Quantified choice of root-mean-square errors of approximation for evaluation and power analysis of small differences between structural equation models

MacCallum, Browne, and Cai (2006) proposed a new framework for evaluation and power analysis of small differences between nested structural equation models (SEMs). In their framework, the null and alternative hypotheses for testing a small difference in fit and its related power analyses were defined by some chosen root-mean-square error of approximation (RMSEA) pairs. In this article, we develop a new method that quantifies those chosen RMSEA pairs and allows a quantitative comparison of them. Our method proposes the use of single RMSEA values to replace the choice of RMSEA pairs for model comparison and power analysis, thus avoiding the differential meaning of the chosen RMSEA pairs inherent in the approach of MacCallum et al. (2006). With this choice, the conventional cutoff values in model overall evaluation can directly be transferred and applied to the evaluation and power analysis of model differences.     

Can scientifically useful hypotheses be tested with correlations?

Historically, interesting psychological theories have been phrased in terms of correlation coefficients, which are standardized covariances, and various statistics derived from them. Methodological practice over the last 40 years, however, has suggested it is necessary to transform such theories into hypotheses on covariances and statistics derived from them. This complication turns out to be unnecessary, because the methodology now exists to test hypotheses on latent structures of correlations directly. Two examples are given. Limitations of correlation structures are also noted.     

Structural modeling and psychometrika: An historical perspective on growth and achievements

The field of linear structural equation modeling with continuous variables is reviewed. Trends in psychometric theory and data analysis across the five decades of publication ofPsychometrika are discussed, especially the clarification of concepts of population and sample, explication of the parametric structure of models, delineation of concepts of exploratory and confirmatory data analysis, expansion of statistical theory in psychometrics, estimation via optimization of an explicit objective function, and implementation of general function minimization methods. Developments in the ideas of factor analysis, latent variables, as well as structural and causal modeling are noted. Some major conceptual achievements involving general covariance structure representations, multiple population models, and moment structures are reviewed. The major statistical achievements of normal theory generalized least squares estimation, elliptical and distribution-free estimation, and higher-moment estimation are discussed. Computer programs that implement some of the theoretical developments are described.This review was supported in part by USPHS grants DA00017 and DA01070.     

On the fit of models to covariances and methodology to the Bulletin.

It is noted that 7 of the 10 top-cited articles in the Psychological Bulletin deal with methodological topics. One of these is the Bentler-Bonett (1980) article on the assessment of fit in covariance structure models. Some context is provided on the popularity of this article. In addition, a citation study of methodology articles appearing in the Bulletin since 1978 was carried out. It verified that publications in design, evaluation, measurement, and statistics continue to be important to psychological research. Some thoughts are offered on the role of the journal in making developments in these areas more accessible to psychologists.     

Initiation and Maintenance of Tobacco Smoking: Changing Personality Correlates in Adolescence and Young Adulthood1

Youthful smokers have been described as extroverted and peer-involved, whereas older smokers are often characterized as depressed and withdrawn. Recognizing this contradiction, we examined cross-sectional and prospective associations between smoking and personality and social constructs assessed every 4 years in a sample (N= 461) originally recruited in junior high school. At Time 1, smoking was positively related to good social relations, extroversion, friends' cigarette use, and cheerfulness. At Times 2–4, smoking was positively related to depression and friends' cigarette use, negatively correlated with good Social Relations, and unrelated to extroversion. Cigarette use was stable over time, but least stable between Times 1 and 2. Findings suggest the instability of early social smoking with peers; those who persist may smoke for tension reduction and self-medication.     

Dimensions of subjective female orgasmic responsiveness

Results of recent psychological research have been at odds with the major physiological evidence on the nature of female orgasmic responsiveness. Although female orgasm appears to be a single process physiologically, subjective reports by women indicate that individual differences in their experience is multidimensional. The basis for the discrepant findings is analyzed via two studies of reported orgasmic experiences in women. One sample of 115 sexually experienced women yielded data that replicated the finding that coital and masturbatory orgasmic responsiveness can be statistically distinguished and independently assessed, thus indicating that sample selection associated with prior research could not explain the result. A separate sample of 101 sexually experienced women were given an instrument that assessed coital responsiveness but differentiated masturbatory responsiveness into dimensions associated with masturbation when alone and with a partner without intercourse. A confirmatory factor analysis substantiated the existence of the three dimensions of female orgasm. However, female orgasmic responsiveness was highly correlated across the three dimensions so that it was possible to isolate a large second-order factor of general orgasmic responsiveness that is consistent with most of the physiological evidence on the unitary nature of orgasm. Correlates of the orgasm scales with background data revealed some discriminant validity for the three dimensions of responsiveness.     

Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.