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.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
Author(s):  
Stefan C. Schmukle ◽  
Jochen Hardt
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Null Model ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Fit Indices ◽  
Cautionary Note ◽  
Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

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 The Antecedents of Tourists’ Behavioral Intentions at Sporting Events: The Case of South Korea

2019 ◽  
Vol 12 (1) ◽  
pp. 333 ◽  
Author(s):  
Yunduk Jeong ◽  
Andrew Yu ◽  
Suk-Kyu Kim
Keyword(s):  
South Korea ◽  
Place Attachment ◽  
Behavioral Intentions ◽  
Structural Equation ◽  
Likelihood Estimation ◽  
Destination Image ◽  
Equation Modeling ◽  
Sporting Events ◽  
Personal Involvement ◽  
Sports Tourism

Mega-sporting events can bring diverse benefits to the hosting areas, such as job creation and image improvement. However, only a handful of studies have explored the antecedents of destination image—which plays a crucial role in eliciting certain tourist behaviors—and personal involvement. To fill this gap, this study evaluates the relationships among personal involvement, destination image, place attachment, and behavioral intentions in the context of sporting event tourism to provide destination managers useful information for sustainable sports tourism development. We gathered information from 374 international tourists at the FINA (Fédération Internationale de Natation—International Swimming Federation) World Masters Championships Gwangju 2019 in South Korea. We used structural equation modeling was used along with maximum likelihood estimation to examine the predicted relationships. The findings show the positive impacts of (a) personal involvement on destination image, (b) destination image on place attachment, and (c) place attachment on behavioral intentions. Furthermore, (d) place attachment dictated the relationship between destination image and behavioral intentions. The findings confirm the significant role personal involvement plays in the improvement of a destination’s image. To ensure sustainable sports tourism, destination managers are advised to pay close attention to research findings on destination image in the development of their plans.

Service quality and complaint management influence fan satisfaction and team identification

2019 ◽  
Vol 47 (2) ◽  
pp. 1-15
Author(s):  
Cindy Lee ◽  
Youngjin Hur
Keyword(s):  
Structural Equation ◽  
Online Survey ◽  
Likelihood Estimation ◽  
Equation Modeling ◽  
Team Identification ◽  
Quality Performance ◽  
Complaint Management ◽  
Interaction Quality ◽  
Performance Quality ◽  
Baseball Team

We explored the influence of facility quality, performance quality, interaction quality, and complaint management on fan satisfaction and team identification. Participants were 283 fans of a Class A minor league baseball team, who completed an online survey on the team’s official social media website. We tested the efficacy of the proposed model using the structural equation modeling bootstrap procedure with maximum likelihood estimation. The results confirmed that complaint management positively influenced interaction quality, and that facility quality, performance quality, and interaction quality positively affected fan satisfaction and team identification. Our findings highlight the importance of complaint management, indicating that organizations need a good complaints management system and employees who are well trained in handling these complaints.

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.

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