I'm running a 3-level logistic model with a single binary outcome via runmlwin. Nicely-sized dataset. No cross-classification. Binary observations occur at regular intervals but the individual exits the study once the outcome is 1 - similar to a discrete-time survival model. The first observation occurs in all individuals, but the 10th observation occurs much less frequently (732 observations distributed across 732 individuals in 109 highest-level groups). I ran it as recommended - first pql then MCMC, using orthogonal option. I had also included parameter expansion at one of the levels.
When I was playing with the model in Stata, residuals at level 2 and 3 looked fine. I checked model fit by simulating expected probabilities for the sample data (the long-hand way - gen p = invlogit(_b[_Ixxx]*_Ixxx +... + v0 + u0), where v0 and u0 are residuals at levels 3 and 2). I was getting mean estimates that were very much higher than the observed probability, particularly for higher observation numbers. The ratio of predicted to mean observed data increased linearly with observation number. Either I have very biased level-1 residuals, or I got the prediction equation wrong.
- graph1.png (27.73 KiB) Viewed 4786 times
I had assumed the model equation I should use in Stata would be as shown in MLwiN interface, but my guess is that I should be including alphas created by parameter expansion to get my predictions right. I have no idea where I might find these. I could just ignore parameter expansion entirely, but my trajectories wouldn't thank me.
All thoughts welcomed.
Cheers,
Stuart