Authors
Michele Scandola & Emmanuele Tidoni
Abstract
The use of Multilevel Linear Models (MLMs) is increasing in Psychology and Neuroscience research. A key aspect of MLMs is choosing a random effects structure according to the experimental needs. To date, opposite suggestions are present in the literature, spanning from keeping all random effects, which produces several singularity and convergence issues and often requires high computational resources, to removing random effects until the best fit is found, with the risk of inflating first-type error. However, defining the random structure to fit a non-singular and convergent model is not straightforward. Moreover, the lack of a standard approach may lead the researcher to make decisions that potentially inflate first-type errors and generate distortions in the estimates. To date, how to deal with singular and non-converging models is an ongoing debate.
We introduce a new way to control for first-type error inflation during model reduction, namely transforming random slopes in complex random intercepts (CRIs). These are multiple random intercepts that represent the complexity of the factors within a given grouping factor. We demonstrate that CRIs can produce reliable results, require less computational and timing resources, and we provide a straightforward procedure to use CRIs in MLMs reduction. Importantly we outline a few criteria and clear recommendations on how and when scholars should reduce singular and non-converging models.
We validated this approach by extensive simulations, a real-case application, and a comprehensive procedure that defines new solutions to avoid overinflated results and potentially standardise the use of MLMs in Psychology and Neuroscience.