Showing papers in "Structural Equation Modeling in 1999"
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
TL;DR: In this paper, a Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification, and two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined.
Abstract: A Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification. Based on a balanced experimental design, samples were generated from a prespecified population covariance matrix and fitted to structural equation models with different degrees of model misspecification. Ten SEM fit indexes were studied. Two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined, especially for misspecified models. These 2 issues do not seem to have drawn enough attention from SEM practitioners. Future research should study not only different models vis‐a‐vis model complexity, but a wider range of model specification conditions, including correctly specified models and models specified incorrectly to varying degrees.
1,516 citations
TL;DR: In this article, the authors suggest the existence of a global self-esteem factor underlying responses to the self-report scale, although the inclusion of method effects is needed to achieve a good model fit.
Abstract: Self‐esteem is one of the most studied constructs in psychology. It has been measured with a variety of methods and instruments. Although Rosenberg's (1965) self‐report scale is one of the most widely used, empirical evidence on factor validity of this scale is somewhat contradictory, with either 1 or 2 factors. The results of this study suggest the existence of a global self‐esteem factor underlying responses to the scale, although the inclusion of method effects is needed to achieve a good model fit.
313 citations
TL;DR: This article used confirmatory factor analysis (CFA) to construct validity of state and trait flow responses to the 9-factor Flow State Scale (Jackson & Marsh, 1996), and external validity criteria, finding that correlations were substantially higher between matching trait and state factors than between nonmatching factors.
Abstract: Three hundred eighty-five athletes from the 1994 World Masters Games completed the 9-factor Flow State Scale (Jackson & Marsh, 1996), anew trait version of the instrument, and external validity criteria. Confirmatory factor analysis (CFA) tested alternative 1st-order and higher order models of responses to each instrument separately, to combined responses from the 2 instruments, and to responses augmented by external validity criteria. There was good support for the construct validity of state and trait flow responses in that a priori 9-factor (for each instrument separately) and 18-factor (for the 2 instruments) models Fit the data well, correlations were substantially higher between matching trait and state factors than between nonmatching factors, and external state and trait validity criteria were predictably related to specific state and trait flow factors. Whereas higher order models positing global trait and state factors could not be distinguished from corresponding lst-order models when responses to each instrument were considered separately, the higher order models fared poorly when state and trait factors were related to each other and to the external criteria. This CFA approach to construct validity may have broad applicability for evaluating multidimensional, hierarchical constructs and for comparing the relative usefulness of 1st-order and higher order representations of such constructs.
143 citations
TL;DR: In this paper, a hierarchical regression analysis with latent variables is presented, where a Cholesky or triangular decomposition of the intercorrelations among the latent predictors is performed.
Abstract: In a hierarchical or fixed-order regression analysis, the independent variables are entered into the regression equation in a prespecified order. Such an analysis is often performed when the extra amount of variance accounted for in a dependent variable by a specific independent variable is the main focus of interest (e.g., Cohen & Cohen, 1983). For example, in the area of reading achievement, there is a general interest in the specific abilities that predict reading development. Because these specific abilities are often correlated with more general abilities, such as verbal intelligence, the latter abilities are controlled for first (e.g., Wagner, Torgesen, & Rashotte, 1994). An additional reason for performing a hierarchical regression analysis is that, in these research applications, as well as in many others, the independent variables are often highly correlated. When correlated independent variables are included simultaneously in the regression model, multicollinearity arises (Cohen & Cohen, 1983). Though regularly used with observed variables, hierarchical regression analysis has not been performed with latent variables. In most applications of structural equation modeling (SEM), the latent predictors have been entered simultaneously into the regression model, although in several cases hierarchical regression analysis would have been the more appropriate approach (e.g., Guthrie et al., 1998; Normandeau & Guay, 1998; Wagner et al., 1994; Wagner et al., 1997). In this article we describe how a hierarchical regression analysis may be conducted in SEM. The main procedure proposed is to perform a Cholesky or triangular decomposition of the intercorrelations among the latent predictors (Harman, 1976; Loehlin, 1996). First the procedure is described and then an example of a hierarchical regression analysis with latent variables is given. Copyright © 1999, Lawrence Erlbaum Associates, Inc.
94 citations
TL;DR: In this paper, the general utility of parsimony in structural equation model selection is discussed, with emphasis on the extent to which one may be willing to routinely use parsimony as the only principle to follow in structural model selection.
Abstract: This article is concerned with issues in structural equation model selection that pertain to the general utility of the well‐known principle of parsimony. An example is provided using data generated by a relatively nonparsimonious simplex model and fitted rather well by a parsimonious growth curve model that belongs to a different class of models. Implications for empirical research are subsequently discussed, with emphasis on the extent to which one may be willing to routinely use parsimony as the only principle to follow in structural model selection.
89 citations
TL;DR: In this article, the authors examine the use of sample weights in the latent variable modeling context and show that ignoring weights can lead to serious bias in latent variable model parameters and that this bias is mitigated by incorporating sample weights.
Abstract: The purpose of this article is to examine the use of sample weights in the latent variable modeling context. A sample weight is the inverse of the probability that the unit in question was sampled and is used to obtain unbiased estimates of population parameters when units have unequal probabilities of inclusion in a sample. Although sample weights are discussed at length in survey research literature, virtually no discussion of sample weights can be found in the latent variable modeling literature. This article examines sample weights in latent variable models applied to the case where a simple random sample is drawn from a population containing a mixture of strata. A bootstrap simulation study is used to compare raw and normalized sample weights to conditions where weights are ignored. The results show that ignoring weights can lead to serious bias in latent variable model parameters and that this bias is mitigated by the incorporation of sample weights. Standard errors appear to be underestimated when ...
73 citations
TL;DR: This article offers an illustrative explanation of why a bootstrapping approach to structural equation modeling must choose to fix an indicator path rather than the latent variable variance in order for the empirical standard errors to be gensrated properly.
Abstract: In traditional applications of latent variable models, each exogenous latent variable must either have its variance parameter fixed or a loading path to a measured indicator variable fixed (either customarily to 1) Without doing so the measurement model will suffer from underidentification, thereby yielding no unique solution when estimating the parameters of interest The choice of whether to fix the variance or the loading is somewhat arbitrary, guided primarily by the researcher's need for inference regarding particular parameters within the model Under conditions of multivariate nonnormal data, the method by which one makes identified the measurement of exogenous latent variables may not be as arbitrary Specifically, as addressed briefly by Arbuckle (1997), when one is utilizing a bootstrapping approach for generating empirical standard errors for parameters of interest, the researcher must choose to fix an indicator path rather than the latent variable variance in order for the empirical standard errors to be gensrated properly This article offers an illustrative explanation of why such an approach is necessary Given the increased attention toward bootstrapping techniques within structural equation modeling, our hope is that a greater awareness and understanding of this unique situation will be facilitated
52 citations
TL;DR: The authors explored the use of the Friedman method of ranks as an inferential procedure for evaluating competing models and found that it has attractive properties, including limited reliance on sample size, limited distributional assumptions, an explicit multiple comparison procedure, and applicability to the comparison of nonnested models.
Abstract: Empirical researchers maximize their contribution to theory development when they compare alternative theory‐inspired models under the same conditions. Yet model comparison tools in structural equation modeling—χ2 difference tests, information criterion measures, and screening heuristics—have significant limitations. This article explores the use of the Friedman method of ranks as an inferential procedure for evaluating competing models. This approach has attractive properties, including limited reliance on sample size, limited distributional assumptions, an explicit multiple comparison procedure, and applicability to the comparison of nonnested models. However, this use of the Friedman method raises important issues regarding the lack of independence of observations and the power of the test.
50 citations
TL;DR: In this paper, two Lagrange multiplier (LM) methods are used in specification searches for adding parameters to models: one based on univariate LM tests and respecification of the model (LM-respecified method) and the other based on a partitioning of multivariate LM test (LM•incremental method).
Abstract: Two Lagrange multiplier (LM) methods may be used in specification searches for adding parameters to models: one based on univariate LM tests and respecification of the model (LM‐respecified method) and the other based on a partitioning of multivariate LM tests (LM‐incremental method). These methods may result in extraneous parameters being included in models due to either sampling error or the model being misspecified. A 2‐stage specification search may be used to reduce errors due to misspecification. In the 1st stage, parameters are added to models based on LM tests to maximize fit. Second, parameters added in the 1st stage are deleted if they are no longer necessary to maintain model fit. Illustrations are presented to demonstrate that errors due to misspecification occur with the LM‐respecified method and are even more likely with the LM‐incremental approach. These illustrations also show how the deletion stage can help eliminate some of these errors.
42 citations
TL;DR: In this article, Rao's distance (RD) is proposed to overcome the limitation of RMSR for model comparison, and a simulation study conducted to empirically investigate the sampling behavior of RD reveals that the true orderings of intermodel proximities are recovered with a...
Abstract: Comparing the fit of alternative models has become a standard procedure for analyzing covariance structure analysis. Comparison of alternative models is typically accomplished by examining the fit of each model to sample data. It is argued that rather than using this indirect approach, one should do direct comparisons of the similarities and differences among competing models. It is shown that among the existing good‐ness‐of‐fit indexes, the root mean square residual (RMSR) is the only one that can be used for this purpose. However, the RMSR fails to satisfy some important statistical desiderata. Rao's Distance (RD), an alternate measure, is shown to overcome this limitation of RMSR. The preference for RD over RMSR for model comparisons is illustrated through a detailed analysis of a particular sample of multitrait‐multimethod data. A simulation study conducted to empirically investigate the sampling behavior of RD reveals that the true orderings of intermodel proximities are recovered (on average) with a...
TL;DR: In this paper, simultaneous group confirmatory factor analyses of the Psychopathy Checklist•Revised (PCL•R; Hare, 1991) were conducted with an alcoholic inpatient sample (N= 740).
Abstract: Simultaneous group confirmatory factor analyses of the Psychopathy Checklist‐Revised (PCL‐R; Hare, 1991) were conducted with an alcoholic inpatient sample (N= 740). Invariance of the item‐factor relations for the 2 highly correlated factors of Personality and Behavioral Features were supported across 3 racial/ethnic groups (African American, Puerto Rican, and White) and across gender groups. Moment structure analysis indicated no significant differences in the latent means across men and women. Alternative covariance structure models were specified within a multitrait‐multimethod framework to evaluate convergent and discriminant validity across different methods of measuring antisociality. A correlated trait‐correlated method model was supported. A factor intercorrelation of .68 was indicated for Personality and Behavioral Features, and a significant correlation (.40) among method factors emerged for the PCL‐R scores across different raters (interviewers and therapists). General support was provided for t...
TL;DR: In this article, an analog to the Scheffe test is proposed to control the Type I error rate across the set of all possible post hoc model modifications in a sequential finite intersection multiple comparison procedure.
Abstract: Regarding post hoc structural equation modeling modification, Kaplan (1990) noted in his response to Steiger (1990), “As there is currently no analogous Scheffe test, the best we can do is to free those restrictions that have the highest probability of being wrong” (p. 201). This article proposes just such an analog to the Scheffe test to be applied to the exploratory model‐modification scenario. This method is a sequential finite‐intersection multiple comparison procedure, controlling the Type I error rate to a desired alpha level across the set of all possible post hoc model modifications.
TL;DR: Growth curve analysis of repeated measures can estimate these patterns for different categories of intervention participants as mentioned in this paper, demonstrating an application of this method using data from a recently completed multisite randomized experiment that compared three different counseling and testing methods for prevention of HIV infection and other sexually transmitted diseases, Project RESPECT.
Abstract: Booster sessions are often recommended to reestablish or reinforce the cognitive messages or behavior changes due to therapeutic and behavioral interventions. To plan intervention‐relevant booster sessions, researchers need to know the pattern(s) of individual change over time in outcome variables and for experimental groups. Growth curve analysis of repeated measures can estimate these patterns for different categories of intervention participants. This article demonstrates an application of this method using data from a recently completed multisite randomized experiment that compared 3 different counseling and testing methods for prevention of HIV infection and other sexually transmitted diseases, Project RESPECT. Reported self‐efficacy for condom use with the main sexual partner is used as an illustrative example. For most experimental groups, self‐efficacy for condom use declined for both female and male respondents soon after the intervention and booster sessions should have been instituted within 3 ...
TL;DR: In this article, an annotated bibliography covers Sewall Wright's development of the method of path coefficients for linear causal models over nearly a 50-year period, including the development of a linear causal model with path coefficients.
Abstract: When Dudley Duncan and others became interested in linear causal models, they discovered a genetic biologist had laid down the groundwork for them over nearly a 50‐year period. This annotated bibliography covers Sewall Wright's development of the method of path coefficients.
Journal Article•
TL;DR: In this article, the authors consider principal component analysis of patterned matrices, multiple analysis of variance based on principal components, and multigroup principal components analysis and demonstrate that these models can be fit readily using LISREL 8 and Mx.
Abstract: The aim of this article is to consider models incorporating principal components from the perspective of structural equation modeling. These models include the principal component analysis of patterned matrices, multiple analysis of variance based on principal components, and multigroup principal component analysis. We demonstrate that these models can be fit readily using the programs LISREL 8 and Mx. The models and certain extensions are discussed, and several illustrations are given.
TL;DR: In this article, a validation study was conducted on the Child Sex Abuse Attitude Scale (CSAAS) using confirmatory factor analysis (CFA) to examine factor structure.
Abstract: A validation study was conducted on the Child Sex Abuse Attitude Scale (CSAAS) using confirmatory factor analysis (CFA) to examine factor structure. The CSAAS was developed based on Festinger's (1957) theory of attitude development resulting in a 4‐factor first‐order structure (cognition, value, affect, and behavior) and a single‐factor 2nd‐order structure (attitude). A sample of 215 school psychologists, members of the National Association of School Psychologists, responded to the CSAAS survey. CFA results supported the hypothesized factor structure of the CSAAS, thus indicating the plausibility of a 4‐factor 1st‐order and a single‐factor higher order structure of the CSAAS.
TL;DR: In this paper, a multi-item scale measuring attitudes associated with purchasing non-prescription contraceptives has been developed to measure both male and female consumer attitudes toward purchasing contraceptives. But the scale is not designed to measure the attitudes of women.
Abstract: The authors develop a multi‐item scale measuring attitudes associated with purchasing nonprescription contraceptives. Although contraceptives represent a common as well as consequential purchase for many people, published research has not addressed measures of attitudes associated with this purchase decision. A scale development method is presented measuring both male and female consumer attitudes toward purchasing contraceptives. Ultimately, a multi‐item scale demonstrating a high degree of invariance across 2 samples (men and women) is developed.