# The Doctoral Dissertation Defense of Yin Chang

Wilson Hall, 1-134

Principal Component Models Applied to Confirmatory Factor Analysis

The Doctoral Dissertation Defense of Yin Chang

Starting at 3:10pm, Thursday, Dec 6th, 2012

1-134 Wilson Hall

**Abstract**

Testing structural equation models, in practice, may not always go smoothly, and the solution that is printed in the output may be an improper solution. The term "improper solution" refers to several possible problems with model estimation. Perhaps the most common problem that researchers have when they begin testing models is an error message that says something like "sigma matrix is not positive definite" or "warning: negative psi matrix." Another improper solution involves "out of bounds" estimates, sometimes referred to as "Heywood cases," which are negative measurement error variances, or negative disturbances. Heywood cases can occasionally be found in the output even without an error message.

The dissertation achieves the following goals: to develop a stable algorithm to estimate parameters, which would be robust to data set variability and converge with high probability; to construct an algorithm which would detect the reason for failure to converge; to develop statistical theory to compute confidence regions for functions of parameters, under non-normality of responses; and to develop statistical theory to perform hypotheses tests, such as goodness of fit tests and model comparison tests.

Based on the large simulation results, it can be demonstrated that the inference procedures for the proposed model work well enough to be used in practice and that the proposed model has advantages over the conventional model, in terms of proportion of proper solutions; average coverage rates of upper one-sided nominal 95% confidence intervals, lower one-sided nominal 95% confidence intervals, and two-sided nominal 95% confidence intervals; and average mean ratios of the width of two-sided nominal 95% confidence intervals.

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