Appendix to accompany “New recommendations on the use of R-squared differences in multilevel model comparisons”: r2MLMcomp R function

r2MLMcomp R function Description:

 This function reads in raw data and multilevel model (MLM) parameter estimates from two separate models under comparison (Model A and Model B) and outputs all R² measures (reviewed and defined in the manuscript’s print Appendix A) for both models as well as all ΔR² measures (defined in the manuscript’s Table 1). Additionally, the function produces side-by-side graphical comparisons of the R² measures for Model A vs. B that can be used to visualize changes in each measure across models (see manuscript description of Figure 2 for an example illustration). This function assumes all level-1 predictors are cluster-mean-centered for reasons described in the manuscript. Any number of level-1 and/or level-2 predictors is supported and any of the level-1 predictors can have random slopes. This function can be used with either the hierarchical or the simultaneous model-building approach described in the manuscript (in which Model B is the more complex model for a given pairwise comparison). Our function can also be used with either nested non-nested model comparisons (in which R² estimates for Model A are subtracted from those for Model B).

r2MLMcomp R function Input:

data – Dataset with rows denoting observations and columns denoting variables

within_covs_modA – List of numbers corresponding to the columns in the dataset of the level-1 predictors used in the Model A MLM (if none used, set to NULL)

between_covs_modA – List of numbers corresponding to the columns in the dataset of the level-2 predictors used in the Model A MLM (if none used, set to NULL)

random_covs_modA – List of numbers corresponding to the columns in the dataset of the level-1 predictors that have random slopes in the Model A MLM (if no random slopes, set to NULL)

gamma_w_modA – Vector of estimates of the fixed component of slopes for all level-1 predictors for Model A, to be entered in the order of the predictors listed by within_covs (if none, set to NULL)

gamma_b_modA – Vector of estimates of the fixed component of the intercept and slopes for all level-2 predictors for Model A, to be entered intercept first followed by level-2 slopes in the order listed by between_covs

Tau_modA – random effect covariance matrix for Model A; note that the first row/column denotes the intercept variance and covariances (if intercept is fixed, set all to 0) and each subsequent row/column denotes a given random slope’s variance and covariances (to be entered in the order listed by random_covs). Variances are on diagonal and covariances are on off-diagonal.

sigma2_modA – level-1 residual variance for Model A

within_covs_modB – List of numbers corresponding to the columns in the dataset of the level-1 predictors used in the Model B MLM (if none used, set to NULL)

between_covs_modB – List of numbers corresponding to the columns in the dataset of the level-2 predictors used in the Model B MLM (if none used, set to NULL)

random_covs_modB – List of numbers corresponding to the columns in the dataset of the level-1 predictors that have random slopes in the Model B MLM (if no random slopes, set to NULL)

gamma_w_modB – Vector of estimates of the fixed component of slopes for all level-1 predictors for Model B, to be entered in the order of the predictors listed by within_covs (if none, set to NULL)

gamma_b_modB – Vector of estimates of the fixed component of the intercept and slopes for all level-2 predictors for Model B, to be entered intercept first followed by level-2 slopes in the order listed by between_covs

Tau_modB – random effect covariance matrix for Model B; note that the first row/column denotes the intercept variance and covariances (if intercept is fixed, set all to 0) and each subsequent row/column denotes a given random slope’s variance and covariances (to be entered in the order listed by random_covs). Variances are on diagonal and covariances are on off-diagonal.

sigma2_modB – level-1 residual variance for Model B

r2MLMcomp R function code and example input:

r2MLMcomp