title: Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models.
abstract: Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.
authors.affiliation: a Department of Psychology , Ernst-Moritz-Arndt-Universität Greifswald.
authors.forename: Andrea
authors.initials: A
authors.lastname: Hildebrandt
authors.affiliation: b Leibniz Institute for Science and Mathematics Education, Kiel University.|c Centre for International Student Assessment, Technische Universität Mönchen.
authors.forename: Oliver
authors.initials: O
authors.lastname: Lüdtke
authors.affiliation: b Leibniz Institute for Science and Mathematics Education, Kiel University.|c Centre for International Student Assessment, Technische Universität Mönchen.
authors.forename: Alexander
authors.initials: A
authors.lastname: Robitzsch
authors.affiliation: d Department of Psychology , Humboldt-Universität zu Berlin.
authors.forename: Christopher
authors.initials: C
authors.lastname: Sommer
authors.affiliation: e Department of Psychology and Education, Universität Ulm.
authors.forename: Oliver
authors.initials: O
authors.lastname: Wilhelm
mesh_terms: D000293:Adolescent; D000367:Age Factors; D000465:Algorithms; D002648:Child; D002675:Child, Preschool; D003071:Cognition; D032882:Comprehension; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D015999:Multivariate Analysis; D012984:Software; D055815:Young Adult
keywords: Local structural equation model; WJ-III tests of cognitive abilities; age differentiation of cognitive abilities; moderated factor analysis; multiple-group mean and covariance structures