

Estimators and stratified sampling 

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I am trying to compare the results of using the ML and the MLR estimators on a CFA for a highly statified sample. To do this I am first looking at the results for the model parameters and standard errors for a model using ML unweighed, MLR with the sampling weights, and ML with the weights specified as frequency weights (which isn't exactly appropriate, but I am interested in understanding what is going on). So, the frequency weighted ML analysis returns the same parameter estimates as the MLR sampling weighted analysis, but the standard errors for the parameters in the ML analysis seem to be based on the N calculated from the implied number of observations in the frequency weights. This makes them very small as the frequency weighted n is much larger than the actual stratigied sample size used for the MLR analysis. So, am I correct in assuming that the SE's are based on the recalculated N, and if so, is there anyway to calculate the SE's in the ML model while using the actual sample size N (trick the program into using an inappropriate N for the analysis) or would the SE's be equal to those in the MLR analysis (as the parameter estimates were) if I was able to do that anyway? thanks 


When frequency weights are used, the N takes that into account and is increased. The frequency weight N is used in the analysis whenever N is involved. So this would reduce the standard errors. There is no way to take the standard errors from ML with frequency weights and convert them into the standard errors for ML with sampling weights. The standard errors for ML with sampling weights would not be the same as the standard errors for MLR with sampling weights. 

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