LISREL / SIMPLIS: Strategien zur Beurteilung der Modellanpassung ...

Dr. Wolfgang Langer - Methoden VI: Aufbaukurs LISREL - WiSe 1999/2000 - 13
5. Bentler’s (1990) Comparative-Fit-Index (CFI):
Gestützt auf ihre Simulationsstudien empfehlen Marsh, Balla & Hau (1996) den von Bentler
entwickelten Comparative-Fit-Index (CFI) zur Beurteilung der globalen Modellanpassung. Er
ist identisch mit dem von McDonald&Marsh (1990) vorgeschlagenen Relative-Noncentrality-
Index (RNI), der sich mit Hilfe der Likelihood-Ratio-$ 2 -Werte des aktuellen und des Nullmodells
berechnen läßt.
Bentler s Comparative Fit Index (CFI) 1990:
CFI 1 2 A
2 0
1 NCP M A
NCP M0
[0;1]
McDonald&Marsh Relative Noncentrality Index (RNI) 1990:
RNI 1 L.R.$2 M A
D.F. MA
L.R.$ 2 M 0
D.F. M0
Berechnung des CFI / RNI für das Pfadmodell:(LPFADAB2.SPL)
RNI 1 L.R.$2 M A
D.F. MA
1
L.R.$ 2 M 0
D.F. M0
303,11 57
3810,24 78
0,9341 oder 0,93
Im Hinblick auf den RNI-Index fassen Marsh, Balla & Hau die Ergebisse ihrer Simulationsstudie
folgendermaßen zusammen:
„RNI. In the present comparison, the RNI was not systematically related to sample size, had
mean values of approximately 1.0 for true approximating models and appropriately reflected
systematic variation in model misspecification. In this respect, it was successful in relation to
its intended goals. The only substantial limitation for this index, perhaps, is its failure to
penalize appropriately for model complexity (i.e., RNIs were larger for overfit models with
superfluous parameter estimates) and to reward model parsimony (i.e., RNIs were smaller for
the parsimonious models that imposed equality constraints known to be true in the population).
... Because the RNI was well behaved in relation to its intended goals and most of the desirable
criteria proposed here, we recommend the continued use of the RNI (or, perhaps, its normed
counterpart, the CFI).“ (Dies 1996, S. 346)