The Unified Approach for Model Evaluation in Structural Equation Modeling

Practical fit indices have been widely used for model fit evaluation in Structural Equation Modeling. This dissertation discusses the properties of the fit indices including their influencing factors. These properties prevent researchers from deriving one-size-fit-all cutoffs for the fit indices. In addition, the past simulation studies on model fit evaluation have several limitations. The major limitation is that most studies have focused on test of exact fit rather than approximate fit which is not consistent with the goal of practical fit indices. This dissertation reviews alternative approaches to account for the limitations and proposes a unified method for model fit evaluation combining the advantages of the alternative approaches. The unified approach allows researchers to test approximate fit and take into account sampling error in model evaluation. Two simulation studies are conducted to investigate the performance of the unified approach comparing to the other model fit evaluation methods. Two types of models are included in this study: confirmatory factor analysis and growth curve models. The results show that the unified approach appropriately rejects severely misspecified models and retains trivially misspecified models across all types of misspecification. Furthermore, the rejection rates are negligibly influenced by model characteristics and sample size. The other model evaluation methods do not have all of the desired properties described above. The unified approach, however, does not always provide model decision when sample size is low or when the level of maximal trivial misspecification specified by users is close to the actual degree of misspecification. If sample size is high and the level of specified maximal trivial misspecification is either lower or higher than the actual degree of misspecification, the unified approach is able to decide between model retention and model rejection. The extensions of the unified approach for nonnormal distribution, missing data, or nested model comparison are provided

The Motivational Thought Frequency scales for increased physical activity and reduced high-energy snacking

The Motivational Thought Frequency (MTF) Scale has previously demonstrated a coherent four-factor internal structure (Intensity, Incentives Imagery, Self-Efficacy Imagery, Availability) in control of alcohol and effective self-management of diabetes. The current research tested the factorial structure and concurrent associations of versions of the MTF for increasing physical activity (MTF-PA) and reducing high-energy snacks (MTF-S).Study 1 examined the internal structure of the MTF-PA and its concurrent relationship with retrospective reports of vigorous physical activity. Study 2 attempted to replicate these results, also testing the internal structure of the MTF-S and examining whether higher MTF-S scores were found in participants scoring more highly on a screening test for eating disorder.In Study 1, 626 participants completed the MTF-PA online and reported minutes of activity in the previous week. In Study 2, 313 participants undertook an online survey that also included the MTF-S and the Eating Attitudes Test (EAT-26).The studies replicated acceptable fit for the four-factor structure on the MTF-PA and MTF-S. Significant associations of the MTF-PA with recent vigorous activity and of the MTF-S with EAT-26 scores were seen, although associations were stronger in Study 1.Strong preliminary support for both the MTF-PA and MTF-S was obtained, although more data on their predictive validity are needed. Associations of the MTF-S with potential eating disorder illustrate that high scores may not always be beneficial to health maintenance

Factor structure and psychometric properties of the Body Appreciation Scale-2 among adolescents and young adults in Danish, Portuguese, and Swedish

In recent years, the study of body image shifted from focusing on the negative aspects to a more extensive view of body image. The present study seeks to validate a measure of positive body image, the Body Appreciation Scale-2 (BAS-2; Tylka & Wood-Barcalow, 2015a) in Denmark, Portugal, and Sweden. Participants (N = 1012) were adolescents and young adults aged from 12 to 19. Confirmatory factor analyses confirmed the one-dimensional factor structure of the scale. Multi-group confirmatory factor analyses indicated that the scale was invariant across sex and country. Further results showed that BAS-2 was positively correlated with self-esteem, psychological well-being, and intuitive eating. It was negatively correlated with BMI among boys and girls in Portugal but not in Denmark and Sweden. Additionally, boys had higher body appreciation than girls. Results indicated that the BAS-2 has good psychometric properties in the three languages

Ignoring Clustering in Confirmatory Factor Analysis: Some Consequences for Model Fit and Standardized Parameter Estimates

In many situations, researchers collect multilevel (clustered or nested) data yet analyze the data either ignoring the clustering (disaggregation) or averaging the micro-level units within each cluster and analyzing the aggregated data at the macro level (aggregation). In this study we investigate the effects of ignoring the nested nature of data in confirmatory factor analysis (CFA). The bias incurred by ignoring clustering is examined in terms of model fit and standardized parameter estimates, which are usually of interest to researchers who use CFA. We find that the disaggregation approach increases model misfit, especially when the intraclass correlation (ICC) is high, whereas the aggregation approach results in accurate detection of model misfit in the macro level. Standardized parameter estimates from the disaggregation and aggregation approaches are deviated toward the values of the macro-and micro-level standardized parameter estimates, respectively. The degree of deviation depends on ICC and cluster size, particularly for the aggregation method. The standard errors of standardized parameter estimates from the disaggregation approach depend on the macro-level item communalities. Those from the aggregation approach underestimate the standard errors in multilevel CFA (MCFA), especially when ICC is low. Thus, we conclude that MCFA or an alternative approach should be used if possible

The Devil is Mainly in the Nuisance Parameters: Performance of Structural Fit Indices Under Misspecified Structural Models in SEM

To provide researchers with a means of assessing the fit of the structural component of structural equation models, structural fit indices- modifications of the composite fit indices, RMSEA, SRMR, and CFI- have recently been developed. We investigated the performance of four of these structural fit indices- RMSEA-P, RMSEA_S, SRMR_S, and CFI_S-, when paired with widely accepted cutoff values, in the service of detecting structural misspecification. In particular, by way of simulation study, for each of seven fit indices- 3 composite and 4 structural-, and the traditional chi-square test of perfect composite fit, we estimated the following rates: a) Type I error rate (i.e., the probability of (incorrect) rejection of a correctly specified structural component), under each of four degrees of misspecification in the measurement component; and b) Power (i.e., the probability of (correct) rejection of an incorrectly specified structural model), under each condition formed of the pairing of one of three degrees of structural misspecification with one of four degrees of measurement component misspecification. In addition to sample size, the impacts of two model features, incidental to model misspecification- number of manifest variables per latent variable and magnitude of factor loading- were investigated. The results suggested that, although the structural fit indices performed relatively better than the composite fit indices, none of the goodness-of-fit index with a fixed cutoff value pairings was capable of delivering an entirely satisfactory Type I error rate/Power balance, [RMSEA_S,.05] failing entirely in this regard. Of the remaining pairings; a) RMSEA-P and CFI_S suffered from a severely inflated Type I error rate; b) despite the fact that they were designed to pick up on structural features of candidate models, all pairings- and especially, RMSEA-P and CFI_S- manifested sensitivities to model features, incidental to structural misspecification; and c) although, in the main, behaving in a sensible fashion, SRMR_S was only sensitive to structural misspecification when it occurred at a relatively high degree

Planned Missing Data Designs for Spline Growth Models in Salivary Cortisol Research

Salivary cortisol is often used as an index of physiological and psychological stress in exercise science and psychoneuroendocrine research. A primary concern when designing research studies examining cortisol stems from the high cost of analysis. Planned missing data designs involve intentionally omitting a random subset of observations from data collection, reducing both the cost of data collection and participant burden. These designs have the potential to result in more efficient, cost-effective analyses with minimal power loss. Using salivary cortisol data from a previous study (Hogue, Fry, Fry, & Pressman, 2013), this article examines statistical power and estimated costs of six different planned missing data designs using growth curve modeling. Results indicate that using a planned missing data design would have provided the same results at a lower cost relative to the traditional, complete data analysis of salivary cortisol

Probing Latent Interactions Estimated with a Residual Centering Approach

Understanding latent interactions is an important need for the structural equation modeler. Plotting and probing latent interactions, however, has not been well defined. We describe methods for plotting and probing two- and three-way latent interactions fit with a variety of approaches (LMS/QML, residual centering, double mean centering). The methods are demonstrated through a small simulation and examples based on existing data