I am dealing with nested data, and I remember from an article by Clark (1973) that nested should be analysed using special models. I’ve looked into mixed-effects models, and I’ve reached a structure with random intercepts by subjects and by items. Is this fine?
In early days, researchers would aggregate the data across these repeated measures to prevent the violation of the assumption of independence of observations, which is one of the most important assumptions in statistics.
When a model has struggled to find enough information in the data to account for every predictor---especially for every random effect---, convergence warnings appear (Brauer & Curtin, 2018; Singmann & Kellen, 2019). In this article, I review the issue of convergence before presenting a new plotting function in R that facilitates the visualisation of the fixed effects fitted by different optimization algorithms (also dubbed optimizers).
In this talk, I will look over the rationale for LMEMs, and demonstrate how to fit them in R (Brauer & Curtin, 2018; Luke, 2017). Challenges will also be covered. For instance, when using the widely-accepted 'maximal' approach, based on fitting all possible random effects for each fixed effect, models sometimes fail to find a solution, or 'convergence'. Advice for the problem of nonconvergence will be demonstrated, based on the progressive lightening of the random effects structure (Singman & Kellen, 2017; for an alternative approach, especially with small samples, see Matuschek et al., 2017). At the end, on a different note, I will present a web application that facilitates data simulation for research and teaching (Bernabeu & Lynott, 2020).