Researchers who work mostly with LMMs sometimes tend to forget this, since for LMMs the cluster-specific effects are equal to the population-average (marginal) effects. To further complicate things we should also remind ourselves that the effects from (G)LMM have cluster-specific interpretations (“subject-specific” in a longitudinal model when clusters = subjects). Let’s create a simple function that generates data from this modelĪll of the estimates are on the log scale, and they do not have an immediate interpretation on the natural scale.
However, it would be easy to use the contents of this post for a longitudinal model where clusters refer to subjects, and the subjects have repeated observations. schools, centers, groups, and the first level are subjects. Each treatment arm has n 2 clusters, and each cluster has n 1 observations. Importantly, the methods in this post can quite easily be tweaked to work with other response distributions. Gambling expenditure is sometimes quite well described by a lognormal distribution, or a (generalized) Gamma distribution. Let’s assume y is the average money (in USD) lost gambling per week (since I do research on gambling disorder). In this model, the natural logarithm of y is normally distributed conditional on the cluster-specific effect u i and the treatment variable T X. This is a classic 2-level multilevel model. How the estimates from a multilevel model can be transformed to answer the same questions as population-average models or fixed effects models.Īs an example, we will use a simple hierarchical design with clusters nested within either a treatment or a control condition.How simulation-based approaches like MCMC make it much easier to make inferences about transformed parameters.In part 2 I will cover a GLMM with a binary outcome, and part 3 will focus on semicontinuous (hurdle/two-part) models when the outcome is a skewed continuous variable that include zeros. Intraclass correlations on the transformed/link/latent scale or on the response/data/original scale.Subject-specific/cluster-specific versus population-average effects (conditional versus marginal effects).Calculating both multiplicative effects (% change) and differences on the untransformed scale.log-transformation of the dependent variable in a multilevel model.
This will be the first part of a three-part tutorial on some of the finer details of (G)LMMs, and how Bayes can make your (frequentist) life easier. In this post, I will deal with linear mixed-effects models (LMM) that use a log-transformed outcome variable. When a multilevel model includes either a non-linear transformation (such as the log-transformation) of the response variable, or of the expectations via a GLM link-function, then the interpretation of the results will be different compared to a standard Gaussian multilevel model specifically, the estimates will be on a transformed scale and not in the original units, and the effects will no longer refer to the average effect in the population, instead they are conditional/cluster-specific.