Interpretation of variance in multilevel logistic regression

Dependent variable: treatment (1) or no-treatment (0).

Independent variables: age, number of drugs used, comorbidity, others...

Multilevel structure: patients clustered within hospitals. Treatment rate varies across different hospitals. Multilevel logistic regression was used.

Findings: First, I ran the empty model with random intercept only and estimated the variance component (between hospital variance in treatment rate). Second, I added independent variables to the model one by one. Adding these variables either decreased or increased the variance component when comparing to empty model. Third, I added all the independent variables together into the model and variance component increased when comparing to empty model.

Conclusion: If I add variable to the model and variance decreases - this variable explains part of between-hospital variance in treatment rate. If I add variable to the model and it does not change variance component - this variable does not explain between-hospital variance.

Question: Please, give me an advice how can I interpret the fact that adding some variables to the model increase variance component.

Thank you in advance for any suggestions!

"However, in logistic and probit regression (and many other generalized linear models), the underlying latent variable is rescaled, so the lowest-level residual variance is again $\pi^2/3$ or unity, respectively. Consequently, the values of the regression coefficients and higher-level variances are also rescaled, in addition to any real changes resulting from the changes in the model. These implicit scale changes make it impossible to compare regression coefficients across models, or to investigate how variance components change. Snijders and Bosker (1999) discuss this phenomenon briefly; a more detailed discussion is given by Fielding (2003, 2004)."