Model Conditioned Data Elasticity in Path Analysis: Assessing the “Confoundability” of Model/Data Characteristics

Much research has been directed at the validity of fit indices in Path Analysis and Structural Equation Modeling (e.g., Browne, MacCallum, Kim, Andersen, & Glaser, 2002; Heene, Hilbert, Draxler, Ziegler, & Bühner, 2011; Hu & Bentler, 1999; Marsh, Hau, & Wen, 2004). Recent developments (e.g., Preacher, 2006; Roberts & Pashler, 2000, 2002) have encouraged researchers to investigate other criteria for comparing models, including model complexity. What has not been investigated is the inherent ability of a particular data set to be fitted with a constrained set of randomly generated linear models, which we call Model Conditioned Data Elasticity (DE). In this article we show how DE can be compared with the problem of equivalent models and a more general problem of the “confoundability” of data/model combinations (see MacCallum, Wegener, Uchino, & Fabrigar, 1993). Using the DE package in R, we show how DE can be assessed through automated computer searches. Finally, we discuss how DE fits within the controversy surrounding the use of fit statistics.

[1]  Taehun Lee,et al.  Parameter Influence in Structural Equation Modeling , 2015 .

[2]  J. Pearl,et al.  EIGHT MYTHS ABOUT CAUSALITY AND STRUCTURAL EQUATION MODELS , 2013 .

[3]  Roger E. Millsap.  A Simulation Paradigm for Evaluating Approximate Fit , 2012 .

[4]  V. Savalei.  The Relationship Between Root Mean Square Error of Approximation and Model Misspecification in Confirmatory Factor Analysis Models , 2012 .

[5]  Jolynn Pek.  Fungible parameter contours and confidence regions in structural equation models , 2012 .

[6]  M. Born,et al.  The Family-Study Interface and Academic Outcomes: Testing a Structural Model , 2011 .

[7]  Moritz Heene,et al.  Masking misfit in confirmatory factor analysis by increasing unique variances: a cautionary note on the usefulness of cutoff values of fit indices. , 2011, Psychological methods.

[8]  Robert W. Lent,et al.  Social cognitive career theory, conscientiousness, and work performance: A meta-analytic path analysis , 2011 .

[9]  Daryl F. Mellard,et al.  A Path Analysis of Reading Comprehension for Adults With Low Literacy , 2010, Journal of learning disabilities.

[10]  J. Rodgers.  The epistemology of mathematical and statistical modeling: a quiet methodological revolution. , 2010, The American psychologist.

[11]  Dorota Kurowicka,et al.  Generating random correlation matrices based on vines and extended onion method , 2009, J. Multivar. Anal..

[12]  R. Purc-Stephenson,et al.  Reporting practices in confirmatory factor analysis: an overview and some recommendations. , 2009, Psychological methods.

[13]  J. Townsend.  Mathematical Psychology: Prospects For The 21 Century: A Guest Editorial. , 2008, Journal of mathematical psychology.

[14]  Niels G. Waller,et al.  Fungible Weights in Multiple Regression , 2008 .

[15]  P. Barrett.  Structural equation modelling : Adjudging model fit , 2007 .

[16]  Tracy L. Morris.  A permutation test for the structure of a covariance matrix , 2007 .

[17]  H. Joe.  Generating random correlation matrices based on partial correlations , 2006 .

[18]  Kristopher J Preacher,et al.  Quantifying Parsimony in Structural Equation Modeling , 2006, Multivariate behavioral research.

[19]  K. Yuan.  Fit Indices Versus Test Statistics , 2005, Multivariate behavioral research.

[20]  H. Marsh,et al.  In Search of Golden Rules: Comment on Hypothesis-Testing Approaches to Setting Cutoff Values for Fit Indexes and Dangers in Overgeneralizing Hu and Bentler's (1999) Findings , 2004 .

[21]  J. Agassi.  The logic of scientific inquiry , 1974, Synthese.

[22]  Keith F Widaman,et al.  On specifying the null model for incremental fit indices in structural equation modeling. , 2003, Psychological methods.

[23]  Reply to Rodgers and Rowe (2002) , 2003 .

[24]  R. MacCallum,et al.  When fit indices and residuals are incompatible. , 2002, Psychological methods.

[25]  I. J. Myung,et al.  When a good fit can be bad , 2002, Trends in Cognitive Sciences.

[26]  P. Meehl,et al.  Risky tests, verisimilitude, and path analysis , 2002 .

[27]  Niels G Waller,et al.  The path analysis controversy: a new statistical approach to strong appraisal of verisimilitude. , 2002, Psychological methods.

[28]  S. Mulaik.  Commentary on Meehl and Waller's (2002) path analysis and verisimilitude. , 2002, Psychological methods.

[29]  R. P. McDonald,et al.  Principles and practice in reporting structural equation analyses. , 2002, Psychological methods.

[30]  K. Bollen,et al.  The Noncentral Chi-square Distribution in Misspecified Structural Equation Models: Finite Sample Results from a Monte Carlo Simulation , 2002, Multivariate behavioral research.

[31]  C. S. Reichardt.  The priority of just-identified, recursive models. , 2002, Psychological methods.

[32]  Joseph Lee Rodgers,et al.  Theory development should begin (but not end) with good empirical fits: a comment on Roberts and Pashler (2000). , 2002, Psychological review.

[33]  Comments on the Meehl-Waller (2002) procedure for appraisal of path analysis models. , 2002, Psychological methods.

[34]  Kristopher J Preacher,et al.  Sample Size in Factor Analysis: The Role of Model Error , 2001, Multivariate behavioral research.

[35]  Gordon W. Cheung,et al.  The Effects of Model Parsimony and Sampling Error on the Fit of Structural Equation Models , 2001 .

[36]  VAN ALSTINE,et al.  Evaluation of Goodness-ofFit Indices for Structural Equation Models , 2001 .

[37]  A. Boomsma.  Reporting Analyses of Covariance Structures , 2000 .

[38]  J. Dunn.  Model complexity: The fit to random data reconsidered , 2000, Psychological research.

[39]  H Pashler,et al.  How persuasive is a good fit? A comment on theory testing. , 2000, Psychological review.

[40]  R. MacCallum,et al.  Applications of structural equation modeling in psychological research. , 2000, Annual review of psychology.

[41]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

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

[43]  P. Bentler,et al.  Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives , 1999 .

[44]  G. A. Marcoulides,et al.  On desirability of parsimony in structural equation model selection , 1999 .

[45]  R. MacCallum,et al.  Power Analysis in Covariance Structure Modeling Using GFI and AGFI. , 1997, Multivariate behavioral research.

[46]  I. J. Myung,et al.  Applying Occam’s razor in modeling cognition: A Bayesian approach , 1997 .

[47]  R. MacCallum,et al.  Power analysis and determination of sample size for covariance structure modeling. , 1996 .

[48]  Steven D. Brown,et al.  Toward a Unifying Social Cognitive Theory of Career and Academic Interest, Choice, and Performance , 1994 .

[49]  Malcolm R. Forster,et al.  How to Tell When Simpler, More Unified, or Less Ad Hoc Theories will Provide More Accurate Predictions , 1994, The British Journal for the Philosophy of Science.

[50]  L. Harlow,et al.  Causation issues in structural equation modeling research , 1994 .

[51]  Duane T. Wegener,et al.  The problem of equivalent models in applications of covariance structure analysis. , 1993, Psychological bulletin.

[52]  D. Massaro,et al.  The paradigm and the fuzzy logical model of perception are alive and well. , 1993, Journal of experimental psychology. General.

[53]  J. Rodgers,et al.  Social contagion and adolescent sexual behavior: a developmental EMOSA model. , 1993, Psychological review.

[54]  J. Cutting,et al.  Selectivity, scope, and simplicity of models: a lesson from fitting judgments of perceived depth. , 1992, Journal of experimental psychology. General.

[55]  S. Hershberger,et al.  A Simple Rule for Generating Equivalent Models in Covariance Structure Modeling. , 1990, Multivariate behavioral research.

[56]  R. P. McDonald,et al.  Choosing a multivariate model: Noncentrality and goodness of fit. , 1990 .

[57]  S. Mulaik,et al.  EVALUATION OF GOODNESS-OF-FIT INDICES FOR STRUCTURAL EQUATION MODELS , 1989 .

[58]  Richard Scheines,et al.  TETRAD: Discovering Causal Structure. , 1988, Multivariate behavioral research.

[59]  N Cliff,et al.  Some Cautions Concerning The Application Of Causal Modeling Methods. , 1983, Multivariate behavioral research.

[60]  P. Bentler.  MULTIVARIATE ANALYSIS WITH LATENT VARIABLES: CAUSAL MODELING , 1980 .

[61]  J. H. Steiger.  Statistically based tests for the number of common factors , 1980 .

[62]  John W. Tukey,et al.  Analyzing data: Sanctification or detective work? , 1969 .