# sandwich standard errors

## sandwich standard errors

02/12/2020

Cluster-robust standard errors usingR Mahmood Arai Department of Economics Stockholm University March 12, 2015 1 Introduction This note deals with estimating cluster-robust standard errors on one and two ... the function sandwich to obtain the variance covariance matrix (Zeileis). One additional downside that many people are unaware of is that by opting for Huber-White errors you lose the nice small sample properties of OLS. MLwiN is giving the standard errors of parameter estimates as 0, but I know from comparison with other software packages that the standard errors should not be 0, PhDs: Advanced quantitative methods in social science and health. Which references should I cite? 2.2) omitting the sub/superscript h, is given by. I'm wondering whether you would like to add an argument allowing to easily compute sandwich (heteroskedasticity-robust), bootstrap, jackknife and possibly other types of variance-covariance matrix and standard errors, instead of the asymptotic ones. Wikipedia and the R sandwich package vignette give good information about the assumptions supporting OLS coefficient standard errors and the mathematical background of the sandwich estimators. See the Generalized linear models part of the item "White's empirical ("sandwich") variance estimator and robust standard errors" in the Frequently-Asked for Statistics (FASTats list) which is a link in the Important Links section on the right side of the Statistical Procedures Community page. I have read a lot about the pain of replicate the easy robust option from STATA to R to use robust standard errors. For those less interested in level-2 effects it can be a viable way to simplify a model when you simply don’t care about a random effect. Using "HC1" will replicate the robust standard errors you would obtain using STATA. (ALM-II). In a previous post we looked at the (robust) sandwich variance estimator for linear regression. Here, you are correcting a problem instead of studying a feature of the data. The take away is that in linear models a sandwich estimator is good enough if you don’t substantively care about group differences. which reduces to the expression in Goldstein (1995, Appendix 2.2) when the model based estimator is used. ↑ Predictably the type option in this function indicates that there are several options (actually "HC0" to "HC4"). Should the comparative SD output when I calculate the residuals be different for each row? Christensen, Ronald (20??). When certain clusters are over-sampled the coefficients can become biased compared to the population. Because of this error you can only rarely effectively model all of the between group correlation by including a random effect in a nonlinear model. Tel: +44 (0)117 928 9000. As I alluded before, if cluster sizes are uneven then coefficients may be biased because more people from group A are in the sample than group B. However, in nonlinear models it can actually help quite a bit more. Beacon House To get the correct standard errors, we can use the vcovHC() function from the {sandwich} package (hence the choice for the header picture of … A journal referee now asks that I give the appropriate reference for this calculation. Sandwich estimators for standard errors are often useful, eg when model based estimators are very complex and difficult to compute and robust alternatives are required. The residual standard deviation describes the difference in standard deviations of observed values versus predicted values in a regression analysis. In a linear model robust or cluster robust standard errors can still help with heteroskedasticity even if the clustering function is redundant. I want to control for heteroscedasticity with robust standard errors. When we suspect, or find evidence on the basis of a test for heteroscedascity, that the variance is not constant, the standard OLS variance should not be used since it gives biased estimate of precision. The covariance matrix is given by. Fourth, as gee is a library it can be accessed from Plink 1 and so provides a computationally feasible strategy for running genome-wide scans in family data. For residuals, sandwich estimators will automatically be used when weighted residuals are specified in the residuals section on weighting for details of residuals produced from weighted models. Freedman, David A. Freedman (2006). Previously, I alluded to being able to deal with clustering problems by using something called Hubert-White cluster robust standard errors –also known as a sandwich estimator because the formula looks like a little sandwich. Fixed effects models attempt to “correct” for clustering by absorbing all of the variation that occurs between clusters. Different estimation techniques are known to produce more error than others with the typical trade-off being time and computational requirements. The authors state: "In fact, robust and classical standard errors that differ need to be seen as bright red flags that signal compelling evidence of uncorrected model misspecification." The standard errors determine how accurate is your estimation. Essentially, you need to use something in the model to explain the clustering or you will bias your coefficients (and marginal effects/predicted probabilities) and not just your SEs. Where is the model fitting information stored in MLwiN? In this case you must model the groups directly or individual-level variables that are affected by group status will be biased. You essentially take the product of the off-diagonal in the variance covariance matrix and build standard errors with between cluster covariance reduced to zero so that between cluster errors may be correlated. In R the function coeftest from the lmtest package can be used in combination with the function vcovHC from the sandwich package to do this. Therefore, we can estimate the variances of OLS estimators (and standard errors) by using ∑ˆ : Var(βˆ)=(X′X)−1XΣ′X(X′X )−1 Standard errors based on this procedure are called (heteroskedasticity) robust standard errors or White-Huber standard errors. If the model based estimator is used this reduces to the expression given by Goldstein (1995, Appendix 2.2), otherwise the cross product matrix estimator is used. Clustering of Errors Cluster-Robust Standard Errors More Dimensions A Seemingly Unrelated Topic Two Families of Sandwich Estimators The OLS estimator of the Var-Cov matrix is: Vˆ O = qVˆ = q(X0X) −1 (where for regress, q is just the residual variance estimate s2 = 1 N−k P N j=1 ˆe 2 i). Regular OLS models can often run with 10-20 observations. When this assumption fails, the standard errors from our OLS regression estimates are inconsistent. In nonlinear models the problem becomes much more difficult. 3 In other words, the coefficients and standard errors can’t be separated. Bristol, BS8 1QU, UK If the errors change appreciably then it is likely due to the fact that some of the between group correlation is not being explained by the random effect. In MLwiN 1.1 access to the sandwich estimators is via the FSDE and RSDE commands. When should you use clustered standard errors? Queens Road A function for extracting the covariance matrix from x is supplied, e.g., sandwich, vcovHC, vcovCL, or vcovHAC from package sandwich. This means that you will get biased standard errors if you have less than 50-100 observations. If you include all but one classroom-level dummy variable in a model then there cannot be any between class variation explained by individual-level variables like student ID or gender. In nonlinear models it can be a good aid to getting a better model but it will never be enough by itself. I'm still not clear how the problem of residuals heteroscedasticity is addressed though, probably because I don't fully understand the standard OLS coefficients variance estimation in the first place. Accuracy of the sandwich-type SEs compared with the empirical SEs at different time series lengths. This means that models for binary, multinomial, ordered,  and count (with the exception of poisson) are all affected. Advanced Linear Modeling, Second Edition. Sandwich estimators for standard errors are often useful, eg when model based estimators are very complex and difficult to compute and robust alternatives are required. An interesting point that often gets overlooked is that it is not an either or choice between using a sandwich estimator and using a multilevel model. Object-oriented software for model-robust covariance matrix estimators. To obtain consistent estimators of the covariance matrix of these residuals (ignoring variation in the fixed parameter estimates) we can choose comparative or diagnostic estimators. A good way to see if your model has some specification error from the random effect is by running it with and without clustered standard errors. Coefficients in the model are untouched by clustered standard errors. 3. University of Bristol Required fields are marked *. In performing my statistical analysis, I have used Stata’s _____ estimation command with the vce(cluster clustvar)option to obtain a robust variance estimate that adjusts for within-cluster correlation. When should you use cluster-robust standard errors? The two approaches are actually quite compatible. This is why in nonlinear models a random effect is a latent variable. Figuring out how much error is in your estimates is a somewhat tedious and computationally intensive process in a nonlinear model. In a linear model you can essentially use a (relatively) simple mathematical solution to calculate the random effect. First, (I think but to be confirmed) felm objects seem not directly compatible with sandwich variances, leading to erroneous results. Your email address will not be published. That is why the standard errors are so important: they are crucial in determining how many stars your table gets. However, one can easily reach its limit when calculating robust standard errors in R, especially when you are new in R. It always bordered me that you can calculate robust standard errors so easily in STATA, but you needed ten lines of code to compute robust standard errors in R. The American Statistician, 60, 299-302. Dave Giles does a wonderful job on his blog of explaining the problem in regards to robust standard errors for nonlinear models. However, both clustered HC0 standard errors (CL-0) and clustered bootstrap standard errors (BS) perform reasonably well, leading to empirical coverages close to the nominal 0.95. OLS coefficient estimates will be the same no matter what type of standard errors you choose. By including either fixed effects or a random effect in the model you are using a variable or variables to directly model the problem. If done properly this can fix both the standard error issues and the biased coefficients. Hence, obtaining the correct SE, is critical ... Interestingly, some of the robust standard errors are smaller than the model-based errors, and the effect of setting is now significant Consider the fixed part parameter estimates. Clustered standard errors will still correct the standard errors but they will now be attached to faulty coefficients. The standard errors are not quite the same. To replicate the standard errors we see in Stata, we need to use type = HC1. Such articles increased from 8 in the period spanning 1997–1999 to about 30 in 2003–2005 to over 100 in 2009–2011. the sandwich estimator also can be a problem, again especially for heavy{tailed design distributions. Petersen's Simulated Data for Assessing Clustered Standard Errors: estfun: Extract Empirical Estimating Functions: Investment: US Investment Data: meat: A Simple Meat Matrix Estimator: vcovBS (Clustered) Bootstrap Covariance Matrix Estimation: vcovCL: Clustered Covariance Matrix Estimation: sandwich: Making Sandwiches with Bread and Meat: vcovPC Cluster-robust standard errors will correct for the same problem that the dummies correct except that it will only do so with a modification to the standard errors. The sandwich estimator is formed by replacing the estimate of the central covariance term, , by an empirical estimator based on the (block diagonal structure) cross product matrix, namely, For residuals the estimated set of residuals for the j-th block at level h, using a similar notation to Goldstein (1995, App. Since we already know that the model above suffers from heteroskedasticity, we want to obtain heteroskedasticity robust standard errors and their corresponding t values. With samples of size 200;300;400 and a response rate of 5%, with Laplace distributed predictors, at the null model the coverage of the usual sandwich method based on 5;000 simulations is … And like in any business, in economics, the stars matter a lot. more How Sampling Distribution Works This means that it is estimated approximately and there will always be some error in that estimation. For calculating robust standard errors in R, both with more goodies and in (probably) a more efficient way, look at the sandwich package. The same applies to clustering and this paper. In a nonlinear model there is no direct way to calculate the random effect accurately. {sandwich} has a ton of options for calculating heteroskedastic- and autocorrelation-robust standard errors. An Introduction to Robust and Clustered Standard Errors Linear Regression with Non-constant Variance Review: Errors and Residuals Errorsare the vertical distances between observations and the unknownConditional Expectation Function.