Are predicted probabilities different when using a logistic GEE model vs. a logistic random effects model?

Question

Are predicted probabilities different when using a logistic GEE model vs. a logistic random intercepts model?

Let's assume for both models you use the same fixed effects and the same variable to account for clustered observations.

I know the odds ratios estimated from a GEE are marginal and the odds ratios estimated from a random effects model are conditional so they will be different values with different interpretations. But will the predicted probabilities, which are calculated using the estimated (log) odds ratios, be different with different interpretations as well?

EDIT I borrowed the image below from this answered question.

To clarify, if I use a mixed logistic model with a random intercept for each student to estimate a predicted probability for someone with the same baseline ability as student C and 4 hours of instruction, will I get probability number 2 (a probability conditional on the random effect). Whereas, if I use a GEE to estimate predicted probability for someone with the same baseline ability as student C and 4 hours of instruction, will I get probability number 1 (a marginal or population averaged probability)?

Answer 1

Yes, the predictions from the two approaches will be different, in the same line as you mentioned for the odds ratios. Namely, the GEE will give you population-averaged predictions and the mixed effects logistic regression subject-specific predictions.

From the latter you can obtain the marginal predictions by marginalizing over the random effects.