GRA 6020 Multivariate Statistics The Structural Equation Model

GRA 6020 Multivariate Statistics The Structural Equation Model Ulf H. Olsson Professor of Statistics

Making Numbers Branch Loan Satisfaction Loyalty Savings Ulf H. Olsson

STATISTICAL SYMBOLS - NOTATION Ulf H. Olsson

CFA and SEM Ulf H. Olsson

The four different chi-squares • C 1 is N-1 times the minimum value of a fit-function • C 2 is N-1 times the minimum value of a weighted (involving a weight matrix) fit function under multivariate normality • C 3 is the Satorra-Bentler Scaled chi-square • C 4 is N-1 times the minimum value of a weighted (involving a weight matrix) fit function under multivariate non-normality Ulf H. Olsson

Asymptotic covariance matrix not provided ULS GLS ML WLS DWLS C 1 0 * * 0 0 C 2 * * * 0 0 C 3 0 0 0 C 4 0 0 0 Ulf H. Olsson

Asymptotic covariance matrix provided ULS GLS ML WLS DWLS C 1 0 * * * 0 C 2 * * * 0 * C 3 * * * 0 * C 4 * * * 0 * Ulf H. Olsson

ESTIMATORS • If the data are continuous and approximately follow a multivariate Normal distribution, then the Method of Maximum Likelihood is recommended. • If the data are continuous and approximately do not follow a multivariate Normal distribution and the sample size is not large, then the Robust Maximum Likelihood Method is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample variances and covariances. • If the data are ordinal, categorical or mixed, then the Diagonally Weighted Least Squares (DWLS) method for Polychoric correlation matrices is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample correlations. Ulf H. Olsson

Non-normality and ordinality • Must have access to raw data • Need the asymptotic covariance matrix • Se datafile: NPV. psf Ulf H. Olsson

Bagozzi’s model • Bagozzis Modell” (The relationships between performance and satisfaction in an industrial sales force) Ulf H. Olsson