An, Yujia. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 71-76). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Review on BFA --- p.2 / Chapter 1.1.2 --- Review on NFA --- p.3 / Chapter 1.1.3 --- Typical model selection criteria --- p.5 / Chapter 1.1.4 --- New model selection criterion and automatic model selection --- p.6 / Chapter 1.2 --- Our contributions --- p.7 / Chapter 1.3 --- Thesis outline --- p.8 / Chapter 2 --- Combination of B and BI architectures for BFA with automatic model selection --- p.10 / Chapter 2.1 --- Implementation of BFA using BYY harmony learning with au- tomatic model selection --- p.11 / Chapter 2.1.1 --- Basic issues of BFA --- p.11 / Chapter 2.1.2 --- B-architecture for BFA with automatic model selection . --- p.12 / Chapter 2.1.3 --- BI-architecture for BFA with automatic model selection . --- p.14 / Chapter 2.2 --- Local minima in B-architecture and BI-architecture --- p.16 / Chapter 2.2.1 --- Local minima in B-architecture --- p.16 / Chapter 2.2.2 --- One unstable result in BI-architecture --- p.21 / Chapter 2.3 --- Combination of B- and BI-architecture for BFA with automatic model selection --- p.23 / Chapter 2.3.1 --- Combine B-architecture and BI-architecture --- p.23 / Chapter 2.3.2 --- Limitations of BI-architecture --- p.24 / Chapter 2.4 --- Experiments --- p.25 / Chapter 2.4.1 --- Frequency of local minima occurring in B-architecture --- p.25 / Chapter 2.4.2 --- Performance comparison for several methods in B-architecture --- p.26 / Chapter 2.4.3 --- Comparison of local minima in B-architecture and BI- architecture --- p.26 / Chapter 2.4.4 --- Frequency of unstable cases occurring in BI-architecture --- p.27 / Chapter 2.4.5 --- Comparison of performance of three strategies --- p.27 / Chapter 2.4.6 --- Limitations of BI-architecture --- p.28 / Chapter 2.5 --- Summary --- p.29 / Chapter 3 --- A Comparative Investigation on Model Selection in Binary Factor Analysis --- p.31 / Chapter 3.1 --- Binary Factor Analysis and ML Learning --- p.32 / Chapter 3.2 --- Hidden Factors Number Determination --- p.33 / Chapter 3.2.1 --- Using Typical Model Selection Criteria --- p.33 / Chapter 3.2.2 --- Using BYY harmony Learning --- p.34 / Chapter 3.3 --- Empirical Comparative Studies --- p.36 / Chapter 3.3.1 --- Effects of Sample Size --- p.37 / Chapter 3.3.2 --- Effects of Data Dimension --- p.37 / Chapter 3.3.3 --- Effects of Noise Variance --- p.39 / Chapter 3.3.4 --- Effects of hidden factor number --- p.43 / Chapter 3.3.5 --- Computing Costs --- p.43 / Chapter 3.4 --- Summary --- p.46 / Chapter 4 --- A Comparative Investigation on Model Selection in Non-gaussian Factor Analysis --- p.47 / Chapter 4.1 --- Non-Gaussian Factor Analysis and ML Learning --- p.48 / Chapter 4.2 --- Hidden Factor Determination --- p.51 / Chapter 4.2.1 --- Using typical model selection criteria --- p.51 / Chapter 4.2.2 --- BYY harmony Learning --- p.52 / Chapter 4.3 --- Empirical Comparative Studies --- p.55 / Chapter 4.3.1 --- Effects of Sample Size on Model Selection Criteria --- p.56 / Chapter 4.3.2 --- Effects of Data Dimension on Model Selection Criteria --- p.60 / Chapter 4.3.3 --- Effects of Noise Variance on Model Selection Criteria --- p.64 / Chapter 4.3.4 --- Discussion on Computational Cost --- p.64 / Chapter 4.4 --- Summary --- p.68 / Chapter 5 --- Conclusions --- p.69 / Bibliography --- p.71

This study was an examination of the effect of type of correlation matrix on the robustness of LISREL maximum likelihood and unweighted least squares structural parameter estimates for models with categorical manifest variables. Two types of correlation matrices were analyzed; one containing Pearson product-moment correlations and one containing tetrachoric, polyserial, and product-moment correlations as appropriate. Using continuous variables generated according to the equations defining the population model, three cases were considered by dichotomizing some of the variables with varying degrees of skewness. When Pearson product-moment correlations were used to estimate associations involving dichotomous variables, the structural parameter estimates were biased when skewness was present in the dichotomous variables. Moreover, the degree of bias was consistent for both the maximum likelihood and unweighted least squares estimates. The standard errors of the estimates were found to be inflated, making significance tests unreliable. The analysis of mixed matrices produced average estimates that more closely approximated the model parameters except in the case where the dichotomous variables were skewed in opposite directions. However, since goodness-of-fit statistics and standard errors are not available in LISREL when tetrachoric and polyserial correlations are used, the unbiased estimates are not of practical significance. Until alternative computer programs are available that employ distribution-free estimation procedures that consider the skewness and kurtosis of the variables, researchers are ill-advised to employ LISREL in the estimation of structural equation models containing skewed categorical manifest variables. / Ph. D.