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Direct linkTenko Raykov; Lisa Calvocoressi; Randall E. Schumacker – Measurement: Interdisciplinary Research and Perspectives, 2024
This paper is concerned with the process of selecting between the increasingly popular bi-factor model and the second-order factor model in measurement research. It is indicated that in certain settings widely used in empirical studies, the second-order model is nested in the bi-factor model and obtained from the latter after imposing appropriate…
Descriptors: Factor Analysis, Decision Making, Computer Software, Measurement Techniques
Raykov, Tenko; Anthony, James C.; Menold, Natalja – Educational and Psychological Measurement, 2023
The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…
Descriptors: Correlation, Evaluation Research, Reliability, Measurement Techniques
Bartholomew, David J.; Deary, Ian J.; Lawn, Martin – Psychological Review, 2009
Modern factor analysis is the outgrowth of Spearman's original "2-factor" model of intelligence, according to which a mental test score is regarded as the sum of a general factor and a specific factor. As early as 1914, Godfrey Thomson realized that the data did not require this interpretation and he demonstrated this by proposing what became…
Descriptors: Psychological Testing, Factor Analysis, Intelligence Tests, Cognitive Ability
Ding, Lin; Beichner, Robert – Physical Review Special Topics - Physics Education Research, 2009
This paper introduces five commonly used approaches to analyzing multiple-choice test data. They are classical test theory, factor analysis, cluster analysis, item response theory, and model analysis. Brief descriptions of the goals and algorithms of these approaches are provided, together with examples illustrating their applications in physics…
Descriptors: Multiple Choice Tests, Factor Analysis, Data Interpretation, Item Response Theory
Dolan, Conor V.; Wicherts, Jelte M.; Molenaar, Peter C. M. – Structural Equation Modeling, 2004
We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators…
Descriptors: Error of Measurement, Factor Analysis, Regression (Statistics), Evaluation Methods
Mehta, Paras D.; Neale, Michael C. – Psychological Methods, 2005
The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (ML-SEM) and to demonstrate the equivalence of general mixed-effects models and ML-SEM. An intuitively appealing graphical representation of complex ML-SEMs is introduced that succinctly describes the underlying model and…
Descriptors: Scripts, Factor Analysis, Structural Equation Models, Modeling (Psychology)
