TY - JOUR
T1 - More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares
AU - Yuan, Ke-hai
AU - Jiang, Ge
AU - Cheng, Ying
N1 - Funding Information:
The research was supported by the National Science Foundation under Grant No. SES-1461355.
Publisher Copyright:
© 2017 The British Psychological Society
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - Data in psychology are often collected using Likert‐type scales, and it has been shown that factor analysis of Likert‐type data is better performed on the polychoric correlation matrix than on the product‐moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice. In either LS or DWLS, the associations among the polychoric correlation coefficients are completely ignored. To mend such a gap between statistical theory and empirical work, this paper proposes new methods, called ridge GLS, for factor analysis of ordinal data. Monte Carlo results show that, for a wide range of sample sizes, ridge GLS methods yield uniformly more accurate parameter estimates than existing methods (LS, DWLS, AGLS). A real‐data example indicates that estimates by ridge GLS are 9–20% more efficient than those by existing methods. Rescaled and adjusted test statistics as well as sandwich‐type standard errors following the ridge GLS methods also perform reasonably well.
AB - Data in psychology are often collected using Likert‐type scales, and it has been shown that factor analysis of Likert‐type data is better performed on the polychoric correlation matrix than on the product‐moment covariance matrix, especially when the distributions of the observed variables are skewed. In theory, factor analysis of the polychoric correlation matrix is best conducted using generalized least squares with an asymptotically correct weight matrix (AGLS). However, simulation studies showed that both least squares (LS) and diagonally weighted least squares (DWLS) perform better than AGLS, and thus LS or DWLS is routinely used in practice. In either LS or DWLS, the associations among the polychoric correlation coefficients are completely ignored. To mend such a gap between statistical theory and empirical work, this paper proposes new methods, called ridge GLS, for factor analysis of ordinal data. Monte Carlo results show that, for a wide range of sample sizes, ridge GLS methods yield uniformly more accurate parameter estimates than existing methods (LS, DWLS, AGLS). A real‐data example indicates that estimates by ridge GLS are 9–20% more efficient than those by existing methods. Rescaled and adjusted test statistics as well as sandwich‐type standard errors following the ridge GLS methods also perform reasonably well.
KW - polychoric correlation
KW - rescaled and adjusted test statistics
KW - root mean square error
KW - sandwich-type standard error
UR - http://www.scopus.com/inward/record.url?scp=85019861864&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019861864&partnerID=8YFLogxK
U2 - 10.1111/bmsp.12098
DO - 10.1111/bmsp.12098
M3 - Article
C2 - 28547838
SN - 0007-1102
VL - 70
SP - 525
EP - 564
JO - British Journal of Mathematical and Statistical Psychology
JF - British Journal of Mathematical and Statistical Psychology
IS - 3
ER -