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Structural equation modeling is a well-known technique for studying relationships among multivariate data. In practice, high dimensional nonnormal data with small to medium sample sizes are very common, and large sample theory, on which almost all modeling statistics are based, cannot be invoked for model evaluation with test statistics. The most natural(More)
Even though data sets in psychology are seldom normal, the statistics used to evaluate covariance structure models are typically based on the assumption of multivariate normality. Consequently, many conclusions based on normal theory methods are suspect. In this paper, we develop test statistics that can be correctly applied to the normal theory maximum(More)
Covariance structure analysis is used to evaluate hypothesized influences among unmeasured latent and observed variables. As implemented, it is not robust to outliers and bad data. Several robust methods in model fitting and testing are proposed. These include direct estimation of M-estimators of structured parameters and a two-stage procedure based on(More)
Model evaluation is one of the most important aspects of structural equation modeling (SEM). Many model fit indices have been developed. It is not an exaggeration to say that nearly every publication using the SEM methodology has reported at least one fit index. Most fit indices are defined through test statistics. Studies and interpretation of fit indices(More)
Data sets in social and behavioural sciences are seldom normal. Influential cases or outliers can lead to inappropriate solutions and problematic conclusions in structural equation modelling. By giving a proper weight to each case, the influence of outliers on a robust procedure can be minimized. We propose using a robust procedure as a transformation(More)
We study several aspects of bootstrap inference for covariance structure models based on three test statistics, including Type I error, power and sample-size determination. Specifically, we discuss conditions for a test statistic to achieve a more accurate level of Type I error, both in theory and in practice. Details on power analysis and sample-size(More)
Commonly used formulae for standard error (SE) estimates in covariance structure analysis are derived under the assumption of a correctly specified model. In practice, a model is at best only an approximation to the real world. It is important to know whether the estimates of SEs as provided by standard software are consistent when a model is misspecified,(More)
Normal-distribution-based maximum likelihood (ML) and multiple imputation (MI) are the two major procedures for missing data analysis. This article compares the two procedures with respects to bias and efficiency of parameter estimates. It also compares formula-based standard errors (SEs) for each procedure against the corresponding empirical SEs. The(More)
This research investigated the relations among clients' keeping relevant secrets in therapy, the working alliance, and symptom change. Clients (N = 83) in outpatient therapy and their therapists (N = 22) at a mental health hospital completed confidential surveys after a session of ongoing therapy. The clients who reported keeping a relevant secret (27.7%)(More)
This paper develops a ridge procedure for structural equation modelling (SEM) with ordinal and continuous data by modelling the polychoric/polyserial/product-moment correlation matrix R. Rather than directly fitting R, the procedure fits a structural model to R(a) =R+aI by minimizing the normal distribution-based discrepancy function, where a > 0.(More)