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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)

- K H Yuan, P M Bentler
- The British journal of mathematical and…
- 1998

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)

- K H Yuan, P M Bentler
- The British journal of mathematical and…
- 1998

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)

- K H Yuan, W Chan, P M Bentler
- The British journal of mathematical and…
- 2000

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)

- K H Yuan, P M Bentler
- The British journal of mathematical and…
- 2001

A small proportion of outliers can distort the results based on classical procedures in covariance structure analysis. We look at the quantitative effect of outliers on estimators and test statistics based on normal theory maximum likelihood and the asymptotically distribution-free procedures. Even if a proposed structure is correct for the majority of the… (More)

- P M Bentler, K H Yuan
- The British journal of mathematical and…
- 1996

Principal component analysis and factor analysis are the most widely used tools for dimension reduction in data analysis. Both methods require some good criterion to judge the number of dimensions to be kept. The classical method focuses on testing the equality of eigenvalues. As real data hardly have this property, practitioners turn to some ad hoc… (More)

- C M Musil, S L Jones, Warner, Van Prooijen, J W Van, Der Kloot +7 others
- 2006

Confirmatory Factor Analysis Byrne, B. M. (2005). Factor analytic models: viewing the structure of an assessment instrument from three perspectives. Issues in multi-item scale testing and development using structural equation models. (1998). Structural equation modeling and its relationship to multiple regression and factor analysis. An improvement on… (More)

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