I ran into an error with my full (but not simple/null) model, so I had to use a different optimizer to avoid the fitting problems. Can I still do an LRT test using those models?
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3$\begingroup$ Why do not use that optimizer on both of them? $\endgroup$– user158565Commented Dec 14, 2018 at 2:06
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1$\begingroup$ Assume you would go ahead and compare your full model fitted with optimizer # 2 against the null model with fitted with optimizer # 1 and the p-value of the likelihood ratio test came out to be significant. Is that because the additional fixed effects in the full model provide a significant improvement over the null model? Or is it because you used different optimizers? You just won't be able to tell because you are simultaneously changing two things: including additional fixed effects in the null model and switching from optimizer # 1 to optimizer # 2. So keep the optimizer the same! $\endgroup$– Isabella GhementCommented Dec 14, 2018 at 3:01
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Provided that both models have converged, you can compare them with a likelihood ratio test (LRT), even if they are fitted with different optimization algorithms.
The theory behind the LRT requires to compare the log-likelihood functions of the two models evaluated at the corresponding maximum likelihood estimates (MLEs). Hence, under the proviso that the two different algorithms successfully find the MLEs of the two models and not a local maximum, the theory holds. To give an example, for a continuous multivariate outcome, you can use the LRT to compare a simple linear regression model that ignores the correlations and is fitted with ordinary least squares with a linear mixed model with random intercepts that is fitted with a quasi-Newton algorithm.
answered Dec 14, 2018 at 5:21