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Shafie, Khalil

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It is widely accepted that blindly specifying an incorrect number of latent classes may result in misidentifying the class membership of observations and in inconsistently estimated parameters. The current dissertation examined the Bayesian method to estimate the number of latent classes in growth mixture models. The procedure for estimating the number of latent classes was developed via Markov chain Monte Carlo using the Metropolis-Hastings algorithm. The key idea was to construct the likelihood function and then specify the prior information toward the number of latent classes (K), and then calculate the posterior distribution for K. Simulated observations were generated by the Metropolis-Hastings sampling technique from the posterior distribution. The average value of K was used under Bayesian method to estimate the number of latent classes. Other growth parameters were produced as by-products. The properties and merits of the proposed procedure were illustrated by means of a simulation study through a written R program. It was found that the Bayesian performance of estimation depended on the informative prior toward the number of latent classes only through the complexity of the growth mixture model. Additionally, the Bayesian method was optimal for both small and large sample sizes. It performs much better when the model consists of many latent classes with larger values of the unknown parameters. These properties could be useful in applied research. However, the number of time points had less influence on the latent class estimation. In conclusion, it can be said that the accuracy of the estimation of the number of components on GMM underperformed for a less complex model and a small sample size. Based on the results of this dissertation, it is suggested that covariates be added when performing sampling of posterior distribution using the Metropolis-Hastings method on the basis of Markov chain Monte Carlo. Procedures relying on the Bayesian approach should be avoided when the mixture of subpopulation is less than three groups. This is mainly because the performance of such estimation techniques is generally poor. Another technique such as reversible jump Markov chain Monte Carlo can be conducted on unconditional growth mixture models under the Bayesian framework.


Bayesian Estimation, Growth Mixture Models, Latent Classes, Likelihood Function, Posterior Distribution, Prior Distribution


293 pages

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