Transcript Making Sense/ Making Numbers/ Making Significance
The General (LISREL) SEM model Ulf H. Olsson Professor of statistics
Making Numbers
Branch Satisfaction Loan Savings Loyalty
Satisfacti on
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Loyalty
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Satisfacti on
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CFA and SEM
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Ulf H. Olsson
CFA and SEM
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Ulf H. Olsson
CFA and SEM
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No differences in estimation and testing Many estimators ML GLS ULS WLS DWLS
Ulf H. Olsson
Notation and Background
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C1 for ML and GLS
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The four different chi-squares
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C1 is N-1 times the minimum value of a fit-function
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C2 is N-1 times the minimum value of a weighted (involving a weight matrix) fit function under multivariate normality
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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
C1 C2 C3 C4
Asymptotic covariance matrix not provided *
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C1 C2 C3 C4
Asymptotic covariance matrix provided
* * * ULS 0 * * * GLS * * * * ML * 0 0 0 WLS * * * * DWLS 0 Ulf H. Olsson
ESTIMATORS
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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
Problems with the chi-square test
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The chi-square tends to be large in large samples if the model does not hold It is based on the assumption that the model holds in the population It is assumed that the observed variables comes from a multivariate normal distribution => The chi-square test might be to strict, since it is based on unreasonable assumptions?!
Ulf H. Olsson
Alternative test- Testing Close fit
Non
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RMSEA
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Ulf H. Olsson
How to Use RMSEA
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Use the 90% Confidence interval for EA
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Use The P-value for EA
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RMSEA as a descriptive Measure
• • • RMSEA< 0.05 Good Fit 0.05 < RMSEA < 0.08 Acceptable Fit RMSEA > 0.10 Not Acceptable Fit Ulf H. Olsson
Other Fit Indices
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RMR
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GFI = 1-(Fm/Fn)
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AGFI= 1 – (k(k+1)/(2df)) (1-GFI)
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Evaluation of Reliability
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MI: Modification Indices
Ulf H. Olsson
Nested Models and parsimony
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Modification Indices
chi-sq is chi-sq with df=
df Nested Models
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Re-specification (Modification indices)
Ulf H. Olsson
RMSEA
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Ulf H. Olsson
RMSEA
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LISREL SYNTAX
Ulf H. Olsson