A general framework for random effects models for binary, ordinal, count type and continuous dependent variables

A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of counts. The distribution of the responses is not restricted to exponential families, which is a severe restriction in generalized mixed models. Generalized mixed models use fixed distributions for responses, for example the Poisson distribution in count data, which has the disadvantage of not accounting for overdispersion. By using a response function and a threshold function, the proposed mixed threshold model can account for a variety of alternative distributions that often show better fits than fixed distributions used within the generalized linear model framework. A particular strength of the model is that it provides a tool for joint modelling, responses may be of different types, some can be discrete, others continuous.