Informed Latent Class-Discriminant Models
H. HOIJTINK, P. GOEDHART, P. VERDONSCHOT, R. NIJBOER, W. AKKERMANS
AND C. TER BRAAK
Utrecht University, The Netherlands
The model presented in this paper is developed for the model based clustering of water samples that are characterized by environmental variables like temperature and the numbers of each of various taxa that are found in the samples. Since the number of taxa (854) and environmental variables (53) are rather large compared to the sample size (664), two measures are taken to reduce the parameters space: (1) instead of estimating a parameter for each taxon, the parameters of hyper-priors (constructed using various characteristics of the taxa) are estimated and (2) using discriminant functions the dimensionality of the space of the environmental variables is reduced.
The model parameters will be estimated using an application of the Gibbs-sampler. A straightforward application of the Gibbs-sampler will not be successful, usually the sampler gets stuck in a local mode of the posterior leading to sub-optimal samples. In this paper an algorithm will be presented that directs the Gibbs-sampler to the global mode of the posterior, and, if you like, to all the other modes of the posterior. The marginal likelihood will be used to select the best model in terms of the number of latent classes and the number of discriminant functions that are used.