Random Intercept Variance

Pseudo R^2 in Model 8

This section explains the logic behind pseudo R^2 in the context of mixed models, focusing on Model 8. Pseudo R^2 measures the proportion of variance explained by the model, indicating how well the model fits the data compared to a model with fewer predictors.

The general formula for pseudo R^2 is:

$$ R^2 = \frac{Explained\ Variance}{Total\ Variance} $$

In this example, we calculate it as follows:

$$ R^2_{\text{intercept}} = \frac{\sigma^2_{\text{intercept, m8a}} - \sigma^2_{\text{intercept, m8b}}}{\sigma^2_{\text{intercept, m8a}}} $$

With the given values:

$$ R^2_{\text{intercept}} = \frac{1.6446069 - 0.3098538}{1.6446069} = 0.811594 \approx 81.2\%$$