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Roderick P. McDonald

Bio: Roderick P. McDonald is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Item response theory & Latent variable. The author has an hindex of 42, co-authored 99 publications receiving 23797 citations. Previous affiliations of Roderick P. McDonald include University of Sydney & Macquarie University.


Papers
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Journal ArticleDOI
TL;DR: Principles for reporting analyses using structural equation modeling are reviewed, and it is recommended that every report give a detailed justification of the model used, along with plausible alternatives and an account of identifiability.
Abstract: Principles for reporting analyses using structural equation modeling are reviewed, with the goal of supplying readers with complete and accurate information. It is recommended that every report give a detailed justification of the model used, along with plausible alternatives and an account of identifiability. Nonnormality and missing data problems should also be addressed. A complete set of parameters and their standard errors is desirable, and it will often be convenient to supply the correlation matrix and discrepancies, as well as goodness-of-fit indices, so that readers can exercise independent critical judgment. A survey of fairly representative studies compares recent practice with the principles of reporting recommended here. Structural equation modeling (SEM), also known as path analysis with latent variables, is now a regularly used method for representing dependency (arguably “causal”) relations in multivariate data in the behavioral and social sciences. Following the seminal

3,834 citations

Journal ArticleDOI
TL;DR: In this paper, the influence of sample size on different goodness-of-fit indices used in confirmatory factor analysis (CFA) was examined and the results are consistent with the observation that the amount of random, unexplained variance varies inversely with sample size.
Abstract: This investigation examined the influence of sample size on different goodness-of-fit indices used in confirmatory factor analysis (CFA). The first two data sets were derived from large normative samples of responses to a multidimensional self-concept instrument and to a multidimensional instrument used to assess students' evaluations of teaching effectiveness. In the third set, data were simulated and generated according to the model to be tested. In the fourth, data were simulated and generated according to a three-factor model that did not have a simple structure. Twelve fit indicators were used to assess goodness-offit in all CFAs. All analyses were conducted with the LISREL V package. One-way ANOVAs and a visual inspection of graphs were used to assess the sample size effect on each index for the four data sets. Despite the inconsistency of the findings with previous claims, the results are consistent with the observation that the amount of random, unexplained variance varies inversely with sample size. Appendices include a set of computed statements, an explanation and listing of the 12 goodness-of-fit indicators, a bibliography, a table of results, and figures showing sample size effect. (Author/LMO) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. ***********************************************************************

3,746 citations

Book
01 Jul 1999
TL;DR: In this article, the authors introduce the concept of a scale and test homogeneity, reliability, and generalizability for total test scores, and propose a scaling theory for test scores.
Abstract: Contents: General Introduction. Items and Item Scores. Item and Test Statistics. The Concept of a Scale. Reliability Theory for Total Test Scores. Test Homogeneity, Reliability, and Generalizability. Reliability--Applications. Prediction and Multiple Regression. The Common Factor Model. Validity. Classical Item Analysis. Item Response Models. Properties of Item Response Models. Multidimensional Item Response Models. Comparing Populations. Alternate Forms and the Problem of Equating. An Introduction to Structural Equation Modeling. Some Scaling Theory. Retrospective. Appendix: Some Rules for Expected Values.

2,928 citations

Journal ArticleDOI
TL;DR: In this article, the Tucker-Lewis index and a new unbiased counterpart of the Bentler-Bonett index are recommended for those investigators who might wish to evaluate fit relative to a null model.
Abstract: It is suggested that Akaike's information criterion cannot be used for model selection in real applications and that there are problems attending the definition of parsimonious fit indices. A normed function of the noncentrality parameter is recommended as an unbiased absolute goodness-of-fit index, and the Tucker-Lewis index and a new unbiased counterpart of the Bentler-Bonett index are recommended for those investigators who might wish to evaluate fit relative to a null model

1,362 citations


Cited by
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Journal ArticleDOI
TL;DR: In this article, the adequacy of the conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice were examined, and the results suggest that, for the ML method, a cutoff value close to.95 for TLI, BL89, CFI, RNI, and G...
Abstract: This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and G...

76,383 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development, and present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests.
Abstract: In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

34,720 citations

Journal ArticleDOI
TL;DR: In this paper, two types of error involved in fitting a model are considered, error of approximation and error of fit, where the first involves the fit of the model, and the second involves the model's shape.
Abstract: This article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, wi...

25,611 citations

Journal ArticleDOI
TL;DR: A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models and two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes.
Abstract: Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statistics for evaluating the fit of a structural model A drawback of existing indexes is that they estimate no known population parameters A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models Two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes CFI avoids the underestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI) FI is a linear function of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extreme underestimation and overestimation often found in NNFI Asymptotically, CFI, FI, NFI, and a new index developed by Bollen are equivalent measures of comparative fit, whereas NNFI measures relative fit by comparing noncentrality per degree of freedom All of the indexes are generalized to permit use of Wald and Lagrange multiplier statistics An example illustrates the behavior of these indexes under conditions of correct specification and misspecification The new fit indexes perform very well at all sample sizes

21,588 citations