweyWest}}. } \value{ \code{kernHAC} returns the same type of object as \code{\link{vcovHAC}} which is typically just the covariance matrix. \code{weightsAndrews} returns a vector of weights. \code{bwAndrews} returns the selected bandwidth parameter. } \references{ Andrews DWK (1991). \dQuote{Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.} \emph{Econometrica}, \bold{59}, 817--858. Newey WK & West KD (1987). \dQuote{A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.} \emph{Econometrica}, \bold{55}, 703--708. } \seealso{\code{\link{vcovHAC}}, \code{\link{NeweyWest}}, \code{\link{weightsLumley}}, \code{\link{weave}}} \examples{ curve(kweights(x, kernel = "Quadratic", normalize = TRUE), from = 0, to = 3.2, xlab = "x", ylab = "k(x)") curve(kweights(x, kernel = "Bartlett", normalize = TRUE), from = 0, to = 3.2, col = 2, add = TRUE) curve(kweights(x, kernel = "Parzen", normalize = TRUE), from = 0, to = 3.2, col = 3, add = TRUE) curve(kweights(x, kernel = "Tukey", normalize = TRUE), from = 0, to = 3.2, col = 4, add = TRUE) curve(kweights(x, kernel = "Truncated", normalize = TRUE), from = 0, to = 3.2, col = 5, add = TRUE) ## fit investment equation data(Investment) fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment) ## compute quadratic spectral kernel HAC estimator kernHAC(fm) kernHAC(fm, verbose = TRUE) ## use Parzen kernel instead, VAR(2) prewhitening, no finite sample ## adjustment and Newey & West (1994) bandwidth selection kernHAC(fm, kernel = "Parzen", prewhite = 2, adjust = FALSE, bw = bwNeweyWest, verbose = TRUE) ## compare with estimate under assumption of spheric errors vcov(fm) } \keyword{regression} \keyword{ts} sandwich/man/vcovCL.Rd0000644000176200001440000002572614272070642014330 0ustar liggesusers\name{vcovCL} \alias{vcovCL} \alias{meatCL} \encoding{UTF-8} \title{Clustered Covariance Matrix Estimation} \description{ Estimation of one-way and multi-way clustered covariance matrices using an object-oriented approach. } \usage{ vcovCL(x, cluster = NULL, type = NULL, sandwich = TRUE, fix = FALSE, \dots) meatCL(x, cluster = NULL, type = NULL, cadjust = TRUE, multi0 = FALSE, \dots) } \arguments{ \item{x}{a fitted model object.} \item{cluster}{a variable indicating the clustering of observations, a \code{list} (or \code{data.frame}) thereof, or a formula specifying which variables from the fitted model should be used (see examples). By default (\code{cluster = NULL}), either \code{attr(x, "cluster")} is used (if any) or otherwise every observation is assumed to be its own cluster.} \item{type}{a character string specifying the estimation type (HC0--HC3). The default is to use \code{"HC1"} for \code{lm} objects and \code{"HC0"} otherwise.} \item{sandwich}{logical. Should the sandwich estimator be computed? If set to \code{FALSE} only the meat matrix is returned.} \item{fix}{logical. Should the covariance matrix be fixed to be positive semi-definite in case it is not?} \item{cadjust}{logical. Should a cluster adjustment be applied?} \item{multi0}{logical. Should the HC0 estimate be used for the final adjustment in multi-way clustered covariances?} \item{\dots}{arguments passed to \code{meatCL}.} } \details{ Clustered sandwich estimators are used to adjust inference when errors are correlated within (but not between) clusters. \code{vcovCL} allows for clustering in arbitrary many cluster dimensions (e.g., firm, time, industry), given all dimensions have enough clusters (for more details, see Cameron et al. 2011). If each observation is its own cluster, the clustered sandwich collapses to the basic sandwich covariance. The function \code{meatCL} is the work horse for estimating the meat of clustered sandwich estimators. \code{vcovCL} is a wrapper calling \code{\link{sandwich}} and \code{\link{bread}} (Zeileis 2006). \code{vcovCL} is applicable beyond \code{lm} or \code{glm} class objects. \code{\link{bread}} and \code{\link{meat}} matrices are multiplied to construct clustered sandwich estimators. The meat of a clustered sandwich estimator is the cross product of the clusterwise summed estimating functions. Instead of summing over all individuals, first sum over cluster. A two-way clustered sandwich estimator \eqn{M} (e.g., for cluster dimensions "firm" and "industry" or "id" and "time") is a linear combination of one-way clustered sandwich estimators for both dimensions (\eqn{M_{id}, M_{time}}) minus the clustered sandwich estimator, with clusters formed out of the intersection of both dimensions (\eqn{M_{id \cap time}}): \deqn{M = M_{id} + M_{time} - M_{id \cap time}}. Additionally, each of the three terms can be weighted by the corresponding cluster bias adjustment factor (see below and Equation 20 in Zeileis et al. 2020). Instead of subtracting \eqn{M_{id \cap time}} as the last subtracted matrix, Ma (2014) suggests to subtract the basic HC0 covariance matrix when only a single observation is in each intersection of \eqn{id} and \eqn{time}. Set \code{multi0 = TRUE} to subtract the basic HC0 covariance matrix as the last subtracted matrix in multi-way clustering. For details, see also Petersen (2009) and Thompson (2011). With the \code{type} argument, HC0 to HC3 types of bias adjustment can be employed, following the terminology used by MacKinnon and White (1985) for heteroscedasticity corrections. HC0 applies no small sample bias adjustment. HC1 applies a degrees of freedom-based correction, \eqn{(n-1)/(n-k)} where \eqn{n} is the number of observations and \eqn{k} is the number of explanatory or predictor variables in the model. HC1 is the most commonly used approach for linear models, and HC0 otherwise. Hence these are the defaults in \code{vcovCL}. However, HC0 and HC1 are less effective than HC2 and HC3 when the number of clusters is relatively small (Cameron et al. 2008). HC2 and HC3 types of bias adjustment are geared towards the linear model, but they are also applicable for GLMs (see Bell and McCaffrey 2002, and Kauermann and Carroll 2001, for details). A precondition for HC2 and HC3 types of bias adjustment is the availability of a hat matrix (or a weighted version therof for GLMs) and hence these two types are currently only implemented for \code{\link{lm}} and \code{\link{glm}} objects. An alternative to the clustered HC3 estimator is the clustered jackknife estimator which is available in \code{\link{vcovBS}} with \code{type = "jackknife"}. In linear models the HC3 and the jackknife estimator coincide (MacKinnon et al. 2022) with the latter still being computationally feasible if the number of observations per cluster is large. In nonlinear models (including non-Gaussian GLMs) the jackknife and the HC3 estimator do not coincide but the jackknife might still be a useful alternative when the HC3 cannot be computed. The \code{cadjust} argument allows to switch the cluster bias adjustment factor \eqn{G/(G-1)} on and off (where \eqn{G} is the number of clusters in a cluster dimension \eqn{g}) See Cameron et al. (2008) and Cameron et al. (2011) for more details about small-sample modifications. The \code{cluster} specification can be made in a number of ways: The \code{cluster} can be a single variable or a \code{list}/\code{data.frame} of multiple clustering variables. If \code{\link[stats]{expand.model.frame}} works for the model object \code{x}, the \code{cluster} can also be a \code{formula}. By default (\code{cluster = NULL}), \code{attr(x, "cluster")} is checked and used if available. If not, every observation is assumed to be its own cluster. If the number of observations in the model \code{x} is smaller than in the original \code{data} due to \code{NA} processing, then the same \code{NA} processing can be applied to \code{cluster} if necessary (and \code{x$na.action} being available). Cameron et al. (2011) observe that sometimes the covariance matrix is not positive-semidefinite and recommend to employ the eigendecomposition of the estimated covariance matrix, setting any negative eigenvalue(s) to zero. This fix is applied, if necessary, when \code{fix = TRUE} is specified. } \value{ A matrix containing the covariance matrix estimate. } \references{ Bell RM, McCaffrey DF (2002). \dQuote{Bias Reduction in Standard Errors for Linear Regression with Multi-Stage Samples}, \emph{Survey Methodology}, \bold{28}(2), 169--181. Cameron AC, Gelbach JB, Miller DL (2008). \dQuote{Bootstrap-Based Improvements for Inference with Clustered Errors}, \emph{The Review of Economics and Statistics}, \bold{90}(3), 414--427. \doi{10.3386/t0344} Cameron AC, Gelbach JB, Miller DL (2011). \dQuote{Robust Inference with Multiway Clustering}, \emph{Journal of Business & Ecomomic Statistics}, \bold{29}(2), 238--249. \doi{10.1198/jbes.2010.07136} Kauermann G, Carroll RJ (2001). \dQuote{A Note on the Efficiency of Sandwich Covariance Matrix Estimation}, \emph{Journal of the American Statistical Association}, \bold{96}(456), 1387--1396. \doi{10.1198/016214501753382309} Ma MS (2014). \dQuote{Are We Really Doing What We Think We Are Doing? A Note on Finite-Sample Estimates of Two-Way Cluster-Robust Standard Errors}, \emph{Mimeo, Availlable at SSRN:} URL \url{https://www.ssrn.com/abstract=2420421}. MacKinnon JG, Nielsen MØ, Webb MD (2022). \dQuote{Cluster-Robust Inference: A Guide to Empirical Practice}, \emph{Journal of Econometrics}, Forthcoming. \doi{10.1016/j.jeconom.2022.04.001} MacKinnon JG, White H (1985). \dQuote{Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties} \emph{Journal of Econometrics}, \bold{29}(3), 305--325. \doi{10.1016/0304-4076(85)90158-7} Petersen MA (2009). \dQuote{Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches}, \emph{The Review of Financial Studies}, \bold{22}(1), 435--480. \doi{10.1093/rfs/hhn053} Thompson SB (2011). \dQuote{Simple Formulas for Standard Errors That Cluster by Both Firm and Time}, \emph{Journal of Financial Economics}, \bold{99}(1), 1--10. \doi{10.1016/j.jfineco.2010.08.016} Zeileis A (2004). \dQuote{Econometric Computing with HC and HAC Covariance Matrix Estimator}, \emph{Journal of Statistical Software}, \bold{11}(10), 1--17. \doi{10.18637/jss.v011.i10} Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators}, \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} Zeileis A, Köll S, Graham N (2020). \dQuote{Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.} \emph{Journal of Statistical Software}, \bold{95}(1), 1--36. \doi{10.18637/jss.v095.i01} } \seealso{\code{\link{vcovHC}}, \code{\link{vcovBS}}} \examples{ ## Petersen's data data("PetersenCL", package = "sandwich") m <- lm(y ~ x, data = PetersenCL) ## clustered covariances ## one-way vcovCL(m, cluster = ~ firm) vcovCL(m, cluster = PetersenCL$firm) ## same ## one-way with HC2 vcovCL(m, cluster = ~ firm, type = "HC2") ## two-way vcovCL(m, cluster = ~ firm + year) vcovCL(m, cluster = PetersenCL[, c("firm", "year")]) ## same ## comparison with cross-section sandwiches ## HC0 all.equal(sandwich(m), vcovCL(m, type = "HC0", cadjust = FALSE)) ## HC2 all.equal(vcovHC(m, type = "HC2"), vcovCL(m, type = "HC2")) ## HC3 all.equal(vcovHC(m, type = "HC3"), vcovCL(m, type = "HC3")) ## Innovation data data("InstInnovation", package = "sandwich") ## replication of one-way clustered standard errors for model 3, Table I ## and model 1, Table II in Berger et al. (2017), see ?InstInnovation ## count regression formula f1 <- cites ~ institutions + log(capital/employment) + log(sales) + industry + year ## model 3, Table I: Poisson model ## one-way clustered standard errors tab_I_3_pois <- glm(f1, data = InstInnovation, family = poisson) vcov_pois <- vcovCL(tab_I_3_pois, InstInnovation$company) sqrt(diag(vcov_pois))[2:4] ## coefficient tables if(require("lmtest")) { coeftest(tab_I_3_pois, vcov = vcov_pois)[2:4, ] } \dontrun{ ## model 1, Table II: negative binomial hurdle model ## (requires "pscl" or alternatively "countreg" from R-Forge) library("pscl") library("lmtest") tab_II_3_hurdle <- hurdle(f1, data = InstInnovation, dist = "negbin") # dist = "negbin", zero.dist = "negbin", separate = FALSE) vcov_hurdle <- vcovCL(tab_II_3_hurdle, InstInnovation$company) sqrt(diag(vcov_hurdle))[c(2:4, 149:151)] coeftest(tab_II_3_hurdle, vcov = vcov_hurdle)[c(2:4, 149:151), ] } } \keyword{regression} sandwich/man/lrvar.Rd0000644000176200001440000000413213452213134014240 0ustar liggesusers\name{lrvar} \alias{lrvar} \title{Long-Run Variance of the Mean} \description{ Convenience function for computing the long-run variance (matrix) of a (possibly multivariate) series of observations. } \usage{ lrvar(x, type = c("Andrews", "Newey-West"), prewhite = TRUE, adjust = TRUE, \dots) } \arguments{ \item{x}{numeric vector, matrix, or time series.} \item{type}{character specifying the type of estimator, i.e., whether \code{\link{kernHAC}} for the Andrews quadratic spectral kernel HAC estimator is used or \code{\link{NeweyWest}} for the Newey-West Bartlett HAC estimator.} \item{prewhite}{logical or integer. Should the series be prewhitened? Passed to \code{\link{kernHAC}} or \code{\link{NeweyWest}}.} \item{adjust}{logical. Should a finite sample adjustment be made? Passed to \code{\link{kernHAC}} or \code{\link{NeweyWest}}.} \item{\dots}{further arguments passed on to \code{\link{kernHAC}} or \code{\link{NeweyWest}}.} } \details{ \code{lrvar} is a simple wrapper function for computing the long-run variance (matrix) of a (possibly multivariate) series \code{x}. First, this simply fits a linear regression model \code{x ~ 1} by \code{\link[stats]{lm}}. Second, the corresponding variance of the mean(s) is estimated either by \code{\link{kernHAC}} (Andrews quadratic spectral kernel HAC estimator) or by \code{\link{NeweyWest}} (Newey-West Bartlett HAC estimator). } \value{For a univariate series \code{x} a scalar variance is computed. For a multivariate series \code{x} the covariance matrix is computed.} \seealso{\code{\link{kernHAC}}, \code{\link{NeweyWest}}, \code{\link{vcovHAC}}} \examples{ suppressWarnings(RNGversion("3.5.0")) set.seed(1) ## iid series (with variance of mean 1/n) ## and Andrews kernel HAC (with prewhitening) x <- rnorm(100) lrvar(x) ## analogous multivariate case with Newey-West estimator (without prewhitening) y <- matrix(rnorm(200), ncol = 2) lrvar(y, type = "Newey-West", prewhite = FALSE) ## AR(1) series with autocorrelation 0.9 z <- filter(rnorm(100), 0.9, method = "recursive") lrvar(z) } \keyword{regression} \keyword{ts} sandwich/man/bread.Rd0000644000176200001440000000315113735441645014205 0ustar liggesusers\name{bread} \alias{bread} \alias{bread.default} \alias{bread.lm} \alias{bread.mlm} \alias{bread.survreg} \alias{bread.coxph} \alias{bread.gam} \alias{bread.nls} \alias{bread.rlm} \alias{bread.hurdle} \alias{bread.zeroinfl} \alias{bread.mlogit} \alias{bread.polr} \alias{bread.clm} \encoding{UTF-8} \title{Bread for Sandwiches} \description{ Generic function for extracting an estimator for the bread of sandwiches. } \usage{ bread(x, \dots) } \arguments{ \item{x}{a fitted model object.} \item{\dots}{arguments passed to methods.} } \value{ A matrix containing an estimator for the expectation of the negative derivative of the estimating functions, usually the Hessian. Typically, this should be an \eqn{k \times k}{k x k} matrix corresponding to \eqn{k} parameters. The rows and columns should be named as in \code{\link{coef}} or \code{\link{terms}}, respectively. The default method tries to extract \code{\link{vcov}} and \code{\link{nobs}} and simply computes their product. } \seealso{\code{\link{lm}}, \code{\link{glm}}} \references{ Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators.} \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} Zeileis A, Köll S, Graham N (2020). \dQuote{Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.} \emph{Journal of Statistical Software}, \bold{95}(1), 1--36. \doi{10.18637/jss.v095.i01} } \examples{ ## linear regression x <- sin(1:10) y <- rnorm(10) fm <- lm(y ~ x) ## bread: n * (x'x)^{-1} bread(fm) solve(crossprod(cbind(1, x))) * 10 } \keyword{regression} sandwich/man/vcovBS.Rd0000644000176200001440000003556414533603730014337 0ustar liggesusers\name{vcovBS} \alias{vcovBS} \alias{vcovBS.default} \alias{vcovBS.lm} \alias{vcovBS.glm} \alias{.vcovBSenv} \encoding{UTF-8} \title{(Clustered) Bootstrap Covariance Matrix Estimation} \description{ Object-oriented estimation of basic bootstrap covariances, using simple (clustered) case-based resampling, plus more refined methods for \code{\link[stats]{lm}} and \code{\link[stats]{glm}} models. } \usage{ vcovBS(x, \dots) \method{vcovBS}{default}(x, cluster = NULL, R = 250, start = FALSE, type = "xy", \dots, fix = FALSE, use = "pairwise.complete.obs", applyfun = NULL, cores = NULL, center = "mean") \method{vcovBS}{lm}(x, cluster = NULL, R = 250, type = "xy", \dots, fix = FALSE, use = "pairwise.complete.obs", applyfun = NULL, cores = NULL, qrjoint = FALSE, center = "mean") \method{vcovBS}{glm}(x, cluster = NULL, R = 250, start = FALSE, type = "xy", \dots, fix = FALSE, use = "pairwise.complete.obs", applyfun = NULL, cores = NULL, center = "mean") } \arguments{ \item{x}{a fitted model object.} \item{cluster}{a variable indicating the clustering of observations, a \code{list} (or \code{data.frame}) thereof, or a formula specifying which variables from the fitted model should be used (see examples). By default (\code{cluster = NULL}), either \code{attr(x, "cluster")} is used (if any) or otherwise every observation is assumed to be its own cluster.} \item{R}{integer. Number of bootstrap replications.} \item{start}{logical. Should \code{coef(x)} be passed as \code{start} to the \code{update(x, subset = ...)} call? In case the model \code{x} is computed by some numeric iteration, this may speed up the bootstrapping.} \item{type}{character (or function). The character string specifies the type of bootstrap to use: In the default and \code{glm} method the three types \code{"xy"}, \code{"fractional"}, and \code{"jackknife"} are available. In the \code{lm} method there are additionally \code{"residual"}, \code{"wild"} (or equivalently: \code{"wild-rademacher"} or \code{"rademacher"}), \code{"mammen"} (or \code{"wild-mammen"}), \code{"norm"} (or \code{"wild-norm"}), \code{"webb"} (or \code{"wild-webb"}). Finally, for the \code{lm} method \code{type} can be a \code{function(n)} for drawing wild bootstrap factors.} \item{\dots}{arguments passed to methods. For the default method, this is passed to \code{update}, and for the \code{lm} method to \code{lm.fit}.} \item{fix}{logical. Should the covariance matrix be fixed to be positive semi-definite in case it is not?} \item{use}{character. Specification passed to \code{\link[stats]{cov}} for handling missing coefficients/parameters.} \item{applyfun}{an optional \code{\link[base]{lapply}}-style function with arguments \code{function(X, FUN, \dots)}. It is used for refitting the model to the bootstrap samples. The default is to use the basic \code{lapply} function unless the \code{cores} argument is specified (see below).} \item{cores}{numeric. If set to an integer the \code{applyfun} is set to \code{\link[parallel]{mclapply}} with the desired number of \code{cores}, except on Windows where \code{\link[parallel]{parLapply}} with \code{makeCluster(cores)} is used.} \item{center}{character. For \code{type = "jackknife"} the coefficients from all jacknife samples (each dropping one observational unit/cluster) can be centered by their \code{"mean"} (default) or by the original full-sample \code{"estimate"}.} \item{qrjoint}{logical. For residual-based and wild boostrap (i.e., \code{type != "xy"}), should the bootstrap sample the dependent variable and then apply the QR decomposition jointly only once? If \code{FALSE}, the boostrap applies the QR decomposition separately in each iteration and samples coefficients directly. If the sample size (and the number of coefficients) is large, then \code{qrjoint = TRUE} maybe significantly faster while requiring much more memory.} } \details{ Clustered sandwich estimators are used to adjust inference when errors are correlated within (but not between) clusters. See the documentation for \code{\link{vcovCL}} for specifics about covariance clustering. This function allows for clustering in arbitrarily many cluster dimensions (e.g., firm, time, industry), given all dimensions have enough clusters (for more details, see Cameron et al. 2011). Unlike \code{vcovCL}, \code{vcovBS} uses a bootstrap rather than an asymptotic solution. Basic (clustered) bootstrap covariance matrix estimation is provided by the default \code{vcovBS} method. It samples clusters (where each observation is its own cluster by default), i.e., using case-based resampling. For obtaining a covariance matrix estimate it is assumed that an \code{\link[stats]{update}} of the model with the resampled \code{subset} can be obtained, the \code{\link[stats]{coef}} extracted, and finally the covariance computed with \code{\link[stats]{cov}}. The \code{update} model is evaluated in the \code{environment(terms(x))} (if available). To speed up computations two further arguments can be leveraged. \enumerate{ \item Instead of \code{\link[base]{lapply}} a parallelized function such as \code{\link[parallel]{parLapply}} or \code{\link[parallel]{mclapply}} can be specified to iterate over the bootstrap replications. For the latter, specifying \code{cores = ...} is a convenience shortcut. \item When specifying \code{start = TRUE}, the \code{coef(x)} are passed to \code{update} as \code{start = coef(x)}. This may not be supported by all model fitting functions and is hence not turned on by default. } The ``xy'' or ``pairs'' bootstrap is consistent for heteroscedasticity and clustered errors, and converges to the asymptotic solution used in \code{vcovCL} as \code{R}, \eqn{n}, and \eqn{g} become large (\eqn{n} and \eqn{g} are the number of observations and the number of clusters, respectively; see Efron 1979, or Mammen 1992, for a discussion of bootstrap asymptotics). For small \eqn{g} -- particularly under 30 groups -- the bootstrap will converge to a slightly different value than the asymptotic method, due to the limited number of distinct bootstrap replications possible (see Webb 2014 for a discussion of this phenomonon). The bootstrap will not necessarily converge to an asymptotic estimate that has been corrected for small samples. The xy approach to bootstrapping is generally only of interest to the practitioner when the asymptotic solution is unavailable (this can happen when using estimators that have no \code{estfun} function, for example). The residual bootstrap, by contrast, is rarely of practical interest, because while it provides consistent inference for clustered standard errors, it is not robust to heteroscedasticity. More generally, bootstrapping is useful when the bootstrap makes different assumptions than the asymptotic estimator, in particular when the number of clusters is small and large \eqn{n} or \eqn{g} assumptions are unreasonable. Bootstrapping is also often effective for nonlinear models, particularly in smaller samples, where asymptotic approaches often perform relatively poorly. See Cameron and Miller (2015) for further discussion of bootstrap techniques in practical applications, and Zeileis et al. (2020) show simulations comparing \code{vcovBS} to \code{vcovCL} in several settings. The jackknife approach is of particular interest in practice because it can be shown to be exactly equivalent to the HC3 (without cluster adjustment, also known as CV3) covariance matrix estimator in linear models (see MacKinnon, Nielsen, Webb 2022). If the number of observations per cluster is large it may become impossible to compute this estimator via \code{\link{vcovCL}} while using the jackknife approach will still be feasible. In nonlinear models (including non-Gaussian GLMs) the jackknife and the HC3 estimator do not coincide but the jackknife might still be a useful alternative when the HC3 cannot be computed. A convenience interface \code{\link{vcovJK}} is provided whose default method simply calls \code{vcovBS(..., type = "jackknife")}. The fractional-random-weight bootstrap (see Xu et al. 2020), first introduced by Rubin (1981) as Bayesian bootstrap, is an alternative to the xy bootstrap when it is computationally challenging or even impractical to reestimate the model on subsets, e.g., when "successes" in binary responses are rare or when the number of parameters is close to the sample size. In these situations excluding some observations completely is the source of the problems, i.e., giving some observations zero weight while others receive integer weights of one ore more. The fractional bootstrap mitigates this by giving every observation a positive fractional weight, drawn from a Dirichlet distribution. These may become close to zero but never exclude an observation completly, thus stabilizing the computation of the reweighted models. The \code{\link[stats]{glm}} method works essentially like the default method but calls \code{\link[stats]{glm.fit}} instead of \code{update}. The \code{\link[stats]{lm}} method provides additional bootstrapping \code{type}s and computes the bootstrapped coefficient estimates somewhat more efficiently using \code{\link[stats]{lm.fit}} (for case-based resampling) or \code{\link[base]{qr.coef}} rather than \code{update}. The default \code{type} is case-based resampling (\code{type = "xy"}) as in the default method. Alternative \code{type} specifications are: \itemize{ \item \code{"residual"}. The residual cluster bootstrap resamples the residuals (as above, by cluster) which are subsequently added to the fitted values to obtain the bootstrapped response variable: \eqn{y^{*} = \hat{y} + e^{*}}{y* = yhat + e*}. Coefficients can then be estimated using \code{qr.coef()}, reusing the QR decomposition from the original fit. As Cameron et al. (2008) point out, the residual cluster bootstrap is not well-defined when the clusters are unbalanced as residuals from one cluster cannot be easily assigned to another cluster with different size. Hence a warning is issued in that case. \item \code{"wild"} (or equivalently \code{"wild-rademacher"} or \code{"rademacher"}). The wild cluster bootstrap does not actually resample the residuals but instead reforms the dependent variable by multiplying the residual by a randomly drawn value and adding the result to the fitted value: \eqn{y^{*} = \hat{y} + e \cdot w}{y* = yhat + e * w} (see Cameron et al. 2008). By default, the factors are drawn from the Rademacher distribution: \code{function(n) sample(c(-1, 1), n, replace = TRUE)}. \item \code{"mammen"} (or \code{"wild-mammen"}). This draws the wild bootstrap factors as suggested by Mammen (1993): \code{sample(c(-1, 1) * (sqrt(5) + c(-1, 1))/2, n, replace = TRUE, prob = (sqrt(5) + c(1, -1))/(2 * sqrt(5)))}. \item \code{"webb"} (or \code{"wild-webb"}). This implements the six-point distribution suggested by Webb (2014), which may improve inference when the number of clusters is small: \code{sample(c(-sqrt((3:1)/2), sqrt((1:3)/2)), n, replace = TRUE)}. \item \code{"norm"} (or \code{"wild-norm"}). The standard normal/Gaussian distribution is used for drawing the wild bootstrap factors: \code{function(n) rnorm(n)}. \item User-defined function. This needs of the form as above, i.e., a \code{function(n)} returning a vector of random wild bootstrap factors of corresponding length. } } \value{ A matrix containing the covariance matrix estimate. } \references{ Cameron AC, Gelbach JB, Miller DL (2008). \dQuote{Bootstrap-Based Improvements for Inference with Clustered Errors}, \emph{The Review of Economics and Statistics}, \bold{90}(3), 414--427. \doi{10.3386/t0344} Cameron AC, Gelbach JB, Miller DL (2011). \dQuote{Robust Inference with Multiway Clustering}, \emph{Journal of Business & Economic Statistics}, \bold{29}(2), 238--249. \doi{10.1198/jbes.2010.07136} Cameron AC, Miller DL (2015). \dQuote{A Practitioner's Guide to Cluster-Robust Inference}, \emph{Journal of Human Resources}, \bold{50}(2), 317--372. \doi{10.3368/jhr.50.2.317} Efron B (1979). \dQuote{Bootstrap Methods: Another Look at the Jackknife}, \emph{The Annals of Statistics}, \bold{7}(1), 1--26. \doi{10.1214/aos/1176344552} MacKinnon JG, Nielsen MØ, Webb MD (2022). \dQuote{Cluster-Robust Inference: A Guide to Empirical Practice}, \emph{Journal of Econometrics}, Forthcoming. \doi{10.1016/j.jeconom.2022.04.001} Mammen E (1992). \dQuote{When Does Bootstrap Work?: Asymptotic Results and Simulations}, \emph{Lecture Notes in Statistics}, \bold{77}. Springer Science & Business Media. Mammen E (1993). \dQuote{Bootstrap and Wild Bootstrap for High Dimensional Linear Models}, \emph{The Annals of Statistics}, \bold{21}(1), 255--285. \doi{10.1214/aos/1176349025} Rubin DB (1981). \dQuote{The Bayesian Bootstrap}, \emph{The Annals of Statistics}, \bold{9}(1), 130--134. \doi{10.1214/aos/1176345338} Webb MD (2014). \dQuote{Reworking Wild Bootstrap Based Inference for Clustered Errors}, Working Paper 1315, \emph{Queen's Economics Department.} \url{https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1315.pdf}. Xu L, Gotwalt C, Hong Y, King CB, Meeker WQ (2020). \dQuote{Applications of the Fractional-Random-Weight Bootstrap}, \emph{The American Statistician}, \bold{74}(4), 345--358. \doi{10.1080/00031305.2020.1731599} Zeileis A, Köll S, Graham N (2020). \dQuote{Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.} \emph{Journal of Statistical Software}, \bold{95}(1), 1--36. \doi{10.18637/jss.v095.i01} } \seealso{\code{\link{vcovCL}}, \code{\link{vcovJK}}} \examples{ ## Petersen's data data("PetersenCL", package = "sandwich") m <- lm(y ~ x, data = PetersenCL) ## comparison of different standard errors suppressWarnings(RNGversion("3.5.0")) set.seed(1) cbind( "classical" = sqrt(diag(vcov(m))), "HC-cluster" = sqrt(diag(vcovCL(m, cluster = ~ firm))), "BS-cluster" = sqrt(diag(vcovBS(m, cluster = ~ firm))), "FW-cluster" = sqrt(diag(vcovBS(m, cluster = ~ firm, type = "fractional"))) ) ## two-way wild cluster bootstrap with Mammen distribution vcovBS(m, cluster = ~ firm + year, type = "wild-mammen") ## jackknife estimator coincides with HC3 (aka CV3) all.equal( vcovBS(m, cluster = ~ firm, type = "jackknife"), vcovCL(m, cluster = ~ firm, type = "HC3", cadjust = FALSE), tolerance = 1e-7 ) } \keyword{regression} \keyword{bootstrap} sandwich/man/vcovHAC.Rd0000644000176200001440000001315413735442444014423 0ustar liggesusers\name{vcovHAC} \alias{vcovHAC} \alias{vcovHAC.default} \alias{meatHAC} \title{Heteroscedasticity and Autocorrelation Consistent (HAC) Covariance Matrix Estimation} \description{ Heteroscedasticity and autocorrelation consistent (HAC) estimation of the covariance matrix of the coefficient estimates in a (generalized) linear regression model. } \usage{ vcovHAC(x, \dots) \method{vcovHAC}{default}(x, order.by = NULL, prewhite = FALSE, weights = weightsAndrews, adjust = TRUE, diagnostics = FALSE, sandwich = TRUE, ar.method = "ols", data = list(), \dots) meatHAC(x, order.by = NULL, prewhite = FALSE, weights = weightsAndrews, adjust = TRUE, diagnostics = FALSE, ar.method = "ols", data = list(), \dots) } \arguments{ \item{x}{a fitted model object.} \item{order.by}{Either a vector \code{z} or a formula with a single explanatory variable like \code{~ z}. The observations in the model are ordered by the size of \code{z}. If set to \code{NULL} (the default) the observations are assumed to be ordered (e.g., a time series).} \item{prewhite}{logical or integer. Should the estimating functions be prewhitened? If \code{TRUE} or greater than 0 a VAR model of order \code{as.integer(prewhite)} is fitted via \code{ar} with method \code{"ols"} and \code{demean = FALSE}.} \item{weights}{Either a vector of weights for the autocovariances or a function to compute these weights based on \code{x}, \code{order.by}, \code{prewhite}, \code{ar.method} and \code{data}. If \code{weights} is a function it has to take these arguments. See also details.} \item{adjust}{logical. Should a finite sample adjustment be made? This amounts to multiplication with \eqn{n/(n-k)} where \eqn{n} is the number of observations and \eqn{k} the number of estimated parameters.} \item{diagnostics}{logical. Should additional model diagnostics be returned? See below for details.} \item{sandwich}{logical. Should the sandwich estimator be computed? If set to \code{FALSE} only the meat matrix is returned.} \item{ar.method}{character. The \code{method} argument passed to \code{\link{ar}} for prewhitening.} \item{data}{an optional data frame containing the variables in the \code{order.by} model. By default the variables are taken from the environment which \code{vcovHAC} is called from.} \item{\dots}{arguments passed to \code{\link{sandwich}} (in \code{vcovHAC}) and \code{\link{estfun}} (in \code{meatHAC}), respectively.} } \details{The function \code{meatHAC} is the real work horse for estimating the meat of HAC sandwich estimators -- the default \code{vcovHAC} method is a wrapper calling \code{\link{sandwich}} and \code{\link{bread}}. See Zeileis (2006) for more implementation details. The theoretical background, exemplified for the linear regression model, is described in Zeileis (2004). Both functions construct weighted information sandwich variance estimators for parametric models fitted to time series data. These are basically constructed from weighted sums of autocovariances of the estimating functions (as extracted by \code{\link{estfun}}). The crucial step is the specification of weights: the user can either supply \code{vcovHAC} with some vector of weights or with a function that computes these weights adaptively (based on the arguments \code{x}, \code{order.by}, \code{prewhite} and \code{data}). Two functions for adaptively choosing weights are implemented in \code{\link{weightsAndrews}} implementing the results of Andrews (1991) and in \code{\link{weightsLumley}} implementing the results of Lumley (1999). The functions \code{\link{kernHAC}} and \code{\link{weave}} respectively are to more convenient interfaces for \code{vcovHAC} with these functions. Prewhitening based on VAR approximations is described as suggested in Andrews & Monahan (1992). The covariance matrix estimators have been improved by the addition of a bias correction and an approximate denominator degrees of freedom for test and confidence interval construction. See Lumley & Heagerty (1999) for details. } \value{A matrix containing the covariance matrix estimate. If \code{diagnostics} was set to \code{TRUE} this has an attribute \code{"diagnostics"} which is a list with \item{bias.correction}{multiplicative bias correction} \item{df}{Approximate denominator degrees of freedom} } \references{ Andrews DWK (1991). \dQuote{Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.} \emph{Econometrica}, \bold{59}, 817--858. Andrews DWK & Monahan JC (1992). \dQuote{An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator.} \emph{Econometrica}, \bold{60}, 953--966. Lumley T & Heagerty P (1999). \dQuote{Weighted Empirical Adaptive Variance Estimators for Correlated Data Regression.} \emph{Journal of the Royal Statistical Society B}, \bold{61}, 459--477. Newey WK & West KD (1987). \dQuote{A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.} \emph{Econometrica}, \bold{55}, 703--708. Zeileis A (2004). \dQuote{Econometric Computing with HC and HAC Covariance Matrix Estimators.} \emph{Journal of Statistical Software}, \bold{11}(10), 1--17. \doi{10.18637/jss.v011.i10} Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators.} \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} } \seealso{\code{\link{weightsLumley}}, \code{\link{weightsAndrews}}, \code{\link{weave}}, \code{\link{kernHAC}}} \examples{ x <- sin(1:100) y <- 1 + x + rnorm(100) fm <- lm(y ~ x) vcovHAC(fm) vcov(fm) } \keyword{regression} \keyword{ts} sandwich/man/kweights.Rd0000644000176200001440000000271413735442674014764 0ustar liggesusers\name{kweights} \alias{kweights} \title{Kernel Weights} \description{ Kernel weights for kernel-based heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimators as introduced by Andrews (1991). } \usage{ kweights(x, kernel = c("Truncated", "Bartlett", "Parzen", "Tukey-Hanning", "Quadratic Spectral"), normalize = FALSE) } \arguments{ \item{x}{numeric.} \item{kernel}{a character specifying the kernel used. All kernels used are described in Andrews (1991).} \item{normalize}{logical. If set to \code{TRUE} the kernels are normalized as described in Andrews (1991).} } \value{ Value of the kernel function at \code{x}. } \references{ Andrews DWK (1991). \dQuote{Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.} \emph{Econometrica}, \bold{59}, 817--858. } \seealso{\code{\link{kernHAC}}, \code{\link{weightsAndrews}}} \examples{ curve(kweights(x, kernel = "Quadratic", normalize = TRUE), from = 0, to = 3.2, xlab = "x", ylab = "k(x)") curve(kweights(x, kernel = "Bartlett", normalize = TRUE), from = 0, to = 3.2, col = 2, add = TRUE) curve(kweights(x, kernel = "Parzen", normalize = TRUE), from = 0, to = 3.2, col = 3, add = TRUE) curve(kweights(x, kernel = "Tukey", normalize = TRUE), from = 0, to = 3.2, col = 4, add = TRUE) curve(kweights(x, kernel = "Truncated", normalize = TRUE), from = 0, to = 3.2, col = 5, add = TRUE) } \keyword{regression} \keyword{ts} sandwich/man/PetersenCL.Rd0000644000176200001440000000251213735444251015130 0ustar liggesusers\name{PetersenCL} \alias{PetersenCL} \title{Petersen's Simulated Data for Assessing Clustered Standard Errors} \description{ Artificial balanced panel data set from Petersen (2009) for illustrating and benchmarking clustered standard errors. } \usage{data("PetersenCL")} \format{ A data frame containing 5000 observations on 4 variables. \describe{ \item{firm}{integer. Firm identifier (500 firms).} \item{year}{integer. Time variable (10 years per firm).} \item{x}{numeric. Independent regressor variable.} \item{y}{numeric. Dependent response variable.} } } \details{ This simulated data set was created to illustrate and benchmark clustered standard errors. The residual and the regressor variable both contain a firm effect, but no year effect. Thus, standard errors clustered by firm are different from the OLS standard errors and similarly double-clustered standard errors (by firm and year) are different from the standard errors clustered by year. } \source{ \url{https://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.htm} } \references{ Petersen MA (2009). \dQuote{Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches}, \emph{The Review of Financial Studies}, \bold{22}(1), 435--480. \doi{10.1093/rfs/hhn053} } \keyword{datasets} sandwich/man/isoacf.Rd0000644000176200001440000000252114277040300014355 0ustar liggesusers\name{isoacf} \alias{isoacf} \alias{pava.blocks} \title{Isotonic Autocorrelation Function} \description{ Autocorrelation function (forced to be decreasing by isotonic regression). } \usage{ isoacf(x, lagmax = NULL, weave1 = FALSE) } \arguments{ \item{x}{numeric vector.} \item{lagmax}{numeric. The maximal lag of the autocorrelations.} \item{weave1}{logical. If set to \code{TRUE} \code{isoacf} uses the \code{acf.R} and \code{pava.blocks} function from the original \code{weave} package, otherwise R's own \code{acf} and \code{isoreg} functions are used.} } \details{ \code{isoacf} computes the autocorrelation function (ACF) of \code{x} enforcing the ACF to be decreasing by isotonic regression. See also Robertson et al. (1988). } \value{ \code{isoacf} returns a numeric vector containing the ACF. } \references{ Lumley T & Heagerty P (1999). \dQuote{Weighted Empirical Adaptive Variance Estimators for Correlated Data Regression.} \emph{Journal of the Royal Statistical Society B}, \bold{61}, 459--477. Robertson T, Wright FT, Dykstra RL (1988). \emph{Order Restricted Statistical Inference}. John Wiley and Sons, New York. } \seealso{\code{\link{weave}}, \code{\link{weightsLumley}}} \examples{ set.seed(1) x <- filter(rnorm(100), 0.9, "recursive") isoacf(x) acf(x, plot = FALSE)$acf } \keyword{regression} \keyword{ts} sandwich/man/vcovOPG.Rd0000644000176200001440000000442413735443027014453 0ustar liggesusers\name{vcovOPG} \alias{vcovOPG} \title{Outer-Product-of-Gradients Covariance Matrix Estimation} \description{ Outer product of gradients estimation for the covariance matrix of the coefficient estimates in regression models. } \usage{ vcovOPG(x, adjust = FALSE, \dots) } \arguments{ \item{x}{a fitted model object.} \item{adjust}{logical. Should a finite sample adjustment be made? This amounts to multiplication with \eqn{n/(n-k)} where \eqn{n} is the number of observations and \eqn{k} the number of estimated parameters.} \item{\dots}{arguments passed to the \code{\link{estfun}} function.} } \details{ In correctly specified models, the \dQuote{meat} matrix (cross product of estimating functions, see \code{\link{meat}}) and the inverse of the \dQuote{bread} matrix (inverse of the derivative of the estimating functions, see \code{\link{bread}}) are equal and correspond to the Fisher information matrix. Typically, an empirical version of the bread is used for estimation of the information but alternatively it is also possible to use the meat. This method is also known as the outer product of gradients (OPG) estimator (Cameron & Trivedi 2005). Using the \pkg{sandwich} infrastructure, the OPG estimator could easily be computed via \code{solve(meat(obj))} (modulo scaling). To employ numerically more stable implementation of the inversion, this simple convenience function can be used: \code{vcovOPG(obj)}. Note that this only works if the \code{estfun()} method computes the maximum likelihood scores (and not a scaled version such as least squares scores for \code{"lm"} objects). } \value{ A matrix containing the covariance matrix estimate. } \references{ Cameron AC and Trivedi PK (2005). \emph{Microeconometrics: Methods and Applications}. Cambridge University Press, Cambridge. Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators.} \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} } \seealso{\code{\link{meat}}, \code{\link{bread}}, \code{\link{sandwich}}} \examples{ ## generate poisson regression relationship x <- sin(1:100) y <- rpois(100, exp(1 + x)) ## compute usual covariance matrix of coefficient estimates fm <- glm(y ~ x, family = poisson) vcov(fm) vcovOPG(fm) } \keyword{regression} \keyword{ts} sandwich/man/vcovHC.Rd0000644000176200001440000001266414227102411014307 0ustar liggesusers\name{vcovHC} \alias{vcovHC} \alias{vcovHC.default} \alias{vcovHC.mlm} \alias{meatHC} \title{Heteroscedasticity-Consistent Covariance Matrix Estimation} \description{ Heteroscedasticity-consistent estimation of the covariance matrix of the coefficient estimates in regression models. } \usage{ vcovHC(x, \dots) \method{vcovHC}{default}(x, type = c("HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4", "HC4m", "HC5"), omega = NULL, sandwich = TRUE, \dots) meatHC(x, type = , omega = NULL, \dots) } \arguments{ \item{x}{a fitted model object.} \item{type}{a character string specifying the estimation type. For details see below.} \item{omega}{a vector or a function depending on the arguments \code{residuals} (the working residuals of the model), \code{diaghat} (the diagonal of the corresponding hat matrix) and \code{df} (the residual degrees of freedom). For details see below.} \item{sandwich}{logical. Should the sandwich estimator be computed? If set to \code{FALSE} only the meat matrix is returned.} \item{\dots}{arguments passed to \code{\link{sandwich}} (in \code{vcovHC}) and \code{\link{estfun}} (in \code{meatHC}), respectively.} } \details{The function \code{meatHC} is the real work horse for estimating the meat of HC sandwich estimators -- the default \code{vcovHC} method is a wrapper calling \code{\link{sandwich}} and \code{\link{bread}}. See Zeileis (2006) for more implementation details. The theoretical background, exemplified for the linear regression model, is described below and in Zeileis (2004). Analogous formulas are employed for other types of models, provided that they depend on a single linear predictor and the estimating functions can be represented as a product of \dQuote{working residual} and regressor vector (Zeileis 2006, Equation 7). When \code{type = "const"} constant variances are assumed and and \code{vcovHC} gives the usual estimate of the covariance matrix of the coefficient estimates: \deqn{\hat \sigma^2 (X^\top X)^{-1}}{sigma^2 (X'X)^{-1}} All other methods do not assume constant variances and are suitable in case of heteroscedasticity. \code{"HC"} (or equivalently \code{"HC0"}) gives White's estimator, the other estimators are refinements of this. They are all of form \deqn{(X^\top X)^{-1} X^\top \Omega X (X^\top X)^{-1}}{(X'X)^{-1} X' Omega X (X'X)^{-1}} and differ in the choice of Omega. This is in all cases a diagonal matrix whose elements can be either supplied as a vector \code{omega} or as a a function \code{omega} of the residuals, the diagonal elements of the hat matrix and the residual degrees of freedom. For White's estimator \code{omega <- function(residuals, diaghat, df) residuals^2} Instead of specifying the diagonal \code{omega} or a function for estimating it, the \code{type} argument can be used to specify the HC0 to HC5 estimators. If \code{omega} is used, \code{type} is ignored. Long & Ervin (2000) conduct a simulation study of HC estimators (HC0 to HC3) in the linear regression model, recommending to use HC3 which is thus the default in \code{vcovHC}. Cribari-Neto (2004), Cribari-Neto, Souza, & Vasconcellos (2007), and Cribari-Neto & Da Silva (2011), respectively, suggest the HC4, HC5, and modified HC4m type estimators. All of them are tailored to take into account the effect of leverage points in the design matrix. For more details see the references. } \value{ A matrix containing the covariance matrix estimate. } \references{ Cribari-Neto F. (2004). \dQuote{Asymptotic Inference under Heteroskedasticity of Unknown Form.} \emph{Computational Statistics & Data Analysis} \bold{45}, 215--233. Cribari-Neto F., Da Silva W.B. (2011). \dQuote{A New Heteroskedasticity-Consistent Covariance Matrix Estimator for the Linear Regression Model.} \emph{Advances in Statistical Analysis}, \bold{95}(2), 129--146. Cribari-Neto F., Souza T.C., Vasconcellos, K.L.P. (2007). \dQuote{Inference under Heteroskedasticity and Leveraged Data.} \emph{Communications in Statistics -- Theory and Methods}, \bold{36}, 1877--1888. Errata: \bold{37}, 3329--3330, 2008. Long J. S., Ervin L. H. (2000). \dQuote{Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model.} \emph{The American Statistician}, \bold{54}, 217--224. MacKinnon J. G., White H. (1985). \dQuote{Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties.} \emph{Journal of Econometrics}, \bold{29}, 305--325. White H. (1980). \dQuote{A Heteroskedasticity-Consistent Covariance Matrix and a Direct Test for Heteroskedasticity.} \emph{Econometrica} \bold{48}, 817--838. Zeileis A (2004). \dQuote{Econometric Computing with HC and HAC Covariance Matrix Estimators.} \emph{Journal of Statistical Software}, \bold{11}(10), 1--17. \doi{10.18637/jss.v011.i10} Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators.} \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} } \seealso{\code{\link{lm}}, \code{\link[car]{hccm}}, \code{\link[lmtest]{bptest}}, \code{\link[car]{ncv.test}}} \examples{ ## generate linear regression relationship ## with homoscedastic variances x <- sin(1:100) y <- 1 + x + rnorm(100) ## model fit and HC3 covariance fm <- lm(y ~ x) vcovHC(fm) ## usual covariance matrix vcovHC(fm, type = "const") vcov(fm) sigma2 <- sum(residuals(lm(y ~ x))^2)/98 sigma2 * solve(crossprod(cbind(1, x))) } \keyword{regression} \keyword{ts} sandwich/man/estfun.Rd0000644000176200001440000000342014277040071014421 0ustar liggesusers\name{estfun} \alias{estfun} \alias{estfun.lm} \alias{estfun.glm} \alias{estfun.mlm} \alias{estfun.rlm} \alias{estfun.polr} \alias{estfun.clm} \alias{estfun.survreg} \alias{estfun.coxph} \alias{estfun.nls} \alias{estfun.hurdle} \alias{estfun.zeroinfl} \alias{estfun.mlogit} \encoding{UTF-8} \title{Extract Empirical Estimating Functions} \description{ Generic function for extracting the empirical estimating functions of a fitted model. } \usage{ estfun(x, \dots) } \arguments{ \item{x}{a fitted model object.} \item{\dots}{arguments passed to methods.} } \value{A matrix containing the empirical estimating functions. Typically, this should be an \eqn{n \times k}{n x k} matrix corresponding to \eqn{n} observations and \eqn{k} parameters. The columns should be named as in \code{\link{coef}} or \code{\link{terms}}, respectively. The estimating function (or score function) for a model is the derivative of the objective function with respect to the parameter vector. The empirical estimating functions is the evaluation of the estimating function at the observed data (\eqn{n} observations) and the estimated parameters (of dimension \eqn{k}). } \seealso{\code{\link{lm}}, \code{\link{glm}}} \references{ Zeileis A (2006). \dQuote{Object-Oriented Computation of Sandwich Estimators.} \emph{Journal of Statistical Software}, \bold{16}(9), 1--16. \doi{10.18637/jss.v016.i09} Zeileis A, Köll S, Graham N (2020). \dQuote{Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.} \emph{Journal of Statistical Software}, \bold{95}(1), 1--36. \doi{10.18637/jss.v095.i01} } \examples{ ## linear regression x <- 1:9 y <- sin(1:9/5) m <- lm(y ~ x) ## estimating function: (y - x'beta) * x estfun(m) residuals(m) * cbind(1, x) } \keyword{regression} sandwich/man/vcovJK.Rd0000644000176200001440000001222214277052101014314 0ustar liggesusers\name{vcovJK} \alias{vcovJK} \alias{vcovJK.default} \encoding{UTF-8} \title{(Clustered) Jackknife Covariance Matrix Estimation} \description{ Object-oriented estimation of jackknife covariances, i.e., based on the centered outer product of leave-on-out estimates of the model coefficients/parameters. } \usage{ vcovJK(x, \dots) \method{vcovJK}{default}(x, cluster = NULL, center = "mean", \dots) } \arguments{ \item{x}{a fitted model object.} \item{cluster}{a variable indicating the clustering of observations, a \code{list} (or \code{data.frame}) thereof, or a formula specifying which variables from the fitted model should be used (see examples). By default (\code{cluster = NULL}), either \code{attr(x, "cluster")} is used (if any) or otherwise every observation is assumed to be its own cluster.} \item{center}{character specifying how to center the coefficients from all jacknife samples (each dropping one observational unit/cluster). By default the coefficients are centered by their \code{"mean"} across the sample or, alternatively, by the original full-sample \code{"estimate"}.} \item{\dots}{arguments passed to methods. For the default method, this is passed to \code{\link{vcovBS}}.} } \details{ Jackknife covariance estimation is based on leave-one-out estimates of the coefficients/parameters of a model. This means that the model is reestimated after dropping each observational unit once, i.e., each individual observation in independent observations or each cluster in dependent data. The covariance matrix is then constructed from the scaled outer product of the centered jackknife estimates. Centering can either be done by the mean of the jackknife coefficients (default) or by the original full-sample estimates. Scaling is done by (N - 1)/N where N is the number of observational units. Recent research has shown that the jackknife covariance estimate have particularly useful properties in practice: they are not downward biased and yield better coverage rates for confidence intervals compared to other "robust" covariance estimates. See MacKinnon et al. (2022) and Hansen (2022) for more details. As jackknife covariances are also based on reestimation of the coefficients on subsamples, their computation is very similar to bootstrap covariances. Hence, the \code{\link{vcovBS}} methods provided in the package all offer an argument \code{vcovBS(..., type = "jackknife")}. This is called by the default \code{vcovJK} method. Therefore, see the arguments of \code{vcovBS} for further details, e.g., for leveraging multicore computations etc. In the linear regression model, the jackknife covariance can actually be computed without reestimating the coefficients but using only the full-sample estimates and certain elements of the so-called hat matrix. Namly the diagonal elements or blocks of elements from the hat matrix are needed for independent observations and clustered data, respectively. These alternative computations of the jackknife covariances are available in \code{\link{vcovHC}} and \code{\link{vcovCL}}, respectively, in both cases with argument \code{type = "HC3"}. To obtain HC3 covariances that exactly match the jackknife covariances, the jackknife has to be centered with the full-sample estimates and the right finite-sample adjustment has to be selected for the HC3. In small to moderate sample sizes, the HC3 estimation techniques are typically much faster than the jackknife. However, in large samples it may become impossible to compute the HC3 covariances while the jackknife approach is still feasible. } \value{ A matrix containing the covariance matrix estimate. } \references{ Bell RM, McCaffrey DF (2002). \dQuote{Bias Reduction in Standard Errors for Linear Regression with Multi-Stage Samples}, \emph{Survey Methodology}, \bold{28}(2), 169--181. Hansen BE (2022). \dQuote{Jackknife Standard Errors for Clustered Regression}, Working Paper, August 2022. \url{https://www.ssc.wisc.edu/~bhansen/papers/tcauchy.html} MacKinnon JG, Nielsen MØ, Webb MD (2022). \dQuote{Cluster-Robust Inference: A Guide to Empirical Practice}, \emph{Journal of Econometrics}, Forthcoming. \doi{10.1016/j.jeconom.2022.04.001} Zeileis A, Köll S, Graham N (2020). \dQuote{Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.} \emph{Journal of Statistical Software}, \bold{95}(1), 1--36. \doi{10.18637/jss.v095.i01} } \seealso{\code{\link{vcovJK}}, \code{\link{vcovHC}}, \code{\link{vcovCL}}} \examples{ ## cross-section data data("PublicSchools", package = "sandwich") m1 <- lm(Expenditure ~ poly(Income, 2), data = PublicSchools) vcovJK(m1, center = "estimate") vcovHC(m1, type = "HC3") * (nobs(m1) - 1)/nobs(m1) ## clustered data data("PetersenCL", package = "sandwich") m2 <- lm(y ~ x, data = PetersenCL) ## jackknife estimator coincides with HC3 (aka CV3) vcovJK(m2, cluster = ~ firm, center = "estimate") vcovCL(m2, cluster = ~ firm, type = "HC3", cadjust = FALSE) } \keyword{regression} \keyword{bootstrap} sandwich/man/weightsLumley.Rd0000644000176200001440000000750013735442221015763 0ustar liggesusers\name{weightsLumley} \alias{weightsLumley} \alias{weave} \title{Weighted Empirical Adaptive Variance Estimation} \description{ A set of functions implementing weighted empirical adaptive variance estimation (WEAVE) as introduced by Lumley and Heagerty (1999). This is implemented as a special case of the general class of kernel-based heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimators as introduced by Andrews (1991), using a special choice of weights. } \usage{ weave(x, order.by = NULL, prewhite = FALSE, C = NULL, method = c("truncate", "smooth"), acf = isoacf, adjust = FALSE, diagnostics = FALSE, sandwich = TRUE, tol = 1e-7, data = list(), \dots) weightsLumley(x, order.by = NULL, C = NULL, method = c("truncate", "smooth"), acf = isoacf, tol = 1e-7, data = list(), \dots) } \arguments{ \item{x}{a fitted model object.} \item{order.by}{Either a vector \code{z} or a formula with a single explanatory variable like \code{~ z}. The observations in the model are ordered by the size of \code{z}. If set to \code{NULL} (the default) the observations are assumed to be ordered (e.g., a time series).} \item{prewhite}{logical or integer. Should the estimating functions be prewhitened? If \code{TRUE} or greater than 0 a VAR model of order \code{as.integer(prewhite)} is fitted via \code{ar} with method \code{"ols"} and \code{demean = FALSE}.} \item{C}{numeric. The cutoff constant \code{C} is by default 4 for method \code{"truncate"} and 1 for method \code{"smooth"}.} \item{method}{a character specifying the method used, see details.} \item{acf}{a function that computes the autocorrelation function of a vector, by default \code{\link{isoacf}} is used.} \item{adjust}{logical. Should a finite sample adjustment be made? This amounts to multiplication with \eqn{n/(n-k)} where \eqn{n} is the number of observations and \eqn{k} the number of estimated parameters.} \item{diagnostics}{logical. Should additional model diagnostics be returned? See \code{\link{vcovHAC}} for details.} \item{sandwich}{logical. Should the sandwich estimator be computed? If set to \code{FALSE} only the middle matrix is returned.} \item{tol}{numeric. Weights that exceed \code{tol} are used for computing the covariance matrix, all other weights are treated as 0.} \item{data}{an optional data frame containing the variables in the \code{order.by} model. By default the variables are taken from the environment which the function is called from.} \item{\dots}{currently not used.} } \details{ \code{weave} is a convenience interface to \code{\link{vcovHAC}} using \code{weightsLumley}: first a weights function is defined and then \code{vcovHAC} is called. Both weighting methods are based on some estimate of the autocorrelation function \eqn{\rho}{r} (as computed by \code{acf}) of the residuals of the model \code{x}. The weights for the \code{"truncate"} method are \deqn{I\{n \rho^2 > C\}}{I{n * r ** 2 > C}} and the weights for the \code{"smooth"} method are \deqn{\min\{1, C n \rho^2\}}{min{1, C * n * r ** 2}} where n is the number of observations in the model an C is the truncation constant \code{C}. Further details can be found in Lumley & Heagerty (1999). } \value{ \code{weave} returns the same type of object as \code{\link{vcovHAC}} which is typically just the covariance matrix. \code{weightsLumley} returns a vector of weights. } \references{ Lumley T & Heagerty P (1999). \dQuote{Weighted Empirical Adaptive Variance Estimators for Correlated Data Regression.} \emph{Journal of the Royal Statistical Society B}, \bold{61}, 459--477. } \seealso{\code{\link{vcovHAC}}, \code{\link{weightsAndrews}}, \code{\link{kernHAC}}} \examples{ x <- sin(1:100) y <- 1 + x + rnorm(100) fm <- lm(y ~ x) weave(fm) vcov(fm) } \keyword{regression} \keyword{ts} sandwich/DESCRIPTION0000644000176200001440000000440414535611612013566 0ustar liggesusersPackage: sandwich Version: 3.1-0 Date: 2023-12-10 Title: Robust Covariance Matrix Estimators Authors@R: c(person(given = "Achim", family = "Zeileis", role = c("aut", "cre"), email = "Achim.Zeileis@R-project.org", comment = c(ORCID = "0000-0003-0918-3766")), person(given = "Thomas", family = "Lumley", role = "aut", email = "t.lumley@auckland.ac.nz", comment = c(ORCID = "0000-0003-4255-5437")), person(given = "Nathaniel", family = "Graham", role = "ctb", email = "npgraham1@gmail.com", comment = c(ORCID = "0009-0002-1215-5256")), person(given = "Susanne", family = "Koell", role = "ctb")) Description: Object-oriented software for model-robust covariance matrix estimators. Starting out from the basic robust Eicker-Huber-White sandwich covariance methods include: heteroscedasticity-consistent (HC) covariances for cross-section data; heteroscedasticity- and autocorrelation-consistent (HAC) covariances for time series data (such as Andrews' kernel HAC, Newey-West, and WEAVE estimators); clustered covariances (one-way and multi-way); panel and panel-corrected covariances; outer-product-of-gradients covariances; and (clustered) bootstrap covariances. All methods are applicable to (generalized) linear model objects fitted by lm() and glm() but can also be adapted to other classes through S3 methods. Details can be found in Zeileis et al. (2020) , Zeileis (2004) and Zeileis (2006) . Depends: R (>= 3.0.0) Imports: stats, utils, zoo Suggests: AER, car, geepack, lattice, lme4, lmtest, MASS, multiwayvcov, parallel, pcse, plm, pscl, scatterplot3d, stats4, strucchange, survival License: GPL-2 | GPL-3 URL: https://sandwich.R-Forge.R-project.org/ BugReports: https://sandwich.R-Forge.R-project.org/contact.html NeedsCompilation: no Packaged: 2023-12-11 08:49:01 UTC; zeileis Author: Achim Zeileis [aut, cre] (), Thomas Lumley [aut] (), Nathaniel Graham [ctb] (), Susanne Koell [ctb] Maintainer: Achim Zeileis Repository: CRAN Date/Publication: 2023-12-11 13:50:02 UTC sandwich/build/0000755000176200001440000000000014535546374013171 5ustar liggesuserssandwich/build/vignette.rds0000644000176200001440000000105214535546374015526 0ustar liggesusersTMs0uc7t-u)tÁ7><Nq#k `[zo zA.3{(8ϧ$duD NoXVTf݁P@ ߡ@ӯ߀ $=OpR @1˴er"*irĒYM0w塉6c#v;/&D (J.*(fcdqE7~o2i],ں[W`mxҞCltV.c3\h brC\g܀6H1CsYvXÔ ք9?Rx22k=|]cmTF %T%R&ۤ3/pB*%`QR|]=7,YZ}m"3W@W!!o ╔=RmRC+BƛgFγEbC9NѕOTAx{yU39_B "ɥq[H|Ŏ_O{nȃ&mE0llsandwich/build/partial.rdb0000644000176200001440000000007514535546345015316 0ustar liggesusersb```b`afd`b1 H020piּb C"{7sandwich/tests/0000755000176200001440000000000014535327010013214 5ustar liggesuserssandwich/tests/Examples/0000755000176200001440000000000013335514117014775 5ustar liggesuserssandwich/tests/Examples/sandwich-Ex.Rout.save0000644000176200001440000007705714463401660021000 0ustar liggesusers R version 4.3.1 (2023-06-16) -- "Beagle Scouts" Copyright (C) 2023 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > pkgname <- "sandwich" > source(file.path(R.home("share"), "R", "examples-header.R")) > options(warn = 1) > library('sandwich') > > base::assign(".oldSearch", base::search(), pos = 'CheckExEnv') > base::assign(".old_wd", base::getwd(), pos = 'CheckExEnv') > cleanEx() > nameEx("InstInnovation") > ### * InstInnovation > > flush(stderr()); flush(stdout()) > > ### Name: InstInnovation > ### Title: Innovation and Institutional Ownership > ### Aliases: InstInnovation > ### Keywords: datasets > > ### ** Examples > > ## Poisson models from Table I in Aghion et al. (2013) > > ## load data set > data("InstInnovation", package = "sandwich") > > ## log-scale variable > InstInnovation$lograndd <- log(InstInnovation$randd) > InstInnovation$lograndd[InstInnovation$lograndd == -Inf] <- 0 > > ## regression formulas > f1 <- cites ~ institutions + log(capital/employment) + log(sales) + industry + year > f2 <- cites ~ institutions + log(capital/employment) + log(sales) + + industry + year + lograndd + drandd > f3 <- cites ~ institutions + log(capital/employment) + log(sales) + + industry + year + lograndd + drandd + dprecites + log(precites) > > ## Poisson models > tab_I_3_pois <- glm(f1, data = InstInnovation, family = poisson) > tab_I_4_pois <- glm(f2, data = InstInnovation, family = poisson) > tab_I_5_pois <- glm(f3, data = InstInnovation, family = poisson) > > ## one-way clustered covariances > vCL_I_3 <- vcovCL(tab_I_3_pois, cluster = ~ company) > vCL_I_4 <- vcovCL(tab_I_4_pois, cluster = ~ company) > vCL_I_5 <- vcovCL(tab_I_5_pois, cluster = ~ company) > > ## replication of columns 3 to 5 from Table I in Aghion et al. (2013) > cbind(coef(tab_I_3_pois), sqrt(diag(vCL_I_3)))[2:4, ] [,1] [,2] institutions 0.009687237 0.002406388 log(capital/employment) 0.482883549 0.135953255 log(sales) 0.820317600 0.041523405 > cbind(coef(tab_I_4_pois), sqrt(diag(vCL_I_4)))[c(2:4, 148), ] [,1] [,2] institutions 0.008460789 0.002242345 log(capital/employment) 0.346008637 0.165274677 log(sales) 0.349190437 0.117219737 lograndd 0.492667825 0.140473107 > cbind(coef(tab_I_5_pois), sqrt(diag(vCL_I_5)))[c(2:4, 148), ] [,1] [,2] institutions 0.007381543 0.002443707 log(capital/employment) 0.440056227 0.131984715 log(sales) 0.183853108 0.063364163 lograndd 0.008971905 0.107406681 > > > > cleanEx() > nameEx("Investment") > ### * Investment > > flush(stderr()); flush(stdout()) > > ### Name: Investment > ### Title: US Investment Data > ### Aliases: Investment > ### Keywords: datasets > > ### ** Examples > > ## Willam H. Greene, Econometric Analysis, 2nd Ed. > ## Chapter 15 > ## load data set, p. 411, Table 15.1 > data(Investment) > > ## fit linear model, p. 412, Table 15.2 > fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment) > summary(fm) Call: lm(formula = RealInv ~ RealGNP + RealInt, data = Investment) Residuals: Min 1Q Median 3Q Max -34.987 -6.638 0.180 10.408 26.288 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -12.53360 24.91527 -0.503 0.622 RealGNP 0.16914 0.02057 8.224 3.87e-07 *** RealInt -1.00144 2.36875 -0.423 0.678 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 17.21 on 16 degrees of freedom (1 observation deleted due to missingness) Multiple R-squared: 0.8141, Adjusted R-squared: 0.7908 F-statistic: 35.03 on 2 and 16 DF, p-value: 1.429e-06 > > ## visualize residuals, p. 412, Figure 15.1 > plot(ts(residuals(fm), start = 1964), + type = "b", pch = 19, ylim = c(-35, 35), ylab = "Residuals") > sigma <- sqrt(sum(residuals(fm)^2)/fm$df.residual) ## maybe used df = 26 instead of 16 ?? > abline(h = c(-2, 0, 2) * sigma, lty = 2) > > if(require(lmtest)) { + ## Newey-West covariances, Example 15.3 + coeftest(fm, vcov = NeweyWest(fm, lag = 4)) + ## Note, that the following is equivalent: + coeftest(fm, vcov = kernHAC(fm, kernel = "Bartlett", bw = 5, prewhite = FALSE, adjust = FALSE)) + + ## Durbin-Watson test, p. 424, Example 15.4 + dwtest(fm) + + ## Breusch-Godfrey test, p. 427, Example 15.6 + bgtest(fm, order = 4) + } Loading required package: lmtest Loading required package: zoo Attaching package: ‘zoo’ The following objects are masked from ‘package:base’: as.Date, as.Date.numeric Breusch-Godfrey test for serial correlation of order up to 4 data: fm LM test = 12.07, df = 4, p-value = 0.01684 > > ## visualize fitted series > plot(Investment[, "RealInv"], type = "b", pch = 19, ylab = "Real investment") > lines(ts(fitted(fm), start = 1964), col = 4) > > > ## 3-d visualization of fitted model > if(require(scatterplot3d)) { + s3d <- scatterplot3d(Investment[,c(5,7,6)], + type = "b", angle = 65, scale.y = 1, pch = 16) + s3d$plane3d(fm, lty.box = "solid", col = 4) + } Loading required package: scatterplot3d > > > > cleanEx() detaching ‘package:scatterplot3d’, ‘package:lmtest’, ‘package:zoo’ > nameEx("NeweyWest") > ### * NeweyWest > > flush(stderr()); flush(stdout()) > > ### Name: NeweyWest > ### Title: Newey-West HAC Covariance Matrix Estimation > ### Aliases: bwNeweyWest NeweyWest > ### Keywords: regression ts > > ### ** Examples > > ## fit investment equation > data(Investment) > fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment) > > ## Newey & West (1994) compute this type of estimator > NeweyWest(fm) (Intercept) RealGNP RealInt (Intercept) 594.1004817 -0.5617817294 36.04992496 RealGNP -0.5617817 0.0005563172 -0.04815937 RealInt 36.0499250 -0.0481593694 13.24912546 > > ## The Newey & West (1987) estimator requires specification > ## of the lag and suppression of prewhitening > NeweyWest(fm, lag = 4, prewhite = FALSE) (Intercept) RealGNP RealInt (Intercept) 359.4170681 -0.3115505035 -4.089319305 RealGNP -0.3115505 0.0002805888 -0.005355931 RealInt -4.0893193 -0.0053559312 11.171472998 > > ## bwNeweyWest() can also be passed to kernHAC(), e.g. > ## for the quadratic spectral kernel > kernHAC(fm, bw = bwNeweyWest) (Intercept) RealGNP RealInt (Intercept) 794.986166 -0.7562570101 48.19485118 RealGNP -0.756257 0.0007537517 -0.06485461 RealInt 48.194851 -0.0648546058 17.58798679 > > > > cleanEx() > nameEx("PublicSchools") > ### * PublicSchools > > flush(stderr()); flush(stdout()) > > ### Name: PublicSchools > ### Title: US Expenditures for Public Schools > ### Aliases: PublicSchools > ### Keywords: datasets > > ### ** Examples > > ## Willam H. Greene, Econometric Analysis, 2nd Ed. > ## Chapter 14 > ## load data set, p. 385, Table 14.1 > data("PublicSchools", package = "sandwich") > > ## omit NA in Wisconsin and scale income > ps <- na.omit(PublicSchools) > ps$Income <- ps$Income * 0.0001 > > ## fit quadratic regression, p. 385, Table 14.2 > fmq <- lm(Expenditure ~ Income + I(Income^2), data = ps) > summary(fmq) Call: lm(formula = Expenditure ~ Income + I(Income^2), data = ps) Residuals: Min 1Q Median 3Q Max -160.709 -36.896 -4.551 37.290 109.729 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 832.9 327.3 2.545 0.01428 * Income -1834.2 829.0 -2.213 0.03182 * I(Income^2) 1587.0 519.1 3.057 0.00368 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 56.68 on 47 degrees of freedom Multiple R-squared: 0.6553, Adjusted R-squared: 0.6407 F-statistic: 44.68 on 2 and 47 DF, p-value: 1.345e-11 > > ## compare standard and HC0 standard errors > ## p. 391, Table 14.3 > coef(fmq) (Intercept) Income I(Income^2) 832.9144 -1834.2029 1587.0423 > sqrt(diag(vcovHC(fmq, type = "const"))) (Intercept) Income I(Income^2) 327.2925 828.9855 519.0768 > sqrt(diag(vcovHC(fmq, type = "HC0"))) (Intercept) Income I(Income^2) 460.8917 1243.0430 829.9927 > > > if(require(lmtest)) { + ## compare t ratio + coeftest(fmq, vcov = vcovHC(fmq, type = "HC0")) + + ## White test, p. 393, Example 14.5 + wt <- lm(residuals(fmq)^2 ~ poly(Income, 4), data = ps) + wt.stat <- summary(wt)$r.squared * nrow(ps) + c(wt.stat, pchisq(wt.stat, df = 3, lower = FALSE)) + + ## Bresch-Pagan test, p. 395, Example 14.7 + bptest(fmq, studentize = FALSE) + bptest(fmq) + + ## Francisco Cribari-Neto, Asymptotic Inference, CSDA 45 + ## quasi z-tests, p. 229, Table 8 + ## with Alaska + coeftest(fmq, df = Inf)[3,4] + coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC0"))[3,4] + coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC3"))[3,4] + coeftest(fmq, df = Inf, vcov = vcovHC(fmq, type = "HC4"))[3,4] + ## without Alaska (observation 2) + fmq1 <- lm(Expenditure ~ Income + I(Income^2), data = ps[-2,]) + coeftest(fmq1, df = Inf)[3,4] + coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC0"))[3,4] + coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC3"))[3,4] + coeftest(fmq1, df = Inf, vcov = vcovHC(fmq1, type = "HC4"))[3,4] + } Loading required package: lmtest Loading required package: zoo Attaching package: ‘zoo’ The following objects are masked from ‘package:base’: as.Date, as.Date.numeric [1] 0.8923303 > > ## visualization, p. 230, Figure 1 > plot(Expenditure ~ Income, data = ps, + xlab = "per capita income", + ylab = "per capita spending on public schools") > inc <- seq(0.5, 1.2, by = 0.001) > lines(inc, predict(fmq, data.frame(Income = inc)), col = 4) > fml <- lm(Expenditure ~ Income, data = ps) > abline(fml) > text(ps[2,2], ps[2,1], rownames(ps)[2], pos = 2) > > > > cleanEx() detaching ‘package:lmtest’, ‘package:zoo’ > nameEx("bread") > ### * bread > > flush(stderr()); flush(stdout()) > > ### Name: bread > ### Title: Bread for Sandwiches > ### Aliases: bread bread.default bread.lm bread.mlm bread.survreg > ### bread.coxph bread.gam bread.nls bread.rlm bread.hurdle bread.zeroinfl > ### bread.mlogit bread.polr bread.clm > ### Keywords: regression > > ### ** Examples > > ## linear regression > x <- sin(1:10) > y <- rnorm(10) > fm <- lm(y ~ x) > > ## bread: n * (x'x)^{-1} > bread(fm) (Intercept) x (Intercept) 1.0414689 -0.2938577 x -0.2938577 2.0823419 > solve(crossprod(cbind(1, x))) * 10 x 1.0414689 -0.2938577 x -0.2938577 2.0823419 > > > > cleanEx() > nameEx("estfun") > ### * estfun > > flush(stderr()); flush(stdout()) > > ### Name: estfun > ### Title: Extract Empirical Estimating Functions > ### Aliases: estfun estfun.lm estfun.glm estfun.mlm estfun.rlm estfun.polr > ### estfun.clm estfun.survreg estfun.coxph estfun.nls estfun.hurdle > ### estfun.zeroinfl estfun.mlogit > ### Keywords: regression > > ### ** Examples > > ## linear regression > x <- 1:9 > y <- sin(1:9/5) > m <- lm(y ~ x) > > ## estimating function: (y - x'beta) * x > estfun(m) (Intercept) x 1 -0.13577304 -0.13577304 2 -0.04481531 -0.08963062 3 0.03061755 0.09185265 4 0.08353989 0.33415956 5 0.10786351 0.53931755 6 0.09864034 0.59184202 7 0.05225971 0.36581794 8 -0.03340770 -0.26726157 9 -0.15892494 -1.43032449 > residuals(m) * cbind(1, x) x [1,] -0.13577304 -0.13577304 [2,] -0.04481531 -0.08963062 [3,] 0.03061755 0.09185265 [4,] 0.08353989 0.33415956 [5,] 0.10786351 0.53931755 [6,] 0.09864034 0.59184202 [7,] 0.05225971 0.36581794 [8,] -0.03340770 -0.26726157 [9,] -0.15892494 -1.43032449 > > > > cleanEx() > nameEx("isoacf") > ### * isoacf > > flush(stderr()); flush(stdout()) > > ### Name: isoacf > ### Title: Isotonic Autocorrelation Function > ### Aliases: isoacf pava.blocks > ### Keywords: regression ts > > ### ** Examples > > set.seed(1) > x <- filter(rnorm(100), 0.9, "recursive") > isoacf(x) [1] 1.00000000 0.75620784 0.52668286 0.31877074 0.17874234 0.10451987 [7] 0.07597397 0.07597397 0.07054562 0.03324149 -0.02266489 -0.02266489 [13] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [19] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [25] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [31] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [37] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [43] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [49] -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 -0.02266489 [55] -0.03242424 -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 [61] -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 [67] -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 [73] -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 [79] -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 [85] -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03500610 -0.03924011 [91] -0.03924011 -0.03924011 -0.03924011 -0.03924011 -0.03924011 -0.03924011 [97] -0.03924011 -0.03924011 -0.03924011 -0.03924011 > acf(x, plot = FALSE)$acf , , 1 [,1] [1,] 1.00000000 [2,] 0.75620784 [3,] 0.52668286 [4,] 0.31877074 [5,] 0.17874234 [6,] 0.10451987 [7,] 0.06774750 [8,] 0.08420043 [9,] 0.07054562 [10,] 0.03324149 [11,] -0.02547696 [12,] -0.08386780 [13,] -0.12702588 [14,] -0.15733924 [15,] -0.22570274 [16,] -0.27858103 [17,] -0.32634007 [18,] -0.31457877 [19,] -0.32132555 [20,] -0.32323138 [21,] -0.28412580 > > > > cleanEx() > nameEx("kweights") > ### * kweights > > flush(stderr()); flush(stdout()) > > ### Name: kweights > ### Title: Kernel Weights > ### Aliases: kweights > ### Keywords: regression ts > > ### ** Examples > > curve(kweights(x, kernel = "Quadratic", normalize = TRUE), + from = 0, to = 3.2, xlab = "x", ylab = "k(x)") > curve(kweights(x, kernel = "Bartlett", normalize = TRUE), + from = 0, to = 3.2, col = 2, add = TRUE) > curve(kweights(x, kernel = "Parzen", normalize = TRUE), + from = 0, to = 3.2, col = 3, add = TRUE) > curve(kweights(x, kernel = "Tukey", normalize = TRUE), + from = 0, to = 3.2, col = 4, add = TRUE) > curve(kweights(x, kernel = "Truncated", normalize = TRUE), + from = 0, to = 3.2, col = 5, add = TRUE) > > > > cleanEx() > nameEx("lrvar") > ### * lrvar > > flush(stderr()); flush(stdout()) > > ### Name: lrvar > ### Title: Long-Run Variance of the Mean > ### Aliases: lrvar > ### Keywords: regression ts > > ### ** Examples > > suppressWarnings(RNGversion("3.5.0")) > set.seed(1) > ## iid series (with variance of mean 1/n) > ## and Andrews kernel HAC (with prewhitening) > x <- rnorm(100) > lrvar(x) [1] 0.007958048 > > ## analogous multivariate case with Newey-West estimator (without prewhitening) > y <- matrix(rnorm(200), ncol = 2) > lrvar(y, type = "Newey-West", prewhite = FALSE) [,1] [,2] [1,] 0.0097884718 0.0005978738 [2,] 0.0005978738 0.0073428222 > > ## AR(1) series with autocorrelation 0.9 > z <- filter(rnorm(100), 0.9, method = "recursive") > lrvar(z) [1] 0.4385546 > > > > cleanEx() > nameEx("meat") > ### * meat > > flush(stderr()); flush(stdout()) > > ### Name: meat > ### Title: A Simple Meat Matrix Estimator > ### Aliases: meat > ### Keywords: regression > > ### ** Examples > > x <- sin(1:10) > y <- rnorm(10) > fm <- lm(y ~ x) > > meat(fm) (Intercept) x (Intercept) 0.54308202 -0.06199868 x -0.06199868 0.21823310 > meatHC(fm, type = "HC") (Intercept) x (Intercept) 0.54308202 -0.06199868 x -0.06199868 0.21823310 > meatHAC(fm) (Intercept) x (Intercept) 0.32259620 0.08446047 x 0.08446047 0.37529225 > > > > cleanEx() > nameEx("sandwich") > ### * sandwich > > flush(stderr()); flush(stdout()) > > ### Name: sandwich > ### Title: Making Sandwiches with Bread and Meat > ### Aliases: sandwich > ### Keywords: regression > > ### ** Examples > > x <- sin(1:10) > y <- rnorm(10) > fm <- lm(y ~ x) > > sandwich(fm) (Intercept) x (Intercept) 0.06458514 -0.04395562 x -0.04395562 0.10690628 > vcovHC(fm, type = "HC") (Intercept) x (Intercept) 0.06458514 -0.04395562 x -0.04395562 0.10690628 > > > > cleanEx() > nameEx("vcovBS") > ### * vcovBS > > flush(stderr()); flush(stdout()) > > ### Name: vcovBS > ### Title: (Clustered) Bootstrap Covariance Matrix Estimation > ### Aliases: vcovBS vcovBS.default vcovBS.lm vcovBS.glm .vcovBSenv > ### Keywords: regression bootstrap > > ### ** Examples > > ## Petersen's data > data("PetersenCL", package = "sandwich") > m <- lm(y ~ x, data = PetersenCL) > > ## comparison of different standard errors > suppressWarnings(RNGversion("3.5.0")) > set.seed(1) > cbind( + "classical" = sqrt(diag(vcov(m))), + "HC-cluster" = sqrt(diag(vcovCL(m, cluster = ~ firm))), + "BS-cluster" = sqrt(diag(vcovBS(m, cluster = ~ firm))), + "FW-cluster" = sqrt(diag(vcovBS(m, cluster = ~ firm, type = "fractional"))) + ) classical HC-cluster BS-cluster FW-cluster (Intercept) 0.02835932 0.06701270 0.07067533 0.06596187 x 0.02858329 0.05059573 0.04878784 0.04965168 > > ## two-way wild cluster bootstrap with Mammen distribution > vcovBS(m, cluster = ~ firm + year, type = "wild-mammen") (Intercept) x (Intercept) 0.004135069 0.000364327 x 0.000364327 0.002659964 > > ## jackknife estimator coincides with HC3 (aka CV3) > all.equal( + vcovBS(m, cluster = ~ firm, type = "jackknife"), + vcovCL(m, cluster = ~ firm, type = "HC3", cadjust = FALSE), + tolerance = 1e-7 + ) [1] TRUE > > > > cleanEx() > nameEx("vcovCL") > ### * vcovCL > > flush(stderr()); flush(stdout()) > > ### Name: vcovCL > ### Title: Clustered Covariance Matrix Estimation > ### Aliases: vcovCL meatCL > ### Keywords: regression > > ### ** Examples > > ## Petersen's data > data("PetersenCL", package = "sandwich") > m <- lm(y ~ x, data = PetersenCL) > > ## clustered covariances > ## one-way > vcovCL(m, cluster = ~ firm) (Intercept) x (Intercept) 4.490702e-03 -6.473517e-05 x -6.473517e-05 2.559927e-03 > vcovCL(m, cluster = PetersenCL$firm) ## same (Intercept) x (Intercept) 4.490702e-03 -6.473517e-05 x -6.473517e-05 2.559927e-03 > ## one-way with HC2 > vcovCL(m, cluster = ~ firm, type = "HC2") (Intercept) x (Intercept) 4.494487e-03 -6.592912e-05 x -6.592912e-05 2.568236e-03 > ## two-way > vcovCL(m, cluster = ~ firm + year) (Intercept) x (Intercept) 4.233313e-03 -2.845344e-05 x -2.845344e-05 2.868462e-03 > vcovCL(m, cluster = PetersenCL[, c("firm", "year")]) ## same (Intercept) x (Intercept) 4.233313e-03 -2.845344e-05 x -2.845344e-05 2.868462e-03 > > ## comparison with cross-section sandwiches > ## HC0 > all.equal(sandwich(m), vcovCL(m, type = "HC0", cadjust = FALSE)) [1] TRUE > ## HC2 > all.equal(vcovHC(m, type = "HC2"), vcovCL(m, type = "HC2")) [1] TRUE > ## HC3 > all.equal(vcovHC(m, type = "HC3"), vcovCL(m, type = "HC3")) [1] TRUE > > ## Innovation data > data("InstInnovation", package = "sandwich") > > ## replication of one-way clustered standard errors for model 3, Table I > ## and model 1, Table II in Berger et al. (2017), see ?InstInnovation > > ## count regression formula > f1 <- cites ~ institutions + log(capital/employment) + log(sales) + industry + year > > ## model 3, Table I: Poisson model > ## one-way clustered standard errors > tab_I_3_pois <- glm(f1, data = InstInnovation, family = poisson) > vcov_pois <- vcovCL(tab_I_3_pois, InstInnovation$company) > sqrt(diag(vcov_pois))[2:4] institutions log(capital/employment) log(sales) 0.002406388 0.135953255 0.041523405 > > ## coefficient tables > if(require("lmtest")) { + coeftest(tab_I_3_pois, vcov = vcov_pois)[2:4, ] + } Loading required package: lmtest Loading required package: zoo Attaching package: ‘zoo’ The following objects are masked from ‘package:base’: as.Date, as.Date.numeric Estimate Std. Error z value Pr(>|z|) institutions 0.009687237 0.002406388 4.025634 5.682195e-05 log(capital/employment) 0.482883549 0.135953255 3.551835 3.825545e-04 log(sales) 0.820317600 0.041523405 19.755548 7.187199e-87 > > ## Not run: > ##D ## model 1, Table II: negative binomial hurdle model > ##D ## (requires "pscl" or alternatively "countreg" from R-Forge) > ##D library("pscl") > ##D library("lmtest") > ##D tab_II_3_hurdle <- hurdle(f1, data = InstInnovation, dist = "negbin") > ##D # dist = "negbin", zero.dist = "negbin", separate = FALSE) > ##D vcov_hurdle <- vcovCL(tab_II_3_hurdle, InstInnovation$company) > ##D sqrt(diag(vcov_hurdle))[c(2:4, 149:151)] > ##D coeftest(tab_II_3_hurdle, vcov = vcov_hurdle)[c(2:4, 149:151), ] > ## End(Not run) > > > > cleanEx() detaching ‘package:lmtest’, ‘package:zoo’ > nameEx("vcovHAC") > ### * vcovHAC > > flush(stderr()); flush(stdout()) > > ### Name: vcovHAC > ### Title: Heteroscedasticity and Autocorrelation Consistent (HAC) > ### Covariance Matrix Estimation > ### Aliases: vcovHAC vcovHAC.default meatHAC > ### Keywords: regression ts > > ### ** Examples > > x <- sin(1:100) > y <- 1 + x + rnorm(100) > fm <- lm(y ~ x) > vcovHAC(fm) (Intercept) x (Intercept) 0.008125428 -0.002043239 x -0.002043239 0.018939164 > vcov(fm) (Intercept) x (Intercept) 8.124921e-03 2.055475e-05 x 2.055475e-05 1.616308e-02 > > > > cleanEx() > nameEx("vcovHC") > ### * vcovHC > > flush(stderr()); flush(stdout()) > > ### Name: vcovHC > ### Title: Heteroscedasticity-Consistent Covariance Matrix Estimation > ### Aliases: vcovHC vcovHC.default vcovHC.mlm meatHC > ### Keywords: regression ts > > ### ** Examples > > ## generate linear regression relationship > ## with homoscedastic variances > x <- sin(1:100) > y <- 1 + x + rnorm(100) > ## model fit and HC3 covariance > fm <- lm(y ~ x) > vcovHC(fm) (Intercept) x (Intercept) 0.008318070 -0.002037159 x -0.002037159 0.019772693 > ## usual covariance matrix > vcovHC(fm, type = "const") (Intercept) x (Intercept) 8.124921e-03 2.055475e-05 x 2.055475e-05 1.616308e-02 > vcov(fm) (Intercept) x (Intercept) 8.124921e-03 2.055475e-05 x 2.055475e-05 1.616308e-02 > > sigma2 <- sum(residuals(lm(y ~ x))^2)/98 > sigma2 * solve(crossprod(cbind(1, x))) x 8.124921e-03 2.055475e-05 x 2.055475e-05 1.616308e-02 > > > > cleanEx() > nameEx("vcovJK") > ### * vcovJK > > flush(stderr()); flush(stdout()) > > ### Name: vcovJK > ### Title: (Clustered) Jackknife Covariance Matrix Estimation > ### Aliases: vcovJK vcovJK.default > ### Keywords: regression bootstrap > > ### ** Examples > > ## cross-section data > data("PublicSchools", package = "sandwich") > m1 <- lm(Expenditure ~ poly(Income, 2), data = PublicSchools) > vcovJK(m1, center = "estimate") (Intercept) poly(Income, 2)1 poly(Income, 2)2 (Intercept) 97.84092 1055.131 1370.855 poly(Income, 2)1 1055.13101 25053.095 31336.158 poly(Income, 2)2 1370.85525 31336.158 46955.800 > vcovHC(m1, type = "HC3") * (nobs(m1) - 1)/nobs(m1) (Intercept) poly(Income, 2)1 poly(Income, 2)2 (Intercept) 97.84092 1055.131 1370.855 poly(Income, 2)1 1055.13101 25053.095 31336.158 poly(Income, 2)2 1370.85525 31336.158 46955.800 > > ## clustered data > data("PetersenCL", package = "sandwich") > m2 <- lm(y ~ x, data = PetersenCL) > > ## jackknife estimator coincides with HC3 (aka CV3) > vcovJK(m2, cluster = ~ firm, center = "estimate") (Intercept) x (Intercept) 4.499186e-03 -6.714627e-05 x -6.714627e-05 2.577098e-03 > vcovCL(m2, cluster = ~ firm, type = "HC3", cadjust = FALSE) (Intercept) x (Intercept) 4.499186e-03 -6.714627e-05 x -6.714627e-05 2.577098e-03 > > > > cleanEx() > nameEx("vcovOPG") > ### * vcovOPG > > flush(stderr()); flush(stdout()) > > ### Name: vcovOPG > ### Title: Outer-Product-of-Gradients Covariance Matrix Estimation > ### Aliases: vcovOPG > ### Keywords: regression ts > > ### ** Examples > > ## generate poisson regression relationship > x <- sin(1:100) > y <- rpois(100, exp(1 + x)) > ## compute usual covariance matrix of coefficient estimates > fm <- glm(y ~ x, family = poisson) > vcov(fm) (Intercept) x (Intercept) 0.004526581 -0.003679570 x -0.003679570 0.008110051 > vcovOPG(fm) (Intercept) x (Intercept) 0.005183615 -0.003086646 x -0.003086646 0.009584083 > > > > cleanEx() > nameEx("vcovPC") > ### * vcovPC > > flush(stderr()); flush(stdout()) > > ### Name: vcovPC > ### Title: Panel-Corrected Covariance Matrix Estimation > ### Aliases: vcovPC meatPC > ### Keywords: regression > > ### ** Examples > > ## Petersen's data > data("PetersenCL", package = "sandwich") > m <- lm(y ~ x, data = PetersenCL) > > ## Beck and Katz (1995) standard errors > ## balanced panel > sqrt(diag(vcovPC(m, cluster = ~ firm + year))) (Intercept) x 0.02220064 0.02527598 > > ## unbalanced panel > PU <- subset(PetersenCL, !(firm == 1 & year == 10)) > pu_lm <- lm(y ~ x, data = PU) > sqrt(diag(vcovPC(pu_lm, cluster = ~ firm + year, pairwise = TRUE))) (Intercept) x 0.02206979 0.02533772 > sqrt(diag(vcovPC(pu_lm, cluster = ~ firm + year, pairwise = FALSE))) (Intercept) x 0.02260277 0.02524119 > > > > > cleanEx() > nameEx("vcovPL") > ### * vcovPL > > flush(stderr()); flush(stdout()) > > ### Name: vcovPL > ### Title: Clustered Covariance Matrix Estimation for Panel Data > ### Aliases: vcovPL meatPL > ### Keywords: regression > > ### ** Examples > > ## Petersen's data > data("PetersenCL", package = "sandwich") > m <- lm(y ~ x, data = PetersenCL) > > ## Driscoll and Kraay standard errors > ## lag length set to: T - 1 (maximum lag length) > ## as proposed by Petersen (2009) > sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "max", adjust = FALSE))) (Intercept) x 0.01618977 0.01426121 > > ## lag length set to: floor(4 * (T / 100)^(2/9)) > ## rule of thumb proposed by Hoechle (2007) based on Newey & West (1994) > sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1994"))) (Intercept) x 0.02289115 0.02441980 > > ## lag length set to: floor(T^(1/4)) > ## rule of thumb based on Newey & West (1987) > sqrt(diag(vcovPL(m, cluster = ~ firm + year, lag = "NW1987"))) (Intercept) x 0.02436219 0.02816896 > > ## the following specifications of cluster/order.by are equivalent > vcovPL(m, cluster = ~ firm + year) (Intercept) x (Intercept) 5.935164e-04 2.222292e-05 x 2.222292e-05 7.934905e-04 > vcovPL(m, cluster = PetersenCL[, c("firm", "year")]) (Intercept) x (Intercept) 5.935164e-04 2.222292e-05 x 2.222292e-05 7.934905e-04 > vcovPL(m, cluster = ~ firm, order.by = ~ year) (Intercept) x (Intercept) 5.935164e-04 2.222292e-05 x 2.222292e-05 7.934905e-04 > vcovPL(m, cluster = PetersenCL$firm, order.by = PetersenCL$year) (Intercept) x (Intercept) 5.935164e-04 2.222292e-05 x 2.222292e-05 7.934905e-04 > > ## these are also the same when observations within each > ## cluster are already ordered > vcovPL(m, cluster = ~ firm) (Intercept) x (Intercept) 5.935164e-04 2.222292e-05 x 2.222292e-05 7.934905e-04 > vcovPL(m, cluster = PetersenCL$firm) (Intercept) x (Intercept) 5.935164e-04 2.222292e-05 x 2.222292e-05 7.934905e-04 > > > > cleanEx() > nameEx("weightsAndrews") > ### * weightsAndrews > > flush(stderr()); flush(stdout()) > > ### Name: weightsAndrews > ### Title: Kernel-based HAC Covariance Matrix Estimation > ### Aliases: weightsAndrews bwAndrews kernHAC > ### Keywords: regression ts > > ### ** Examples > > curve(kweights(x, kernel = "Quadratic", normalize = TRUE), + from = 0, to = 3.2, xlab = "x", ylab = "k(x)") > curve(kweights(x, kernel = "Bartlett", normalize = TRUE), + from = 0, to = 3.2, col = 2, add = TRUE) > curve(kweights(x, kernel = "Parzen", normalize = TRUE), + from = 0, to = 3.2, col = 3, add = TRUE) > curve(kweights(x, kernel = "Tukey", normalize = TRUE), + from = 0, to = 3.2, col = 4, add = TRUE) > curve(kweights(x, kernel = "Truncated", normalize = TRUE), + from = 0, to = 3.2, col = 5, add = TRUE) > > ## fit investment equation > data(Investment) > fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment) > > ## compute quadratic spectral kernel HAC estimator > kernHAC(fm) (Intercept) RealGNP RealInt (Intercept) 788.6120652 -0.7502080996 49.78912814 RealGNP -0.7502081 0.0007483977 -0.06641343 RealInt 49.7891281 -0.0664134303 17.71735491 > kernHAC(fm, verbose = TRUE) Bandwidth chosen: 1.744749 (Intercept) RealGNP RealInt (Intercept) 788.6120652 -0.7502080996 49.78912814 RealGNP -0.7502081 0.0007483977 -0.06641343 RealInt 49.7891281 -0.0664134303 17.71735491 > > ## use Parzen kernel instead, VAR(2) prewhitening, no finite sample > ## adjustment and Newey & West (1994) bandwidth selection > kernHAC(fm, kernel = "Parzen", prewhite = 2, adjust = FALSE, + bw = bwNeweyWest, verbose = TRUE) Bandwidth chosen: 2.814444 (Intercept) RealGNP RealInt (Intercept) 608.3101258 -0.5089107386 -64.93690203 RealGNP -0.5089107 0.0004340803 0.04689293 RealInt -64.9369020 0.0468929322 15.58251456 > > ## compare with estimate under assumption of spheric errors > vcov(fm) (Intercept) RealGNP RealInt (Intercept) 620.7706170 -0.5038304429 8.47475285 RealGNP -0.5038304 0.0004229789 -0.01145679 RealInt 8.4747529 -0.0114567949 5.61097245 > > > > cleanEx() > nameEx("weightsLumley") > ### * weightsLumley > > flush(stderr()); flush(stdout()) > > ### Name: weightsLumley > ### Title: Weighted Empirical Adaptive Variance Estimation > ### Aliases: weightsLumley weave > ### Keywords: regression ts > > ### ** Examples > > x <- sin(1:100) > y <- 1 + x + rnorm(100) > fm <- lm(y ~ x) > weave(fm) (Intercept) x (Intercept) 0.007957440 -0.001936926 x -0.001936926 0.018775226 > vcov(fm) (Intercept) x (Intercept) 8.124921e-03 2.055475e-05 x 2.055475e-05 1.616308e-02 > > > > ### *