Analytical Strategies for Structural Equation Models with Missing Data

Structural Equation Model (SEM) with missing data is common in empirical studies. This thesis examined the use of auxiliary variables in inclusive strategies as well as the assessment of fit in SEM when data are Missing at Random (MAR). Study-1 showed that the high-order items (e.g., interaction or quadratic terms) could be essential for an effective inclusive strategy, even in instances when we are certain that the inclusive strategy only with the linear items has already achieved MAR. The non-parsimony by these inclusive items does not impair the parsimony in the eventual interpretation of the model. Study-2 provided empirical estimates of a safe sample size to include fixed covariates in regression analyses. Each increment of 55 in the sample size would allow the entry of one more covariate to the model with the assurance that the confidence radius of the original parameters will increase less than 1% at the probability level of 99.9%. Furthermore, Study-2 supported that suppression of sampling error through an effective inclusive strategy in path analysis would lead to the deterioration of the standardized Goodness-of-Fit (GOF) of the population, which suggests the general preference of unstandardized fit assessments. Given the MAR condition, Study-3 and Study-4 proposed two Multiple Imputation (MI) procedures to assess the unstandardized fit of an embedded SEM respectively with and without explicit constrained parameters. In Study-3, the parsimonious model interpretation was validated through the confidence region of non-parsimonious parameters. Study-4 defined the populations of the residuals of reproduced covariance matrix and provided estimates of their Wald standard errors.;With MAR data, Study-5 compared the RMSEA point estimates using EM and Full Information Maximum Likelihood (FIML) methods. The EM method gave smaller Root Mean Square Errors for large sample size or non-close fit population. In situations with an extreme violation of the MAR assumption and a rather low missing rate m not-greater than 5%, Study-6 calculated the limits of distort rates of mean and standard deviation (SD) statistics of an originally normal variable. With the population SD as the base unit, the empirical estimates of the upper bounds are 2m for absolute distort in observed mean, and 3m and 0.5m for negative and positive distorts in observed SD respectively. Study-7 investigated the censored regression model implemented in SEM software Mplus and found that when there were minor disturbances in the input data, the results of the model would no longer be valid. It was advised to substitute the values of censored variables which were affected by the obvious ceiling effect with the precise censor criterion to ensure that there were no values exceeding the criterion.;In the appendix, consensus from the researcher community in confidence levels and in hypothesized criterion effect sizes were discussed and compared in Study-8. In social and psychological studies, there was greater consensus in the confidence levels over that in the hypothesized criterion effect sizes. This subsequently leads to popularity in the reports of interval estimates over those of p values, and reports of robust Wald confidence intervals provided by MI over those of precise p values by FIML for SEM with MAR data. Study-9, also in the appendix, provided the interactive web applications for the statistics codes as used in this thesis or other similar studies.