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Selecting polychoric instrumental variables in confirmatory factor analysis: An alternative specification test and effects of instrumental variables
Author(s) -
Jin Shaobo,
Cao Chunzheng
Publication year - 2018
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12128
Subject(s) - polychoric correlation , instrumental variable , ordinal data , specification , econometrics , statistics , mathematics , confirmatory factor analysis , variables , sample size determination , sample (material) , structural equation modeling , correlation , chemistry , geometry , chromatography
The polychoric instrumental variable ( PIV ) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small‐sample properties of the specification tests for testing the validity of instrumental variables ( IV s). Second, we investigate the effects of using different numbers of IV s. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study. Simulation results show that the modified specification tests with all available IV s are able to detect model misspecification. In terms of estimation accuracy, the PIV approach where the IV s outnumber the endogenous variables by one produces a lower bias but a higher variation than the PIV approach with more IV s for correctly specified factor loadings at small samples.