Cluster Standard Errors with fitlm

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Joshua on 17 Jun 2021
Commented: Joshua on 22 Sep 2021
I have panel data (county, year) and want to run a regression with individual-specific effects that are uncorrelated (a fixed effects regression in economics parlance). Does fitlm automatically cluster the standard errors? If not, is there a way to do this?
Aditya Patil on 22 Sep 2021
Can you have a look at the examples provided in https://www.mathworks.com/help/stats/fitlme.html and let me know if this serves your usage? By providing random effect as (1 + x | g), you should be able to have correlation within group errors, while errors outside group will be uncorrelated.
Joshua on 22 Sep 2021
Fitlme does not provide the option to cluster errors in estimation of the coefficient variance matrix. Nor does it provide the option to return the estimated data covariance matrix, which could be used to cluster the coefficient standard errors.
I wrote a function that estimates the Cluster Robust Variance matrix based the idea that X is 'augmented' prior to input.
Here is a fixed effects estimation. I apologize that it is not well commented.
%%%SCRIPT
%%GENERATE DUMMY MATRIX
id = unique(ID);
for ii = 1:G
D(:,ii) = (ID == id(ii)); %#ok<SAGROW>
end
%AUGMENT MATRIX
Md = eye(N)-((D*inv(D'*D))*D');
%ESTIMATE COEFFICIENTS
b = (inv(X'*Md*X))*(X'*Md*y);
%FIXED EFFECTS ERROR
efe = Md*y-(Md*X*b);
%COEFFIENT VARIANCE
crobust = (G/(G-1))*((N-1)/(N-G-K)); %correction
Vrobust = CRV(Md*X,efe,ID,crobust);
%FUNCTION
function V = CRV(X,e,ID,c)
if nargin<4
[N,K] = size(X); G = numel(unique(ID)); c = (G/(G-1))*((N-1)/(N-K));
end
if numel(c)>1
error('correction is not a scalar value');
end
%CLUSTER ROBUST VARIANCE MATRIX
g = unique(ID); G = numel(g);
%initialize 'Meat' matrix
M = 0;
for ii = 1:G
selvec = g(ii) == ID;
wi = e(selvec);
M = M+X(selvec,:)'*(wi*wi')*X(selvec,:);
end
V = c*inv(X'*X)*M*inv(X'*X);

Aditya Patil on 16 Jul 2021
Currently, clustered standard errors is not supported in Statistics and Machine Learning Toolbox. I have brought the request to the notice of concerned developers.