Structural Equation Models: Inference (23)

Chair: Patrick Malone, Tuesday 21st July, 10.50 - 12.10, Lowercroft, School of Pythagoras. 

Wai Chan and Joyce L.-Y. Kwan, Department of Psychology, Chinese University of Hong Kong. Testing standardized effects in Structural Equation Modeling: A model reparameterization approach. (042)

Patrick S. Malone, Amanda J. Fairchild, Andrea Lamont, Thomas F. Northrup and David P. MacKinnon, Department of Psychology, University of South Carolina, USA. Confidence intervals for indirect effects in multiply imputed data. (125)

Li-Jen Weng and Hsin-Yun Liu, Department of Psychology, National Taiwan University. The role of number of parameters for sample size consideration in Structural Equation Modeling. (137)

Yutaka Kano and Keiji Takai Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Japan. Should complete-case analysis always be avoided? SEM for incomplete data with non-ignorable missing. (108)

ABSTRACTS

Testing standardized effects in Structural Equation Modeling: A model reparameterization approach. (042)
Wai Chan and Joyce L.-Y. Kwan
In structural equation modeling (SEM), statistical inferences about the model parameters are primarily limited to the testing of the unstandardized effects. This is because most SEM programs, such as AMOS, EQS, and LISREL, currently do not provide the estimated standard errors of the standardized parameters in their standard program output. In behavioral sciences, testing and comparing the standardized effects are important, especially when the observed variables are measured by very different scales. In this article, a method based on model reparameterization technique is proposed for estimating the standard error of the standardized effect. Examples are given to illustrate how the proposed method is implemented using EQS. We will compare the results with two other SEM software programs: LISREL and Mplus. While the former is capable of estimating the standard error indirectly by specifying a set of nonlinear constraints in model fitting, the latter one is able to compute the standard error estimate in its latest version.

Confidence intervals for indirect effects in multiply imputed data. (125)
Patrick S. Malone, Amanda J. Fairchild, Andrea Lamont, Thomas F. Northrup and David P. MacKinnon
The work of MacKinnon and colleagues has identified bootstrap resampling approaches and methods based on the distribution of the product as the preferred methods for confidence interval estimation for the indirect effects in general structural equation modeling. A problem arises in situations with missing data where raw data full information maximum likelihood solutions are difficult or awkward to implement, leaving multiple imputation as the only method to adjust for partially complete data. The motivating example for this situation is a scoring system requiring complete data which is not based on the common factor model. An example of this would be a measurement model indicating a respondent's use of any of several substances. There are no established procedures for generating asymmetric confidence intervals for the indirect effect with multiple imputation. In this presentation we report results of a pilot simulation study to evaluate several methods for confidence interval estimation with multiply imputed data sets. These methods can be organized in terms of methods that compute confidence intervals in each multiply imputed data set versus methods that combine results across multiply imputed data sets.

The role of number of parameters for sample size consideration in Structural Equation Modeling. (137)
Li-Jen Weng and Hsin-Yun Liu
Sample size determination is an important issue for applications of structural equation modeling (SEM) because the statistical theory of SEM is based on large sample theory. A number of authors have suggested that the ratio of sample size to the number of parameters estimated (the n:q ratio) should be taken into consideration while determining the necessary sample sizes in SEM. The present simulation study was designed to examine the effect of the n:q ratio on the performance of chi-square test statistics and various fit indices used in SEM. Contrast to the recent findings by Jackson (2001, 2003), the n:q ratio was found to yield a substantial effect on chi-square bias and fit indices. In addition, the interaction of n:q ratio and model size showed a medium effect on some fit indices. Whether an optimal n:q ratio exists for sample size consideration in SEM was also explored. The findings suggest that the n:q ratio and model size should be taken into account in determining sample sizes for applications of SEM.

Should complete-case analysis always be avoided? SEM for incomplete data with non-ignorable missing. (108)
Yutaka Kano and Keiji Takai
Statisticians do not suggest complete-case analysis or analysis after listwise deletions, for incomplete data, particularly when the data are not missing completely at random. Complete-case analysis, however, has often been made in practice. In this talk, we first show the missing-data mechanism that depends on latent variables is not ignorable in a latent variate model. Second, the complete-case analysis via normal-distribution-based inference gives rise to consistent and asymptotically normal estimators for important parameters in general linear latent variate models, in spite of the nonignorability. Complete-case analysis enjoys a huge advantage that missing-data mechanisms are not necessarily specified. Thus, the complete-case analysis is useful in general linear latent variate models when missing values are not so many and deletion of incomplete cases causes minimal loss of information. Finally, normal-theory standard errors of the estimators are shown to remain valid for nonnormal population distributions, even with nonignorable missing data.