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Ridge structural equation modelling with correlation matrices for ordinal and continuous data
Author(s) -
Yuan KeHai,
Wu Ruilin,
Bentler Peter M.
Publication year - 2011
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 - 10.1348/000711010x497442
Subject(s) - polychoric correlation , mathematics , ordinal data , ridge , statistics , moment (physics) , mean squared error , rate of convergence , convergence (economics) , pearson product moment correlation coefficient , econometrics , correlation , computer science , geometry , paleontology , computer network , channel (broadcasting) , physics , classical mechanics , economics , biology , economic growth
This paper develops a ridge procedure for structural equation modelling (SEM) with ordinal and continuous data by modelling the polychoric/polyserial/product‐moment correlation matrix R . Rather than directly fitting R , the procedure fits a structural model to R a = R + a I by minimizing the normal distribution‐based discrepancy function, where a > 0. Statistical properties of the parameter estimates are obtained. Four statistics for overall model evaluation are proposed. Empirical results indicate that the ridge procedure for SEM with ordinal data has better convergence rate, smaller bias, smaller mean square error, and better overall model evaluation than the widely used maximum likelihood procedure.