Final answer:
Fixed effects models are used when the effects of variables are not considered random across entities, while random effects models are applicable when individual differences are random and uncorrelated with predictors. Alternative methods like Generalized estimating equations and phylogenetically independent contrasts are used depending on data structure and research goals.
Step-by-step explanation:
When determining when to use fixed effects vs random effects models, it's essential to consider the nature of your data and the research questions being addressed. Fixed effects models are appropriate when you are interested in analyzing the impact of variables that vary within a given entity but are consistent across all entities.
On the other hand, random effects models are suitable when you assume that the individual differences are random and uncorrelated with the predictor variables, often used when data points are nested within random layers, such as students within schools.
Generalized estimating equations (GEE) and phylogenetically independent contrasts (PIC) offer alternative approaches, each with its specific applications and potential pitfalls. GEE accounts for correlations among observations, while PIC deals with evolutionary relationships but may be sensitive to phylogenetic distance errors or extinction risks among other issues. The choice between these models should be guided by the structure of your data and research objectives, with the understanding that no one method is superior for all situations.