An introduction to the full random effects model

The full random‐effects model (FREM) is a method for determining covariate effects in mixed‐effects models. Covariates are modeled as random variables, described by mean and variance. The method captures the covariate effects in estimated covariances between individual parameters and covariates. This approach is robust against issues that may cause reduced performance in methods based on estimating fixed effects (e.g., correlated covariates where the effects cannot be simultaneously identified in fixed‐effects methods). FREM covariate parameterization and transformation of covariate data records can be used to alter the covariate‐parameter relation. Four relations (linear, log‐linear, exponential, and power) were implemented and shown to provide estimates equivalent to their fixed‐effects counterparts. Comparisons between FREM and mathematically equivalent full fixed‐effects models (FFEMs) were performed in original and simulated data, in the presence and absence of non‐normally distributed and highly correlated covariates. These comparisons show that both FREM and FFEM perform well in the examined cases, with a slightly better estimation accuracy of parameter interindividual variability (IIV) in FREM. In addition, FREM offers the unique advantage of letting a single estimation simultaneously provide covariate effect coefficient estimates and IIV estimates for any subset of the examined covariates, including the effect of each covariate in isolation. Such subsets can be used to apply the model across data sources with different sets of available covariates, or to communicate covariate effects in a way that is not conditional on other covariates.