linear mixed models - estimating R square

Linear mixed models (LMMs) are a versatile statistical framework for analyzing data with both fixed and random effects, allowing for the incorporation of correlated data structures and nested hierarchical designs. Estimating R-squared in LMMs presents unique challenges due to the presence of random effects, which can inflate traditional R-squared metrics. Various approaches have been proposed to address this issue, such as marginal and conditional R-squared, which respectively measure the variance explained by fixed effects alone and by both fixed and random effects. Additionally, pseudo-R-squared measures like Nakagawa's R-squared provide alternatives that capture the proportion of variance explained by the fixed effects while accounting for model complexity. Careful consideration of model assumptions and the interpretation of R-squared metrics is crucial in LMM analysis to ensure accurate assessment of model fit and explanatory power.