| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 95 === Latent Class Model is applied in the area of psychology and science of behaviors. After obtaining the original data, researchers will classify the respondents and analyze mutual relationship among them to get statistical inferences. This paper mainly emphasizes on district data and applies EM(Expectation Maximization) algorithm to estimate the proportions of groups from the latent classes of the respondents.
The simulated data used in parameter estimation is generated by employing Monte Carlo simulation. The empirical experiments were then carried on a total of 160 combinations based on the number of latent classes, the number of questions, the sample size and the initial value approaches. Each experiment is repeated 1000 times then applied EM (Expectation Maximization) algorithm. The algorithm is combined with E-step and M-step. With estimated values and theoretical values to induce its statistical inference including the bias and the Mean Square Error of the underlying parameters.
The empirical results show the negative correlation between sample size and bias. Also, as the number of latent classes increases, the estimation of the underlying parameters gets poor. As for the initial value approaches used herein, the first and the second one demonstrated their superiority. Besides parameter estimation, the multiple regression on five related variables shows significant relationship.
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