Structural Equation Modeling
HeiFai Cheng
Advising Professor Xiaohui Zhong
Department of Mathematics, University of Detroit Mercy
The objective of the essay is to study the Structural Equation Modeling (SEM) and apply it to real life example. Structural equation modeling is a statistical technique that combines multivariate modeling methods, such as regression analysis, factor analysis and simultaneous equation modeling. The procedure in SEM includes data treatment, factor analysis, model building with latent variables, and interpretation of the model. The first step is Data treatment, where we discuss how to treat undesired data like outliners and missing data using methods such as regression substitution. In factor analysis, exploratory factor analysis (EFA) helps determine the amount of common factors while confirmatory factor analysis (CFA) interpret how well the hypothetical model is. After the model is built, correlation, multivariate and other characteristics between factors and variables can be studied.
During the winter semester, University of Detroit Mercy conducted a pilot survey on public opinion regarding public transit in Southeast Michigan. The goal of the survey is to understand the public’s perspective on current conditions and future directions for the public transit system of the Southeast Michigan Region. In this essay, SEM was applied to the data acquired from the survey. As a result, models were built to establish the relations between three dependent variables and the four factors extracted. The three dependent variables are the willingness he publics are going to contribute to improve the public transit system, the amount of such contribution, and degree of trust of the publics to the government agencies in handling the money. The four factors extracted are the usage of public transit, the satisfaction of public transit, the importance of public transit, and the influence of public transit on the community as large. Using the statistical software SPSS and AMOS, the following models are built:
With the models, we are able to study the different relations between the factors and variables.
Mathematical Analysis 