| The commonly used approaches to estimating the parameters of structural equation models, such as the maximum likelihood and the normal theory generalized least squares, assume that the measured variables are continuous and have a multivariate normal distribution. In practice, current applications of the structural equation modeling approach to real data often involve violations of these assumptions. To overcome these problems, a non-parametric approach, the Residual Bootstrap, was introduced in this dissertation to estimate a structural equation model. The Residual Bootstrap was demonstrated to be robust to non-normality and to categorical endogenous variables for moderate sample size. It was investigated by using simulation study data and real life data from the Palmerton Lead Exposure study conducted by the Environmental Health Department of the University of Cincinnati. The Residual Bootstrap was also compared to the maximum likelihood method and the so-called Vector Bootstrap for the parameter estimates, their standard errors, confidence intervals, and the chi-square test statistics and the goodness-of-index. All the results consistently showed that the Residual Bootstrap can provide much more accurate estimates than the other two methods. It suggested that the Residual Bootstrap could be used as an alternative analysis tool when the maximum likelihood method fails, and provide additional supporting evidence in case of controversial results. |
