LR test for mixed models using restricted maximum likelihood estimation method

[Zhiqiu Ye]

Hi members,
I have a question about the Likelihood Ratio test (LR test) for the mixed model with random slopes versus the model with random intercept only, while a restricted maximum likelihood (REML) method is used.
In Stata manual (page 314) in the section of xtmixed, it’s said that “LR tests with REML require identical fixed-effects specifications for both models…. if we fit the models using the REML option, we would have to confine our tests to models comparing different variance structures and not different β_s.
In my analysis, model A contains only random intercept, model B contains both random intercept and random slopes. I used REML method to obtain the estimates for both models. I then used LR test to test the significance of the components with random slopes. Is LR test appropriate here based on the aforementioned Stata note?
Many thanks,
Zhiqiu Ye

[Marcos Almeida]

Hello Zhiqiu,

Welcome to the Stata Forum!

First, I just wish to underline that -mixed - (instead of the previous - xtmixed -) is the updated command to perform linear mixed models in recent Stata versions, such as 13 and 14.

Second, and according to the recommendations I cite from an excellent book on the matter (West, Welch and Gatecki, Linear Mixed Models: a practical guide using statistical software. 2nd edition. CRC Press, 2015, p.37), REML should be chosen "when testing hypotheses about covariance parameters", and preferrably in the final model, whereas ML should be chosen "when testing hypotheses about fixed effects".

Hopefully that heps,

Best,

Marcos