scholarly journals How to Estimate Absolute-Error Components in Structural Equation Models of Generalizability Theory

Psych ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 113-133
Author(s):  
Terrence D. Jorgensen
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Generalizability Theory ◽  
Simulated Data ◽  
Absolute Error ◽  
Data Matrix ◽  
Equation Modeling ◽  
Error Components ◽  
Planned Missing Data ◽  
Mean Structure

Structural equation modeling (SEM) has been proposed to estimate generalizability theory (GT) variance components, primarily focusing on estimating relative error to calculate generalizability coefficients. Proposals for estimating absolute-error components have given the impression that a separate SEM must be fitted to a transposed data matrix. This paper uses real and simulated data to demonstrate how a single SEM can be specified to estimate absolute error (and thus dependability) by placing appropriate constraints on the mean structure, as well as thresholds (when used for ordinal measures). Using the R packages lavaan and gtheory, different estimators are compared for normal and discrete measurements. Limitations of SEM for GT are demonstrated using multirater data from a planned missing-data design, and an important remaining area for future development is discussed.

scholarly journals Causality on longitudinal data: Stable specification search in constrained structural equation modeling

2017 ◽  
Vol 27 (12) ◽  
pp. 3814-3834 ◽  
Author(s):  
Ridho Rahmadi ◽  
Perry Groot ◽  
Marieke HC van Rijn ◽  
Jan AJG van den Brand ◽  
Marianne Heins ◽  
...  
Keyword(s):  
Longitudinal Data ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Simulated Data ◽  
Chronic Fatigue ◽  
Causal Modeling ◽  
Model Complexity ◽  
Equation Modeling ◽  
Data Set ◽  
Finite Data

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting, we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

scholarly journals Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code

Psych ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 197-232
Author(s):  
Yves Rosseel
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Missing At Random ◽  
Equation Modeling ◽  
Computationally Efficient ◽  
Log Likelihood ◽  
Efficient Expression ◽  
Special Case

This paper discusses maximum likelihood estimation for two-level structural equation models when data are missing at random at both levels. Building on existing literature, a computationally efficient expression is derived to evaluate the observed log-likelihood. Unlike previous work, the expression is valid for the special case where the model implied variance–covariance matrix at the between level is singular. Next, the log-likelihood function is translated to R code. A sequence of R scripts is presented, starting from a naive implementation and ending at the final implementation as found in the lavaan package. Along the way, various computational tips and tricks are given.

scholarly journals Examining the ParticipACTION brand using the brand equity pyramid

2018 ◽  
Vol 8 (4) ◽  
pp. 378-396 ◽  
Author(s):  
Alexander Lithopoulos ◽  
Peter A. Dacin ◽  
Tanya R. Berry ◽  
Guy Faulkner ◽  
Norm O’Reilly ◽  
...  
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Brand Equity ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Equation Modeling ◽  
Content Type ◽  
Activity Promotion ◽  
Confirmatory Factor

Purpose The brand equity pyramid is a theory that explains how people develop loyalty and an attachment to a brand. The purpose of this study is to test whether the predictions made by the theory hold when applied to the brand of ParticipACTION, a Canadian non-profit organization that promotes active living. A secondary objective was to test whether this theory predicted intentions to be more physically active. Design/methodology/approach A research agency conducted a cross-sectional, online brand health survey on behalf of ParticipACTION. Exploratory factor analysis and confirmatory factor analysis established the factor structure. Structural equation modeling was used to test the hypothesized model. Findings A nationally representative sample of Canadian adults (N = 1,191) completed the survey. Exploratory factor analysis and confirmatory factor analysis supported a hypothesized five-factor brand equity framework (i.e. brand identity, brand meaning, brand responses, brand resonance and intentions). A series of structural equation models also provided support for the hypothesized relationships between the variables. Practical implications Though preliminary, the results provide a guide for understanding the branding process in the activity-promotion context. The constructs identified as being influential in this process can be targeted by activity-promotion organizations to improve brand strength. A strong organizational brand could augment activity-promotion interventions. A strong brand may also help the organization better compete against other brands promoting messages that are antithetical to their own. Originality/value This is the first study to test the brand equity pyramid using an activity-promotion brand. Results demonstrate that the brand equity pyramid may be useful in this context.

scholarly journals Newborn Adiposity and Cord Blood C-Peptide as Mediators of the Maternal Metabolic Environment and Childhood Adiposity

2021 ◽  
Author(s):  
Jami L. Josefson ◽  
Denise M. Scholtens ◽  
Alan Kuang ◽  
Patrick M. Catalano ◽  
Lynn P. Lowe ◽  
...  
Keyword(s):  
Fat Mass ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Child Outcomes ◽  
Equation Modeling ◽  
P Value ◽  
C Peptide ◽  
Childhood Adiposity ◽  
Maternal Bmi ◽  
Maternal Glucose

<b>OBJECTIVE</b> <p>Excessive childhood adiposity is a risk factor for adverse metabolic health. The objective was to investigate associations of newborn body composition and cord C-peptide with childhood anthropometrics and explore whether these newborn measures mediate associations of maternal mid-pregnancy glucose and BMI with childhood adiposity.</p> <p><b>RESEARCH DESIGN AND METHODS</b></p> <p>Data on mother/offspring pairs (N=4832) from the epidemiological Hyperglycemia and Adverse Pregnancy Outcome (HAPO) Study and HAPO Follow Up Study (HAPO FUS) were analyzed. Linear regression was used to study associations between newborn and childhood anthropometrics. Structural equation modeling was used to explore newborn anthropometric measures as potential mediators of the associations of maternal BMI and glucose during pregnancy with childhood anthropometric outcomes. </p> <p><b>RESULTS</b></p> <p>In models including maternal glucose and BMI adjustments, newborn adiposity as measured by sum of skinfolds was associated with child outcomes (adjusted mean difference, 95% CI, p-value) BMI(0.26,0.12-0.39,<0.001), BMI z-score(0.072,0.033-0.11,<0.001), fat mass (kg)(0.51,0.26-0.76,<0.001), percent bodyfat(0.61, 0.27-0.95,<0.001), and sum of skinfolds (mm)(1.14,0.43-1.86,0.0017). Structural equation models demonstrated significant mediation by newborn sum of skinfolds and cord C-peptide of maternal BMI effects on childhood BMI(proportion of total effect 2.5% and 1%, respectively), fat mass(3.1%,1.2%), percent bodyfat(3.6%,1.8%), and sum of skinfolds (2.9%,1.8%), and significant mediation by newborn sum of skinfolds and cord C-peptide of maternal glucose effects on child fat mass (proportion of total association 22.0% and 21.0%, respectively), percent bodyfat (15.0%,18.0%), and sum of skinfolds (15.0%,20.0%).</p> <p><b>CONCLUSIONS</b></p> <p>Newborn adiposity is independently associated with childhood adiposity and, along with fetal hyperinsulinemia, mediates, in part, associations of maternal glucose and BMI with childhood adiposity. </p>

scholarly journals Improving generalizability coefficient estimate accuracy: A way to incorporate auxiliary information

2018 ◽  
Vol 11 (2) ◽  
pp. 205979911879139 ◽  
Author(s):  
Zhehan Jiang ◽  
Kevin Walker ◽  
Dexin Shi ◽  
Jian Cao
Keyword(s):  
Structural Equation Modeling ◽  
Structural Equation ◽  
Generalizability Theory ◽  
Theory Model ◽  
Bias Reduction ◽  
Equation Modeling ◽  
Coefficient Estimate ◽  
Auxiliary Variables ◽  
Modeling Approach ◽  
Generalizability Coefficient

Initially proposed by Marcoulides and further expanded by Raykov and Marcoulides, a structural equation modeling approach can be used in generalizability theory estimation. This article examines the utility of incorporating auxiliary variables into the structural equation modeling approach when missing data is present. In particular, the authors assert that by adapting a saturated correlates model strategy to structural equation modeling generalizability theory models, one can reduce any biased effects caused by missingness. Traditional approaches such as an analysis of variance do not possess such a feature. This article provides detailed instructions for adding auxiliary variables into a structural equation modeling generalizability theory model, demonstrates the corresponding benefits of bias reduction in generalizability coefficient estimate via simulations, and discusses issues relevant to the proposed approach.

scholarly journals Analytical power calculations for structural equation modeling: A tutorial and Shiny app

2020 ◽  
Author(s):  
Suzanne Jak ◽  
Terrence D. Jorgensen ◽  
Mathilde G. E. Verdam ◽  
Frans J. Oort ◽  
Louise Elffers
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Statistical Significance ◽  
Equation Modeling ◽  
Ratio Test ◽  
Power Calculations ◽  
Shiny App ◽  
Computationally Intensive

Abstract Conducting a power analysis can be challenging for researchers who plan to analyze their data using structural equation models (SEMs), particularly when Monte Carlo methods are used to obtain power. In this tutorial, we explain how power calculations without Monte Carlo methods for the χ2 test and the RMSEA tests of (not-)close fit can be conducted using the Shiny app “power4SEM”. power4SEM facilitates power calculations for SEM using two methods that are not computationally intensive and that focus on model fit instead of the statistical significance of (functions of) parameters. These are the method proposed by Satorra and Saris (Psychometrika 50(1), 83–90, 1985) for power calculations of the likelihood ratio test, and that described by MacCallum, Browne, and Sugawara (Psychol Methods 1(2) 130–149, 1996) for RMSEA-based power calculations. We illustrate the use of power4SEM with examples of power analyses for path models, factor models, and a latent growth model.

scholarly journals The Impact of Intraclass Correlation on the Effectiveness of Level-Specific Fit Indices in Multilevel Structural Equation Modeling

2016 ◽  
Vol 77 (1) ◽  
pp. 5-31 ◽  
Author(s):  
Hsien-Yuan Hsu ◽  
Jr-Hung Lin ◽  
Oi-Man Kwok ◽  
Sandra Acosta ◽  
Victor Willson
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Intraclass Correlation ◽  
Monte Carlo Study ◽  
Multilevel Structural Equation Modeling ◽  
Equation Modeling ◽  
Saturated Model ◽  
Fit Indices ◽  
The Impact ◽  
Multilevel Structural Equation

Several researchers have recommended that level-specific fit indices should be applied to detect the lack of model fit at any level in multilevel structural equation models. Although we concur with their view, we note that these studies did not sufficiently consider the impact of intraclass correlation (ICC) on the performance of level-specific fit indices. Our study proposed to fill this gap in the methodological literature. A Monte Carlo study was conducted to investigate the performance of (a) level-specific fit indices derived by a partially saturated model method (e.g., [Formula: see text] and [Formula: see text]) and (b) [Formula: see text] and [Formula: see text] in terms of their performance in multilevel structural equation models across varying ICCs. The design factors included intraclass correlation (ICC: ICC1 = 0.091 to ICC6 = 0.500), numbers of groups in between-level models (NG: 50, 100, 200, and 1,000), group size (GS: 30, 50, and 100), and type of misspecification (no misspecification, between-level misspecification, and within-level misspecification). Our simulation findings raise a concern regarding the performance of between-level-specific partial saturated fit indices in low ICC conditions: the performances of both [Formula: see text] and [Formula: see text] were more influenced by ICC compared with [Formula: see text] and SRMRB. However, when traditional cutoff values ( RMSEA≤ 0.06; CFI, TLI≥ 0.95; SRMR≤ 0.08) were applied, [Formula: see text] and [Formula: see text] were still able to detect misspecified between-level models even when ICC was as low as 0.091 (ICC1). On the other hand, both [Formula: see text] and [Formula: see text] were not recommended under low ICC conditions.

scholarly journals A 'Weight of Evidence' approach to evaluating structural equation models

One Ecosystem ◽  
2020 ◽  
Vol 5 ◽  
Author(s):  
James Grace
Keyword(s):  
Structural Equation Modeling ◽  
Model Selection ◽  
Model Evaluation ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Weight Of Evidence ◽  
Equation Modeling ◽  
Future Studies ◽  
Current State ◽  
History Of

It is possible that model selection has been the most researched and most discussed topic in the history of both statistics and structural equation modeling (SEM). The reason for this is because selecting one model for interpretive use from amongst many possible models is both essential and difficult. The published protocols and advice for model evaluation and selection in SEM studies are complex and difficult to integrate with current approaches used in biology. Opposition to the use of p-values and decision thresholds has been voiced by the statistics community, yet certain phases of model evaluation have been historically tied to reliance on p-values. In this paper, I outline an approach to model evaluation, comparison and selection based on a weight-of-evidence paradigm. The details and proposed sequence of steps are illustrated using a real-world example. At the end of the paper, I briefly discuss the current state of knowledge and a possible direction for future studies.

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