# Robust Covariance Matrix Estimators with sandwich package in R

## How to Download and Use the Sandwich Package in R

If you are looking for a robust and versatile way to estimate the covariance matrix of your model parameters in R, you might want to check out the sandwich package. This package provides a range of covariance matrix estimators that are consistent even when some of the model assumptions are violated, such as heteroscedasticity, autocorrelation, or clustering. In this article, we will show you how to download and use the sandwich package in R, and explain some of its features and alternatives.

## What is the Sandwich Package?

The sandwich package is a package for R that implements various robust covariance matrix estimators, also known as sandwich covariances. These estimators are useful when you want to perform inference on your model parameters, such as hypothesis tests or confidence intervals, but you suspect that some of the model assumptions are not met. For example, if your model suffers from heteroscedasticity (unequal variance of the error terms), autocorrelation (correlation of the error terms over time), or clustering (dependence of the observations within groups), then the usual covariance matrix estimator might be biased and lead to incorrect inference. In this case, you can use a sandwich covariance matrix estimator that is consistent under these violations, and plug it into your inference procedure.

## sandwich package r download

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### Features of the Sandwich Package

The sandwich package has several features that make it a powerful and flexible tool for robust covariance matrix estimation. Some of these features are:

It is object-oriented, meaning that it can work with many different model classes, such as lm, glm, survreg, coxph, mlogit, polr, hurdle, zeroinfl, ivreg, betareg, and more. You don't need to modify or adjust your model object to use the sandwich package.

It provides a wide range of sandwich covariances for different types of data and models, such as cross-sectional, time series, clustered, panel, longitudinal, generalized linear, survival, count, ordinal, zero-inflated, instrumental variable, beta regression, and more. You can choose the appropriate covariance matrix estimator for your situation.

It is modular and extensible, meaning that you can easily combine different components of the sandwich covariances, such as the bread (the inverse of the Fisher information matrix) and the meat (the cross-product of the score functions), or create your own custom components. You can also extend the sandwich package to new model classes by providing S3 methods for estfun (the score function) and bread (the Fisher information matrix).

### Alternatives to the Sandwich Package

The sandwich package is not the only option for robust covariance matrix estimation in R. There are some other packages that offer similar or complementary functionality. Some of these packages are:

lmtest: This package provides various tests for linear models based on different types of robust covariances. It also has a coeftest function that allows you to perform hypothesis tests on your model coefficients using any covariance matrix estimator.

multiwayvcov: This package extends the sandwich package to allow for multiway clustering of standard errors. It also provides functions for computing degrees of freedom adjustments for clustered standard errors.

plm: This package provides functions for panel data analysis based on linear models. It also offers various robust covariance matrix estimators for panel data models.

pcse: This package implements panel-corrected standard errors for panel data models with cross-sectional dependence.

## How to Install and Load the Sandwich Package in RHow to Install and Load the Sandwich Package in R

Installing and loading the sandwich package in R is very easy. You can follow these steps:

sandwich package r tutorial

sandwich package r example

sandwich package r documentation

sandwich package r robust standard errors

sandwich package r heteroscedasticity

sandwich package r autocorrelation

sandwich package r cluster

sandwich package r vcov

sandwich package r coeftest

sandwich package r lmtest

sandwich package r bread

sandwich package r meat

sandwich package r kernel

sandwich package r weights

sandwich package r estimators

sandwich package r glm

sandwich package r survreg

sandwich package r coxph

sandwich package r mlogit

sandwich package r polr

sandwich package r hurdle

sandwich package r zeroinfl

sandwich package r vcovHAC

sandwich package r vcovCL

sandwich package r vcovHC

sandwich package r vcovPL

sandwich package r vcovOPG

sandwich package r vcovPC

sandwich package r vcovBS

sandwich package r vcovJK

sandwich package r vcovLumley

sandwich package r vcovCRHC0

sandwich package r vcovCRHC1

sandwich package r vcovCRHC2

sandwich package r vcovCRHC3

sandwich package r vcovCRHC4

sandwich package r vcovCRHC5

sandwich package r vcovCRHC6

sandwich package r NeweyWest

sandwich package r WeilZinbarg

sandwich package r AndrewsHansenTest

sandwich package r AndrewsTest

sandwich package r HansenTest

sandwich package r KieferTest

sandwich package r NeweyWestTest

sandwich package r Waldtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.lmtest.

### Installing from CRAN

The sandwich package is available on CRAN, the Comprehensive R Archive Network, which is the official repository of R packages. To install the sandwich package from CRAN, you can use the install.packages function in R. For example, you can run this code in your R console:

install.packages("sandwich")

This will download and install the latest version of the sandwich package and its dependencies from CRAN. You only need to do this once, unless you want to update the package to a newer version.

### Installing from GitHub

If you want to install the development version of the sandwich package, which might have some new features or bug fixes that are not yet on CRAN, you can install it from GitHub, which is a platform for hosting and sharing code. To install the sandwich package from GitHub, you need to have the devtools package installed in R. You can install the devtools package from CRAN using the same install.packages function. For example, you can run this code in your R console:

install.packages("devtools")

Once you have the devtools package installed, you can use the install_github function to install the sandwich package from GitHub. For example, you can run this code in your R console:

devtools::install_github("sandwich-org/sandwich")

This will download and install the latest development version of the sandwich package and its dependencies from GitHub. You might need to do this more often, as the development version might change frequently.

### Loading the Sandwich Package

After installing the sandwich package, you need to load it into your R session before you can use it. To load the sandwich package, you can use the library function in R. For example, you can run this code in your R console:

library(sandwich)

## This will load the sandwich package and make its functions available for use. You need to do this every time you start a new R session. How to Use the Sandwich Package in R

Now that you have installed and loaded the sandwich package in R, you can start using it to estimate robust covariance matrices for your models. The sandwich package provides a generic function called vcovHC, which stands for variance-covariance matrix heteroscedasticity-consistent, that can be applied to any model object that has methods for estfun and bread. The vcovHC function returns a sandwich covariance matrix estimator that is consistent under heteroscedasticity of unknown form. You can then use this estimator in your inference procedure, such as coeftest from the lmtest package, to obtain robust standard errors, t-statistics, and p-values for your model coefficients.

The vcovHC function has several arguments that allow you to customize the sandwich covariance matrix estimator according to your data and model. Some of these arguments are:

type: This argument specifies the type of sandwich estimator to use. The default is type = "HC3", which is a bias-corrected estimator that performs well in small samples. Other options are type = "HC0", which is the original estimator proposed by White (1980), type = "HC1", which is a simple degrees of freedom adjustment, type = "HC2", which is another bias-corrected estimator, and type = "HC4", which is a weighted estimator that accounts for leverage points.

__order.by__: This argument specifies the ordering of the observations for computing the sandwich estimator. The default is__order.by__= NULL, which means no ordering. This is suitable for cross-sectional data. Other options are__order.by__= timevar, which means ordering by a time variable. This is suitable for time series data. You can also specify a vector or a formula for the ordering.

cluster: This argument specifies the clustering variable for computing the sandwich estimator. The default is cluster = NULL, which means no clustering. This is suitable for independent data. Other options are cluster = groupvar, which means clustering by a group variable. This is suitable for clustered or panel data. You can also specify a vector or a formula for the clustering.

In addition to the vcovHC function, the sandwich package also provides other functions for different types of robust covariance matrix estimators, such as vcovHAC, vcovCL, and vcovBS. These functions have similar arguments and usage as vcovHC, but they are designed for different scenarios. We will briefly describe each of these functions below.

### Basic Sandwich Covariance Matrix Estimator

The basic sandwich covariance matrix estimator is given by:

where is the inverse of the Fisher information matrix, and is the cross-product of the score functions.

The basic sandwich covariance matrix estimator is consistent under the assumption of correct specification of the model and independence of the observations. However, it might be inefficient or biased if these assumptions are violated. Therefore, it is usually modified or adjusted to account for various forms of misspecification or dependence.

The basic sandwich covariance matrix estimator can be computed using the vcov function from the sandwich package. For example, if you have a linear model object called lmfit, you can run this code in your R console:

vcov(lmfit)

### This will return the basic sandwich covariance matrix estimator for lmfit. Heteroscedasticity-Consistent Covariance Matrix Estimator

The heteroscedasticity-consistent covariance matrix estimator is a modification of the basic sandwich covariance matrix estimator that accounts for the possibility of unequal variance of the error terms across observations. It is given by:

where is the residual for observation i, and is the score function for observation i.

The heteroscedasticity-consistent covariance matrix estimator is consistent under the assumption of correct specification of the model and independence of the observations, but it does not require the assumption of homoscedasticity (equal variance of the error terms). However, it might be inefficient or biased in small samples, so it is usually further modified or adjusted to improve its finite-sample performance. There are several types of heteroscedasticity-consistent covariance matrix estimators, such as HC0, HC1, HC2, HC3, and HC4, that differ in their bias-correction or weighting schemes.

The heteroscedasticity-consistent covariance matrix estimator can be computed using the vcovHC function from the sandwich package. For example, if you have a linear model object called lmfit, you can run this code in your R console:

vcovHC(lmfit)

### This will return the default heteroscedasticity-consistent covariance matrix estimator for lmfit, which is type = "HC3". You can change the type argument to choose a different type of estimator. Heteroscedasticity- and Autocorrelation-Consistent Covariance Matrix Estimator

The heteroscedasticity- and autocorrelation-consistent covariance matrix estimator is a modification of the basic sandwich covariance matrix estimator that accounts for the possibility of both unequal variance and correlation of the error terms across observations. It is given by:

where is the residual for observation i, is the score function for observation i, and is a weight function that depends on the distance between observations i and j.

The heteroscedasticity- and autocorrelation-consistent covariance matrix estimator is consistent under the assumption of correct specification of the model and weak dependence of the observations, but it does not require the assumptions of homoscedasticity or no autocorrelation. However, it might be inefficient or biased in small samples or under strong dependence, so it is usually further modified or adjusted to improve its finite-sample performance or robustness. There are several types of heteroscedasticity- and autocorrelation-consistent covariance matrix estimators, such as Newey-West, Andrews, Driscoll-Kraay, and Kiefer, that differ in their choice of weight function or bandwidth parameter.

The heteroscedasticity- and autocorrelation-consistent covariance matrix estimator can be computed using the vcovHAC function from the sandwich package. For example, if you have a linear model object called lmfit, you can run this code in your R console:

vcovHAC(lmfit)

### This will return the default heteroscedasticity- and autocorrelation-consistent covariance matrix estimator for lmfit, which is type = "HC3". You can change the type argument to choose a different type of estimator. You can also specify the __order.by__ argument to indicate the ordering of the observations, and the kernel argument to choose a different weight function. Clustered Covariance Matrix Estimator

The clustered covariance matrix estimator is a modification of the basic sandwich covariance matrix estimator that accounts for the possibility of dependence of the observations within clusters or groups. It is given by:

where is the residual for observation i, is the score function for observation i, and G is the number of clusters or groups.

The clustered covariance matrix estimator is consistent under the assumption of correct specification of the model and independence of the clusters or groups, but it does not require the assumption of independence of the observations within clusters or groups. However, it might be inefficient or biased in small samples or under few clusters, so it is usually further modified or adjusted to improve its finite-sample performance or robustness. There are several types of clustered covariance matrix estimators, such as CR0, CR1, CR2, and CR3, that differ in their degrees of freedom adjustment or weighting schemes.

The clustered covariance matrix estimator can be computed using the vcovCL function from the sandwich package. For example, if you have a linear model object called lmfit, you can run this code in your R console:

vcovCL(lmfit, cluster = groupvar)

### This will return the default clustered covariance matrix estimator for lmfit, which is type = "CR2". You can change the type argument to choose a different type of estimator. You can also specify the cluster argument to indicate the clustering variable. Bootstrap Covariance Matrix Estimator

The bootstrap covariance matrix estimator is a modification of the basic sandwich covariance matrix estimator that uses a resampling technique to estimate the covariance matrix of the model parameters. It is given by:

where is the model parameter estimate based on the b-th bootstrap sample, is the average of the model parameter estimates across all bootstrap samples, and B is the number of bootstrap samples.

The bootstrap covariance matrix estimator is consistent under the assumption of correct specification of the model and weak dependence of the observations, but it does not require any parametric assumptions about the distribution of the error terms or the model parameters. However, it might be computationally intensive or sensitive to the choice of bootstrap method or sample size, so it is usually used as a complement or a check for other covariance matrix estimators.

The bootstrap covariance matrix estimator can be computed using the vcovBS function from the sandwich package. For example, if you have a linear model object called lmfit, you can run this code in your R console:

vcovBS(lmfit)

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