maximum liklihood

Question

I am analyzing a sample of 59 subjects using linear mixed effect model. Would using a maximum likelihood is appropriate here or should I use the restricted maximum likelihood and why?

Answer 1

When fitting linear mixed effect models, you have the option to use either maximum likelihood (ML) or restricted maximum likelihood (REML) methods to estimate the model parameters.

In general, ML assumes that the random effects have a mean of zero and estimates the variance components of the random effects and the fixed effects parameters jointly. On the other hand, REML assumes that the random effects have non-zero means and estimates the variance components of the random effects conditional on the fixed effects parameters.

In your case, since you have a relatively small sample size of 59 subjects, using REML may be more appropriate. This is because REML can provide better estimates of the variance components in the presence of small sample sizes, and it can also reduce the bias in the estimates of the fixed effects parameters.

Furthermore, ML can be biased downwards in small samples, while REML provides unbiased estimates of the variance components of the random effects. However, REML has the disadvantage of being more computationally intensive than ML and may take longer to converge, especially for complex models.

In summary, if you have a relatively small sample size and you are interested in unbiased estimates of the variance components, using REML may be more appropriate. However, if you have a large sample size and you are interested in obtaining joint estimates of the variance components and fixed effects parameters, using ML may be more appropriate.