Can the One-Parameter Logistic Model Be a Spurious Finding for a Heterogeneous Population?

ABSTRACT Utilizing the perspective of finite mixture modeling, this note considers whether a finding of a plausible one-parameter logistic model could be spurious for a population with substantial unobserved heterogeneity. A theoretically and empirically important setting is discussed involving the mixture of two latent classes, with the less restrictive two-parameter logistic model holding within each of the classes while the more restrictive one-parameter logistic model is plausible overall. A numerical example is presented then of obtaining the one-parameter logistic model as a spurious result in a finite mixture study. Implications for behavioral and social research are discussed in light of these findings.

[1]  T. Raykov,et al.  Revisiting the Bi-Factor Model: Can Mixture Modeling Help Assess Its Applicability? , 2019 .

[2]  Ariel Linden.  Review of Tenko Raykov and George Marcoulides's a Course in Item Response Theory and Modeling with Stata , 2018, The Stata Journal: Promoting communications on statistics and Stata.

[3]  G. A. Marcoulides,et al.  Evaluation of Measurement Instrument Criterion Validity in Finite Mixture Settings , 2016, Educational and psychological measurement.

[4]  Willem J. van der Linden,et al.  Unidimensional Logistic Response Models , 2016 .

[5]  G. A. Marcoulides,et al.  Examining Population Heterogeneity in Finite Mixture Settings Using Latent Variable Modeling , 2016 .

[6]  Scale Reliability Evaluation With Heterogeneous Populations , 2015, Educational and psychological measurement.

[7]  Christian Geiser,et al.  Data Analysis with Mplus , 2012 .

[8]  C. Stein,et al.  Structural equation modeling. , 2012, Methods in molecular biology.

[9]  Dimitris Rizopoulos,et al.  ltm: An R Package for Latent Variable Modeling and Item Response Analysis , 2006 .

[10]  Dimitrios Rizopoulos.  ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses , 2006 .

[11]  B. Muthén,et al.  Investigating population heterogeneity with factor mixture models. , 2005, Psychological methods.

[12]  B. Muthén.  Latent Variable Mixture Modeling , 2001 .

[13]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[14]  F. Lord.  Applications of Item Response Theory To Practical Testing Problems , 1980 .