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

Ulf H. Olsson Making Numbers Loyalty Branch Loan Savings Satisfaction

Ulf H. Olsson STATISTICAL SYMBOLS - NOTATION

Ulf H. Olsson CFA and SEM

Ulf H. Olsson The four different chi-squares C1 is N-1 times the minimum value of a fit-function C2 is N-1 times the minimum value of a weighted (involving a weight matrix) fit function under multivariate normality C3 is the Satorra-Bentler Scaled chi-square C4 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 ULSGLSMLWLSDWLS C10**00 C2***00 C C400000

Ulf H. Olsson Asymptotic covariance matrix provided ULSGLSMLWLSDWLS C10***0 C2***0* C3***0* C4***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)