Model Fit and Item Factor Analysis: Overfactoring,Underfactoring, and a Program to Guide Interpretation

In exploratory item factor analysis (IFA), researchers may use model fit statistics and commonly invoked fit thresholds to help determine the dimensionality of an assessment. However, these indices and thresholds may mislead as they were developed in a confirmatory framework for models with continuous, not categorical, indicators. The present study used Monte Carlo simulation methods to investigate the ability of popular model fit statistics (chi-square, root mean square error of approximation, the comparative fit index, and the Tucker–Lewis index) and their standard cutoff values to detect the optimal number of latent dimensions underlying sets of dichotomous items. Models were fit to data generated from three-factor population structures that varied in factor loading magnitude, factor intercorrelation magnitude, number of indicators, and whether cross loadings or minor factors were included. The effectiveness of the thresholds varied across fit statistics, and was conditional on many features of the underlying model. Together, results suggest that conventional fit thresholds offer questionable utility in the context of IFA.     

The contribution of executive function and social understanding to preschoolers’ letter and math skills

The influence of executive function and social understanding on letter and math skills was examined in 129 3–5-year-olds. Tasks were administered to measure working memory, inhibition, social understanding, letter and math skills, and vocabulary. Using latent variable analyses, multiple models were compared in order to examine the influence of executive function and social understanding on participants’ emerging academic skills. In the best-fitting model, working memory contributed to letter and math skills, over and above inhibition, social understanding, age, and vocabulary. Inhibition and social understanding did not uniquely contribute to letter and math skills, but significant relations were found among working memory, inhibition, and social understanding. Findings are discussed with respect to improving ways to examine the complex relations among preschoolers’ executive function, social understanding, and school readiness skills.     

Organizational Commitment in the Military: Application of a Profile Approach

According to the 3-component model of commitment, the individual components of commitment—affective (AC), normative (NC), and continuance (CC)—combine to form profiles, and these profiles have different implications for behavior and well-being. We tested these propositions in a military context and also examined conditions (perceived organizational support, organizational justice, job satisfaction, and satisfaction with leadership) that might contribute to the development of commitment profiles. Latent profile analyses of data from 6,501 respondents to the 2010 Canadian Forces Retention Survey revealed 6 distinct profiles. Personnel with profiles reflecting strong AC and NC reported the most favorable work conditions, stay intentions, and well-being; uncommitted personnel and those with CC-dominant profiles reported the least favorable conditions, were most active in job search activities, and scored highest on anxiety and depression. The value of taking a profile approach, and the implications of managing work conditions to promote optimal profiles, are discussed.     

Examining Spirituality Over Time: Latent Growth Curve and Individual Growth Curve Analyses

SUMMARY

Research on spirituality and religiousness has gained growing attention in recent years; however, most studies have used cross-sectional designs. As research on this topic evolves, there has been increasing recognition of the need to examine these constructs and their effects through the use of longitudinal designs. Beyond repeated-measures ANOVA and OLS regression models, what tools are available to examine these constructs over time? The purpose of this paper is to provide an overview of two cutting-edge statistical techniques that will facilitate longitudinal investigations of spirituality and religiousness: latent growth curve analysis using structural equation modeling (SEM) and individual growth curve models. The SEM growth curve approach examines change at the group level, with change over time expressed as a single latent growth factor. In contrast, individual growth curve models consider longitudinal change at the level of the person. While similar results may be obtained using either method, researchers may opt for one over the other due to the strengths and weaknesses associated with these methods. Examples of applications of both approaches to longitudinal studies of spirituality and religiousness are presented and discussed, along with design and data considerations when employing these modeling techniques.     

COMPARING PLEASURE AND PAIN: THE FUNDAMENTAL MATHEMATICAL EQUIVALENCE OF REWARD GAIN AND SHOCK REDUCTION UNDER VARIABLE INTERVAL SCHEDULES

The relationship between positive and negative reinforcement and the symmetry of Thorndike's law of effect are unresolved issues in operant psychology. Here we show that, for a given pattern of responding on variable interval (VI) schedules with the same programmed rate of food rewards (positive reinforcement VI) or electric shocks (negative reinforcement VI), there is a fundamental mathematical equivalence between reward gain and shock reduction. We also provide the first normative account of how animals should respond on a negative VI schedule, showing that it is better to space responses evenly than to respond with a variable interresponse time (IRT). Published data from rats, however, indicate that these animals respond irregularly, often with a burst of activity immediately following a shock. While this is irrational in the experimental setting, it may represent an appropriate response to the heterogeneity of stimuli commonly encountered in natural environments. We discuss the broader implications of our analysis for understanding how animals evaluate appetitive and aversive stimuli.     

Implementing continuous non-normal skewed distributions in latent growth mixture modeling: An assessment of specification errors and class enumeration

Abstract

Recent advances have allowed for modeling mixture components within latent growth modeling using robust, skewed mixture distributions rather than normal distributions. This feature adds flexibility in handling non-normality in longitudinal data, through manifest or latent variables, by directly modeling skewed or heavy-tailed latent classes rather than assuming a mixture of normal distributions. The aim of this study was to assess through simulation the potential under- or over-extraction of latent classes in a growth mixture model when underlying data follow either normal, skewed-normal, or skewed-t distributions. In order to assess this, we implement skewed-t, skewed-normal, and conventional normal (i.e., not skewed) forms of the growth mixture model. The skewed-t and skewed-normal versions of this model have only recently been implemented, and relatively little is known about their performance. Model comparison, fit, and classification of correctly specified and mis-specified models were assessed through various indices. Findings suggest that the accuracy of model comparison and fit measures are dependent on the type of (mis)specification, as well as the amount of class separation between the latent classes. A secondary simulation exposed computation and accuracy difficulties under some skewed modeling contexts. Implications of findings, recommendations for applied researchers, and future directions are discussed; a motivating example is presented using education data.     

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.