When I estimate a logistic binomial regression with an allowed to vary effect on a second and a third level, the overall intercept represents the average log-odds for any level one unit in any higher level unit:

$\text{logit}(\pi_{ijk}) = \beta_0 + \mu_{jk} + \mu_{k}$

Where $\beta_0$ is the fixed intercept and $\mu_{jk}$ and $\mu_{k}$ are the random cluster effects.

$\beta_0$ is estimated as -3.525 in this case (or 2.9% probability of success: $\pi_{ijk} = \frac{e^{\beta_{0}}}{1+e^{\beta_{0}}}$).

However, the model where no random effects are allowed (or the general mean):

$\text{logit}(\pi_{ijk}) = \beta_0$

gives -2.932 log-odds or 5% probability of success.

Does the decrease of overall intercept mean there were more clusters with low probability than with high probability?

PS: I also switch from MQL to PQL when going to the random intercept model (since PQL is not possible for the fixed effect only model). It could have to do with that too.


1 Answer 1


It seems that it depends whether you take the cluster specific median or the population mean. The -3.525 was the cluster specific median, which is the value within the median level 2 within the median level 3. I guess if the median is smaller than the mean, you could say there are more lower value clusters than there are higher level clusters.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.