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The General LISREL MODEL and Non-normality

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Title: The General LISREL MODEL and Non-normality


1
The General LISREL MODELand Non-normality
  • Ulf H. Olsson
  • Professor of Statistics

2
The General LISREL model
3
Syntax
  • DA NI? NO??? MACM
  • CM FI?????.cov
  • MO NX? NY?? NK? NE? BEFU,FI
  • PA LX
  • 1 0 0
  • Etc
  • PA LY
  • 1 0
  • 1 0
  • Etc
  • FR
  • FI ..
  • pd
  • ou

4
Bivariate normal distribution
5
(No Transcript)
6
(No Transcript)
7
Non-normality (Interval Scale continuous
variables)
  • Skewness
  • Kurtosis

8
Making Numbers
S sample covariance
? parameter vector
s(?) model implied covariance
9
Making Numbers
10
Making Numbers
11
Making Numbers
12
Making Numbers
13
Making Numbers
Generally
14
ESTIMATORS
  • Maximum Likelihood (ML)
  • NWLS
  • RML
  • Generalized Least Squares (GLS)
  • Asymptotic Distribution Free (ADF)
  • Diagonally Weighted Least Squares(DWLS)
  • Unweighted Least Squares(ULS)

15
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.

16
Estimation
  • 1) No AC provided
  • ML, GLS or ULS
  • 2) AC provided
  • ML
  • WLS (ADF)
  • DWLS
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