Question about continuous distributions in GLMM
On 9 May 2018 at 20:16, Victoria Ortiz <vicrotas at gmail.com> wrote:
Hi, I'm so sorry for the delay in the response, I was with a lot of work. With "variance components" I mean the partition of the total variance into the different factors that explain it. Our interest is to have a quantification of the portion of the variance explained by the different factors, both random and fixed. Translated to the biology of our data, this means to estimate genetic, genotype x environment variation, and environment variation of the total phenotypic variation for a given trait in a population. In particular, the objective is to compare this estimators between diferent populations analyzed separately. Additionaly, reading another topics of this mail list, I found that the classical model for testing the interaction and obtain the variance components would be a model like the following: m2 <- lmer ( variable ~ fixed factor 1 * fixed factor 2 + (1 | random factor) + (1 | fixed factor 1:random factor2) + (1 | fixed factor 2:random factor) + (1| fixed factor 1:fixed factor 2:random factor)) So, with this model, in the summary I can see the partition of the total variance of the random effects. Is this right?
Yes, this model will decompose the variance of the response into variance components for the random effects and the residual variance.
Finally, if I want the p-values of the random effects, I should analize the full and reduce models sequentially. Also, I found that another way to do it is with the 'ranova' function from the lmerTest package, but the results are very dissimilar. I don't know in wich analysis should I trust, I think that in this case the sequentially one is correct.
Can you quantify how these approaches are different? If you run lmerTest::ranova(m2) it should provide (REML) likelihood ratio tests of the random terms by deleting these from the full model one-by-one. Note that if the model is fitted with REML (default) the tests are REML-likelihood ratio tests - otherwise ML likelihood ratio tests. Perhaps you use anova(m2, reduce_m2) or equivalently anova(m2, reduce_m2, refit=TRUE) which produce ML likelihood ratio tests while fitting your model with REML and that is the source of the difference? [For tests of random effect terms I recommend the REML likelihood ratio tests produced by lmerTest::ranova over the ML LR tests produced by anova(m2, reduce_m2, refit=TRUE) but other tools, e.g. package RLRsim may produce even more accurate tests]. Cheers Rune