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)
Exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), path analysis, and structural equation modeling (SEM) have long histories in clinical research. Although CFA has largely superseded EFA, CFAs of multidimensional constructs typically fail to meet standards of good measurement: goodness of fit, measurement invariance, lack of differential item functioning, and well-differentiated factors in support of discriminant validity. Part of the problem is undue reliance on overly restrictive CFAs in which each item loads on only one factor. Exploratory SEM (ESEM), an overarching integration of the best aspects of CFA/SEM and traditional EFA, provides confirmatory tests of a priori factor structures, relations between latent factors and multigroup/multioccasion tests of full (mean structure) measurement invariance. It incorporates all combinations of CFA factors, ESEM factors, covariates, grouping/multiple-indicator multiple-cause (MIMIC) variables, latent growth, and complex structures that typically have required CFA/SEM. ESEM has broad applicability to clinical studies that are not appropriately addressed either by traditional EFA or CFA/SEM.
The Flow State Scale (FSS) is a new measure of flow in sport and physical activity settings. The nine FSS scales of the 36-item instrument represent the dimensions of flow discussed by Csikszentmihalyi (1990, 1993), and each scale is measured by four items. Development of items was based on (a) past research with flow state both within and outside of sport settings, (b) qualitative analysis of interviews with elite athletes, and (c) quantitative analyses conducted in the present investigation. Internal consistency estimates for the nine FSS scales were reasonable (alpha M = 33) for administration of the scale to 394 athletes. Confirmatory factor analyses supported the nine scales. Consistent with the theoretical basis of the FSS, there was also support for a hierarchical model in which one global (higher order) flow factor explained correlations among the nine first-order FSS factors. Suggestions for use of the scale and for further research are discussed.
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