On a general theoretical framework of reliability.

Reliability is an essential measure of how closely observed scores represent latent scores (reflecting constructs), assuming some latent variable measurement model. We present a general theoretical framework of reliability, placing emphasis on measuring the association between latent and observed scores. This framework was inspired by McDonald's (Psychometrika, 76, 511) regression framework, which highlighted the coefficient of determination as a measure of reliability.

Percentage of variance accounted for in structural equation models: The rediscovery of the goodness of fit index.

This article delves into the often-overlooked metric of percentage of variance accounted for in structural equation models (SEM). The goodness of fit index (GFI) provides the percentage of variance of the sum of squared covariances explained by the model. Despite being introduced over four decades ago, the GFI has been overshadowed in favor of fit indices that prioritize distinctions between close and nonclose fitting models.

Assessing the Accuracy of Errors of Measurement. Implications for Assessing Reliable Change in Clinical settings.

Item response theory (IRT) models are non-linear latent variable models for discrete measures, whereas factor analysis (FA) is a latent variable model for continuous measures. In FA, the standard error (SE) of individuals' scores is common for all individuals. In IRT, the SE depends on the individual's score, and the SE function is to be provided.

Impact of a year-round school calendar on children's BMI and fitness: Final outcomes from a natural experiment.

Background: Structure may mitigate children's accelerated summer BMI gain and cardiorespiratory-fitness (CRF) loss.

Objectives: Examine BMI and CRF change during school and summer for year-round and traditional calendar school children.

Methods: Three schools (N = 2279, 1 year-round) participated in this natural experiment.

Evaluating SEM Model Fit with Small Degrees of Freedom.

Research has revealed that the performance of root mean square error of approximation (RMSEA) in assessing structural equation models with small degrees of freedom () is suboptimal, often resulting in the rejection of correctly specified or closely fitted models. This study investigates the performance of standardized root mean square residual (SRMR) and comparative fit index (CFI) in small models with various levels of factor loadings, sample sizes, and model misspecifications. We find that, in comparison with RMSEA, population SRMR and CFI are less susceptible to the effects of .

The impact of summer vacation on children's obesogenic behaviors and body mass index: a natural experiment.

Background: Children's BMI gain accelerates during summer. The Structured Days Hypothesis posits that the lack of the school day during summer vacation negatively impacts children's obesogenic behaviors (i.e.

Dynamics of sleep, sedentary behavior, and moderate-to-vigorous physical activity on school versus nonschool days.

Study Objectives: Studies examining time-use activity behaviors (sleep, sedentary behavior, and physical activity) on school days compared with nonschool days have examined these behaviors independently, ignoring their interrelated nature, limiting our ability to optimize the health benefits of these behaviors. This study examines the associations of school-day (vs. nonschool day) with time-use activity behaviors.

The Effect of Estimation Methods on SEM Fit Indices.

We examined the effect of estimation methods, maximum likelihood (ML), unweighted least squares (ULS), and diagonally weighted least squares (DWLS), on three population SEM (structural equation modeling) fit indices: the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual (SRMR). We considered different types and levels of misspecification in factor analysis models: misspecified dimensionality, omitting cross-loadings, and ignoring residual correlations. Estimation methods had substantial impacts on the RMSEA and CFI so that different cutoff values need to be employed for different estimators.

Fitting Ordinal Factor Analysis Models With Missing Data: A Comparison Between Pairwise Deletion and Multiple Imputation.

This study compares two missing data procedures in the context of ordinal factor analysis models: pairwise deletion (PD; the default setting in Mplus) and multiple imputation (MI). We examine which procedure demonstrates parameter estimates and model fit indices closer to those of complete data. The performance of PD and MI are compared under a wide range of conditions, including number of response categories, sample size, percent of missingness, and degree of model misfit.

The potential of a year-round school calendar for maintaining children's weight status and fitness: Preliminary outcomes from a natural experiment.

Purpose: To evaluate the potential of a year-round school calendar (180-day school year distributed across 12 months) as an intervention compared to a traditional school calendar (180-day school year distributed across 9 months) for mitigating children's weight gain and fitness loss via a natural experiment.

Methods: Height, weight, and cardiorespiratory fitness (CRF) (i.e.

Estimating causal effects in linear regression models with observational data: The instrumental variables regression model.

Instrumental variable methods are an underutilized tool to enhance causal inference in psychology. By way of incorporating predictors of the predictors (called "instruments" in the econometrics literature) into the model, instrumental variable regression (IVR) is able to draw causal inferences of a predictor on an outcome. We show that by regressing the outcome y on the predictors x and the predictors on the instruments, and modeling correlated disturbance terms between the predictor and outcome, causal inferences can be drawn on y on x if the IVR model cannot be rejected in a structural equation framework.

Understanding the Model Size Effect on SEM Fit Indices.

This study investigated the effect the number of observed variables () has on three structural equation modeling indices: the comparative fit index (CFI), the Tucker-Lewis index (TLI), and the root mean square error of approximation (RMSEA). The behaviors of the population fit indices and their sample estimates were compared under various conditions created by manipulating the number of observed variables, the types of model misspecification, the sample size, and the magnitude of factor loadings. The results showed that the effect of on the population CFI and TLI depended on the type of specification error, whereas a higher was associated with lower values of the population RMSEA regardless of the type of model misspecification.

The Meaning of Aggression Varies Across Culture: Testing the Measurement Invariance of the Refined Aggression Questionnaire in Samples From Spain, the United States, and Hong Kong.

Cultural differences in aggression are still poorly understood. The purpose of this article is to assess whether a tool for measuring aggression has the same meaning across cultures. Analyzing samples from Spain ( = 262), the United States ( = 344), and Hong Kong ( = 645), we used confirmatory factor analysis to investigate measurement invariance of the refined version of the Aggression Questionnaire (Bryant & Smith, 2001 ).

Restricted Recalibration of Item Response Theory Models.

In item response theory (IRT), it is often necessary to perform restricted recalibration (RR) of the model: A set of (focal) parameters is estimated holding a set of (nuisance) parameters fixed. Typical applications of RR include expanding an existing item bank, linking multiple test forms, and associating constructs measured by separately calibrated tests. In the current work, we provide full statistical theory for RR of IRT models under the framework of pseudo-maximum likelihood estimation.

The Relationship Between the Standardized Root Mean Square Residual and Model Misspecification in Factor Analysis Models.

We argue that the definition of close fitting models should embody the notion of substantially ignorable misspecifications (SIM). A SIM model is a misspecified model that might be selected, based on parsimony, over the true model should knowledge of the true model be available. Because in applications the true model (i.

Evaluating Factorial Invariance: An Interval Estimation Approach Using Bayesian Structural Equation Modeling.

In this study, we introduce an interval estimation approach based on Bayesian structural equation modeling to evaluate factorial invariance. For each tested parameter, the size of noninvariance with an uncertainty interval (i.e.

Changes in children's sleep and physical activity during a 1-week versus a 3-week break from school: a natural experiment.

Study Objectives: To examine changes in elementary aged children's sleep and physical activity during a 1-week and a 3-week school break.

Methods: Sleep and physical activity of elementary children (n = 154, age = 5-9 years, 44.8% female, 65.

Assessing the Size of Model Misfit in Structural Equation Models.

When a statistically significant mean difference is found, the magnitude of the difference is judged qualitatively using an effect size such as Cohen's d. In contrast, in a structural equation model (SEM), the result of the statistical test of model fit is often disregarded if significant, and inferences are drawn using "close" models retained based on point estimates of sample statistics (goodness-of-fit indices). However, when a SEM cannot be retained using a test of exact fit, all substantive inferences drawn from it are suspect.

Improving Psychological Measurement: Does It Make a Difference? A Comment on Nesselroade and Molenaar (2016).

Nesselroade and Molenaar advocate the use of an idiographic filter approach. This is a fixed-effects approach, which may limit the number of individuals that can be simultaneously modeled, and it is not clear how to model the presence of subpopulations. Most important, Nesselroade and Molenaar's proposal appears to be best suited for modeling long time series on a few variables for a few individuals.

There's More Than Catastrophizing in Chronic Pain: Low Frustration Tolerance and Self-Downing Also Predict Mental Health in Chronic Pain Patients.

Among the potential range of irrational beliefs that could be used as predictors of physical and mental health, catastrophizing is the process that has received most attention in chronic pain research. Other irrational processes such as demandingness, low frustration tolerance, and self-downing have rarely been studied. The goal of this study was to explore whether this wider range of beliefs is associated with health in chronic pain patients beyond catastrophizing.

Item diagnostics in multivariate discrete data.

Researchers who evaluate the fit of psychometric models to binary or multinomial items often look at univariate and bivariate residuals to determine how a poorly fitting model can be improved. There is a class of z statistics and also a class of generalized X₂ statistics that can be used for examining these marginal fits. We describe these statistics and compare them with regard to the control of Type I error and statistical power.

Social problem solving in chronic pain: An integrative model of coping predicts mental health in chronic pain patients.

Despite several models of coping have been proposed in chronic pain, research is not integrative and has not yet identified a reliable set of beneficial coping strategies. We intend to offer a comprehensive view of coping using the social problem-solving model. Participants were 369 chronic pain patients (63.