Effect of Dichotomization on the Latent Structure of Data

We investigated whether dichotomous data showed the same latent structure as the interval-level data from which they originated. Given constancy of dimensionality and factor loadings reflecting the latent structure of data, the focus was on the variance of the latent variable of a confirmatory factor model. This variance was shown to summarize the information provided by the factor loadings. The results of a simulation study did not reveal exact correspondence of the variances of the latent variables derived from interval-level and dichotomous data but shrinkage. Since shrinkage occurred systematically, methods for recovering the original variance were fleshed out and evaluated.

[1]  Rajiv Vaidyanathan,et al.  Dictionary of statistics and methodology : #a #nontechnical guide for the social sciences , 1994 .

[2]  Robust Means Modeling , 2012 .

[3]  Phil Wood.  Confirmatory Factor Analysis for Applied Research , 2008 .

[4]  H. Fischer.  A History of the Central Limit Theorem , 2011 .

[5]  Todd D. Little,et al.  A Non-arbitrary Method of Identifying and Scaling Latent Variables in SEM and MACS Models , 2006 .

[6]  W. Holmes Finch,et al.  Latent Variable Modeling with R , 2015 .

[7]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[8]  Kohji Yamamura,et al.  Transformation using (x + 0.5) to stabilize the variance of populations , 1999, Researches on Population Ecology.

[9]  W. Paul Vogt,et al.  The SAGE Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences , 2015 .

[10]  Patrick Suppes,et al.  Basic measurement theory , 1962 .

[11]  S. Morgenthaler,et al.  Advantages of Variance Stabilization , 2012 .

[12]  S. Troche,et al.  The EV Scaling Method for Variances of Latent Variables , 2019, Methodology.

[13]  Stephen G. West,et al.  Structural equation models with non-normal variables: Problems and remedies , 1995 .

[14]  Explore Configuring,et al.  A Simulation Study to , 2004 .

[15]  Max Mether.  The history of the central limit theorem , 2003 .

[16]  Robert S. Leiken,et al.  A User’s Guide , 2011 .

[17]  K. Widaman.  On Common Factor and Principal Component Representations of Data: Implications for Theory and for Confirmatory Replications , 2018, Structural Equation Modeling: A Multidisciplinary Journal.

[18]  K. Schweizer.  A Threshold-Free Approach to the Study of the Structure of Binary Data , 2013 .

[19]  J. Graham.  Congeneric and (Essentially) Tau-Equivalent Estimates of Score Reliability , 2006 .

[20]  Douglas M. Hawkins,et al.  Interactive LISREL : user's guide , 2001 .

[21]  Andrew Maul,et al.  Method Effects and the Meaning of Measurement , 2013, Front. Psychol..

[22]  R. P. McDonald,et al.  Test Theory: A Unified Treatment , 1999 .

[23]  Dorothea Krampen,et al.  A Semi-Hierarchical Confirmatory Factor Model for Speeded Data , 2020 .

[24]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[25]  K. Jöreskog.  A general method for analysis of covariance structures , 1970 .

[26]  Guan Yu,et al.  Variance stabilizing transformations of Poisson, binomial and negative binomial distributions , 2009 .

[27]  J. Mcardle.  Latent variable modeling of differences and changes with longitudinal data. , 2009, Annual review of psychology.

[28]  L. Corrado.  Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models , 2005 .

[29]  N. Blunch.  Latent Curve Models , 2020, Encyclopedia of Personality and Individual Differences.

[30]  A Comparison of Confirmatory Factor Analysis of Binary Data on the Basis of Tetrachoric Correlations and of Probability-Based Covariances: A Simulation Study , 2015 .

[31]  S. Troche,et al.  Scaling the Variance of a Latent Variable While Assuring Constancy of the Model , 2019, Front. Psychol..

[32]  K. Schweizer,et al.  Is the Item-Position Effect in Achievement Measures Induced by Increasing Item Difficulty? , 2017 .