Hello

I am performing a two-level HGLM analysis with a binary outcome (with a random intercept, one random slope, no cross-level interactions) using HLM 6.0 software, and would like to calculate the proportion of total variance explained by the model. I'm using the method described by Snijders & Bosker (2012, p. 305), in which explained variance (sigma-squared F) is represented by the variance of the linear predictor.

Snijders & Bosker suggest the following calculation of the linear predictor (using the estimated coefficients for the intercept and slopes of level-1 predictors, and plugging in the values of the predictors):

Linear predictor = Gamma00 + Gamma10*X1ij + Gamma20*X2ij  (etc.).

Is it valid to also include the between-group variance explained, i.e. the model-estimated intercept for each group, in the calculation of the linear predictor? I'm wondering because it looks like the fitted values generated by HLM in the level-1 residual file (FITVAL) are adjusted by the Empirical Bayes estimate of the group intercept (EBINTRCP) like this:

fitted value = Gamma00 + EBINTRCP-j + Gamma10*X1ij + Gamma20*X2ij (etc.).

The proportion of total variance explained would then be calculated:

[Variance of fitted values] / ( [Variance of fitted values] + [residual between-group variance tau00] + [within-group variance 3.29] )

Is this a valid approach?
Thank you,