Using the Bollen-Stine bootstrapping method for evaluating approximate fit

Accepting that a model will not exactly fit any empirical data, global approximate fit indices quantify the degree of misfit. Recent research (Chen et al., 2008) has shown that using fixed conventional cut-points for approximate fit indices can lead to decision errors. Instead of using fixed cut-points for evaluating approximate fit indices, this study focuses on the meaning of approximate fit and introduces a new method to evaluate approximate fit indices. Millsap (2012) introduced a simulation-based method to evaluate approximate fit indices. A limitation of Millsap’s work was that a rather strong assumption of multivariate normality was implied in generating simulation data. In this study, the Bollen-Stine bootstrapping procedure (Bollen & Stine, 1993) is proposed to supplement the former study. When data are non-normal, the conclusions derived from Millsap’s (2012) simulation method and the Bollen-Stine method can differ. Examples are given to illustrate the use of the Bollen-Stine bootstrapping procedure for evaluating RMSEA. Comparisons are made with the simulation method. The results are discussed, and suggestions are given for the use of proposed method

Parenting Self-Efficacy and Parenting Practices over Time in Mexican American Families

Drawing on social cognitive theory, this study used a longitudinal cross-lagged panel design and a structural equation modeling approach to evaluate parenting self-efficacy\u27s reciprocal and causal associations with parents\u27 positive control practices over time to predict adolescents\u27 conduct problems. Data were obtained from teachers, mothers, and adolescents in 189 Mexican American families living in the southwest U.S. After accounting for contemporaneous reciprocal relationships between parenting self-efficacy (PSE) and positive control, results indicated that parenting self-efficacy predicted future positive control practices rather than the reverse. PSE also showed direct effects on decreased adolescent conduct problems. PSE functioned in an antecedent causal role in relation to parents\u27 positive control practices and adolescents\u27 conduct problems in this sample. These results support the cross-cultural applicability of social cognitive theory to parenting in Mexican American families. An implication is that parenting interventions aimed at preventing adolescent conduct problems need to focus on elevating the PSE of Mexican American parents with low levels of PSE. In addition, future research should seek to specify the most effective strategies for enhancing PSE

Applied Tests of Design Skills — Part 1: Divergent Thinking

A number of cognitive skills relevant to conceptual design were identified previously. They include divergent thinking (DT), visual thinking (VT), spatial reasoning (SR), qualitative reasoning (QR), and problem formulation (PF). A battery of standardized tests is being developed for these design skills. This paper focuses only on the divergent thinking test. This particular test has been given to over 500 engineering students and a smaller number of practicing engineers. It is designed to evaluate four direct measures (fluency, flexibility, originality, and quality) and four indirect measures (abstractability, afixability, detailability, and decomplexability). The eight questions on the test overlap in some measures and the responses can be used to evaluate several measures independently (e.g., fluency and originality can be evaluated separately from the same idea set). The data on the twenty-three measured variables were factor analyzed using both exploratory and confirmatory procedures. A four-factor solution with correlated (oblique) factors was deemed the best available solution after examining solutions with more factors. The indirect measures did not appear to correlate strongly either among themselves or with the other direct measures. The four-factor structure was then taken into a confirmatory factor analytic procedure that adjusted for the missing data. It was found to provide a reasonable fit. Estimated correlations among the four factors (F) ranged from a high of 0.32 for F1 and F2 to a low of 0.06 for F3 and F4. All factor loadings were statistically significant

Tolerance intervals: Alternatives to credibility intervals in validity generalization research

In validity generalization research, the estimated mean and variance of the true validity distribution are often used to construct a credibility interval, an interval containing a specified proportion of the true validity distribution. The statistical interpretation of this interval in the literature has varied between Bayesian and classical (frequentist) viewpoints. Credibility intervals are here discussed from the frequentist perspective. These are known as "tolerance intervals" in the statistical literature. Two new methods for constructing a credibility interval are presented. Unlike the current method of constructing the credibility interval, tolerance intervals have known performance characteristics across repeated applications, justifying confidence statements. The new methods may be useful in validity generalization research involving a small or moderate number of validation studies. Index terms: Bayesian statistics, Credibility intervals, Metaanalysis, Tolerance intervals, True validity distribution, Validity generalization

On the misuse of manifest variables in the detection of measurement bias.

Measurement invariance (lack of bias) of a manifest variable Y with respect to a latent variable W is defined as invariance of the conditional distribution of Y given W over selected subpopulations. Invariance is commonly assessed by studying subpopulation differences in the conditional distribution of Y given a manifest variable Z, chosen to substitute for W. A unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented. Theorems are provided that give conditions for measurement invariance, and for invariance of the conditional distribution of Y given Z. Additional theorems and examples explore the Bayes sufficiency of Z, stochastic ordering in W, local independence of Y and Z, exponential families, and the reliability of Z. It is shown that when Bayes sufficiency of Z fails, the two forms of invariance will often not be equivalent in practice. Bayes sufficiency holds under Rasch model assumptions, and in long tests under certain conditions. It is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias, or the lack of bias