Interpreting xtmixed results

[Sam Leone]

Hello All,

I am analysing data from a functional MRI study in which we have multiple observations per subject, so I am using the xtmixed command to run a multilevel linear mixed-effects model. Unfortunately, I am having trouble interpreting the random effects in the Stata output table. Specifically, what exactly do sd(_cons) and sd(_Residual) signify?

This post from Chuck Huber (http://blog.stata.com/tag/xtmixed/) does an excellent job explaining mixed-effects models in general, but I still have some confusion. It seems as though Stata is merely partitioning the error term from a standard OLS regression into multiple pieces, such that the standard deviations of the random-effects parameters are the averages of the deviations from their respective means. Yet if this is true, then it is not clear to me why the fixed effects from "xtmixed" would be different than the fixed effects from "regress." The estimation process must be different somehow? It seems I am missing something basic.

Any help or guidance on this question would be much appreciated! Cheers,

Sam

[Carlo Lazzaro]

Sam.
the explanation you're after is reported at pages 294-296, Stata 13.1 .pdf manual under the -mixed- entry; assuming you're using Stata 13.1, -xtmixed- is in fact the out-of-date command replaced by -mixed-

[Sam Leone]

Thanks for the feedback, Carlo!

I will check out the Stata manual. Hopefully it answers all of my questions.

Sam

[Roman Mostazir]

Hello All,

I am analysing data from a functional MRI study in which we have multiple observations per subject, so I am using the xtmixed command to run a multilevel linear mixed-effects model. Unfortunately, I am having trouble interpreting the random effects in the Stata output table. Specifically, what exactly do sd(_cons) and sd(_Residual) signify?

Sam

If you have an outcome Y, You have an overall mean (hypothetical population mean) and the variances around it. For a repeated measure design the overall mean remains same but the variance get partitioned. Since each individuals are repeatedly measured, you expect each of them to have different means/intercepts within their measures, thus the term is ''random intercepts''. Now the sd(cons) from Stata output presents the average SD/variance i.e. the average deviations of the random intercepts from the overall population mean. The other terms for it is Level-2 residuals/between subject deviance. The sd(_residual) represents the level-1 residuals i.e. average deviations of individuals from their own intercepts i.e. within subject deviance.

This two helps to calculate the intra-class correlation and also helps to understand the variability at different units of your nested measures.

It seems as though Stata is merely partitioning the error term from a standard OLS regression into multiple pieces, such that the standard deviations of the random-effects parameters are the averages of the deviations from their respective means. Yet if this is true, then it is not clear to me why the fixed effects from "xtmixed" would be different than the fixed effects from "regress." The estimation process must be different somehow? It seems I am missing something basic.

Any help or guidance on this question would be much appreciated! Cheers,

Sam

In any model, we are interested in explaining the variance/deviations from the mean for each added variable. In the OLS, the model deviations are calculated as the deviation of each data point from the mean. Unlike OLS, in nested data, the model deviations are the deviations of individuals means from overall means rather than deviations of all data points for an individual from the mean. Therefore, the explainable variance for each added variable in the model for OLS and nested model are different and thus their estimations are.

An extreme hypothetical example, , if you have 10 time repeated measures on some 10 people and each of the time, the measurements are exactly same, estimates from an OLS and a nested model will not differ as the means for two model will exactly same and the variances for two model will be same too. But if the ten measures for each individuals are different, then the overall means remain same but the estimable variance of the nested model will be different (mean-individual means) than the variance of the OLS model (mean-all data points).

best,