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Hello. I am hoping someone will be able to clarify a point on this for me. I see from the Mlwin supplement, when fitting a multilevel/longitudinal model to an outcome which is being treated as continuous, it is possible to estimate both between subject/within subject variances, and additionally allow for autocorrelated errors at level 1. However, when fitting a multilevel model to an outcome which is non-normal, my understanding is that common options are either to fit a population averaged model (which allows for autocorrelation between successive timepoints), or a subject specific model (which allows for between subject variances, with the within subject variances a fixed function of pi). Does this mean then that with non-normal outcomes it is not possible to simultaneously fit a subject specific model and also allow for autocorrelated errors at level 1, in the way one can with normal outcomes, and if so is there a simple mathematical explanation for this?

That's right. If you have a binary response you need to move to a multivariate model. see
Barbosa and Goldstein (2000), Quality and quantity, 34, pp323-330

Thanks very much for clarifying this and pointing me in the right direction. Is it the case that the multivariate approach only works for Bernoulli responses (ie 0 or 1) rather than grouped binomial data (eg 3 successes out of 7 trials) in Mlwin?