Parameter estimation for a finite mixture of distributions for dichotomous longitudinal data: Comparing algorithms

For longitudinal data, mixed models are often used, since they allow analysts to take account of the correlation between different observations from the same individual. The finite mixture model may be considered as a special case of a mixed model. In this document, attention will be given to the maximum likelihood method. The maximization of the likelihood function for a finite mixture of distributions is generally more difficult than in the usual case of a single distribution and can require considerable time. The objective of this project was therefore primarily to identify the one or more algorithms that best meet the criteria of run time and of efficiency in finding the solution. To achieve this objective, a simulation study was carried out. Only the situation in which the dependent variable is dichotomous was considered. This situation is very useful in practice, since among other things it can be used to model discrete durations, such as the length of time in "low income" status.