Fitting Multilevel Models When Predictors and Group Effects Correlate

Within-level Group Factorial Invariance with Multilevel Data: Multilevel Factor Mixture and Multilevel MIMIC Models

This study suggests two approaches to factorial invariance testing with multilevel data when the groups are at the within level: multilevel factor mixture model for known classes (ML FMM) and multilevel multiple indicators multiple causes model (ML MIMIC). The adequacy of the proposed approaches was investigated using Monte Carlo simulations. Additionally, the performance of different types of ...

Propagation Models and Fitting Them for the Boolean Random Sets

In order to study the relationship between random Boolean sets and some explanatory variables, this paper introduces a Propagation model. This model can be applied when corresponding Poisson process of the Boolean model is related to explanatory variables and the random grains are not affected by these variables. An approximation for the likelihood is used to find pseudo-maximum likelihood esti...

Power Transformations When Fitting Theoretical Models to Data

Multilevel Models Where the Random Effects Are Correlated with the Fixed Predictors

For small group sizes, the multilevel iterative generalised least squares (IGLS) estimator is biased and inconsistent where the random effects are correlated with the fixed predictors. Consistent estimates of the parameters of endogenous variables may be obtained using instrumental variables or conditioning on group level effects. In this paper we review various approaches to ensure consistency...

Fitting Linear Mixed-Effects Models using lme4

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixedand random-effects terms. The formula and data together determine a numerical repr...