How to report overall results of an nlme mixed effects model

Question

I want to report the results of an one factorial lme from the nlme package. I want to know the overall effect of A on y. To do so I would compare the model with a Null model:

m1 <- lme(y~A,random=~1|B/C,data=data,weights=varIdent(form = ~1|A),method="ML")

m0 <- lme(y~1,random=~1|B/C,data=data,weights=varIdent(form = ~1|A),method="ML")

I am using maximum likelihood because I am comparing models with different main effects. stats::anova(m0,m1) gives me a significant p value, meaning that there is a significant effect of A on y. However, in contrast to lmer models made with lme4, no Chi2 values are given. First: Is this approach valid? And second: What is the best way to report the result? Thanks for your answers

Answer 1

An anova with lme should give you the same information as with lmer. Both use what's called a deviance test or likelihood ratio test. The L.ratio part in the table returned by anova is simply the difference in the loglikelihood of the two models multiplied by -2. A deviance test tests this value against a Chi2 distribution with the difference in model parameters (in your case 1) degrees of freedom. So the value reported under L.ratio for lme models is the same as the Chi2 value reported for lmer models (assuming the models are the same of course, and lmer rounds the value to a decimal).

The approach is valid and you could report the value under L.ratio along with the degrees of freedom and p-value, but I would add more information in your report such as the fixed and random coefficients of both models and other parameters that you've added (such as the difference in variance for levels of A specified under weights). If you're only interested in the fixed effect of A than a Wald test should also be appropriate though REML estimates are recommended in cases with a small number of groups (Snijders & Bosker, 2012). The test statistic is the t-value and associated p-value in the model summary output summary(m1). Chapter 6 in Snijders & Bosker (2012) gives a great explanation on tests for fixed and random parameters. Along with reporting examples.