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

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.

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Power analysis for parameter estimation in structural equation modeling: A discussion and tutorial

10.31234/osf.io/pj67b ◽

2020 ◽

Author(s):

Yilin Andre Wang ◽

Mijke Rhemtulla

Keyword(s):

Structural Equation Modeling ◽

Sample Size ◽

Latent Variables ◽

Power Analysis ◽

Structural Equation ◽

Structural Equation Models ◽

Regression Coefficient ◽

Equation Modeling ◽

Shiny App ◽

Target Effect

Despite the widespread and rising popularity of structural equation modeling (SEM) in psychology, there is still much confusion surrounding how to choose an appropriate sample size for SEM. Currently available guidance primarily consists of sample size rules of thumb that are not backed up by research, and power analyses for detecting model misfit. Missing from most current practices is power analysis to detect a target effect (e.g., a regression coefficient between latent variables). In this paper we (a) distinguish power to detect model misspecification from power to detect a target effect, (b) report the results of a simulation study on power to detect a target regression coefficient in a 3-predictor latent regression model, and (c) introduce a Shiny app, pwrSEM, for user-friendly power analysis for detecting target effects in structural equation models.

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Analyzing Observed Composite Differences Across Groups

Methodology ◽

10.1027/1614-2241/a000049 ◽

2013 ◽

Vol 9 (1) ◽

pp. 1-12 ◽

Cited By ~ 101

Author(s):

Holger Steinmetz

Keyword(s):

Monte Carlo ◽

Structural Equation Modeling ◽

Measurement Invariance ◽

Structural Equation ◽

Monte Carlo Study ◽

Equation Modeling ◽

Factor Loadings ◽

Latent Mean Differences ◽

Partial Invariance ◽

Mean Differences

Although the use of structural equation modeling has increased during the last decades, the typical procedure to investigate mean differences across groups is still to create an observed composite score from several indicators and to compare the composite’s mean across the groups. Whereas the structural equation modeling literature has emphasized that a comparison of latent means presupposes equal factor loadings and indicator intercepts for most of the indicators (i.e., partial invariance), it is still unknown if partial invariance is sufficient when relying on observed composites. This Monte-Carlo study investigated whether one or two unequal factor loadings and indicator intercepts in a composite can lead to wrong conclusions regarding latent mean differences. Results show that unequal indicator intercepts substantially affect the composite mean difference and the probability of a significant composite difference. In contrast, unequal factor loadings demonstrate only small effects. It is concluded that analyses of composite differences are only warranted in conditions of full measurement invariance, and the author recommends the analyses of latent mean differences with structural equation modeling instead.

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Supplemental Material for On the Likelihood Ratio Test in Structural Equation Modeling When Parameters Are Subject to Boundary Constraints

Psychological Methods ◽

10.1037/1082-989x.11.4.439.supp ◽

2006 ◽

Keyword(s):

Structural Equation Modeling ◽

Likelihood Ratio ◽

Likelihood Ratio Test ◽

Structural Equation ◽

Equation Modeling ◽

Ratio Test ◽

Boundary Constraints

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

Psych ◽

10.3390/psych3020017 ◽

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.

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Key Determinants of Airline Loyalty Modeling in Thailand

Sustainability ◽

10.3390/su12104165 ◽

2020 ◽

Vol 12 (10) ◽

pp. 4165 ◽

Cited By ~ 1

Author(s):

Dissakoon Chonsalasin ◽

Sajjakaj Jomnonkwao ◽

Vatanavongs Ratanavaraha

Keyword(s):

Airline Industry ◽

Structural Equation ◽

Statistical Significance ◽

Perceived Quality ◽

Equation Modeling ◽

Structural Factors ◽

Proposed Model ◽

Airline Passengers ◽

Domestic Airline

The airline industry in Thailand has grown enormously over the past decade. Competition among airline companies to reach market share and profit has been intense, requiring strong strategic abilities. To increase the service quality of such companies, identifying factors related to the context of airlines is important for policymakers. Thus, this study aims to present empirical data on structural factors related to the loyalty of domestic airline passengers. Structural equation modeling was used to confirm the proposed model. The questionnaire was used to survey and collect data from 1600 airline passengers. The results indicate that satisfaction, trust, perceived quality, relationship, and image of airlines positively influenced loyalty with a statistical significance of α = 0.05. Moreover, the study found that expectation and perceived quality indirectly influenced loyalty. The findings provide a reference for airline operators to clearly understand the factors that motivate passenger loyalty, which can be used to develop the sustainability of marketing strategies and support competitiveness.

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Examining the ParticipACTION brand using the brand equity pyramid

Journal of Social Marketing ◽

10.1108/jsocm-11-2017-0071 ◽

2018 ◽

Vol 8 (4) ◽

pp. 378-396 ◽

Cited By ~ 3

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.

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Structural Equation Modeling Applied to Socioeconomic Indicators in the Production of Sugarcane, in the State of Goiás

International Journal of Business Administration ◽

10.5430/ijba.v10n5p53 ◽

2019 ◽

Vol 10 (5) ◽

pp. 53

Author(s):

Jean Marc Nacife ◽

Frederico A. Loureiro Soares ◽

Marconi Batista Teixeira ◽

Leonardo Nazário S. dos Santos ◽

Gustavo Castoldi

Keyword(s):

Structural Equation Modeling ◽

Production System ◽

Structural Equation ◽

Statistical Significance ◽

Methodological Approach ◽

Production Costs ◽

Equation Modeling ◽

Structural Quality ◽

Sugarcane Production ◽

Path Diagram

Agribusiness has played a strategic role for Brazil's development with the challenge of sustainable agriculture. It is proposed to determine, through Structural Equation Modeling (SEM), the validity and effects of the relationships between socioeconomic factors of the sugarcane production system in Quirinópolis, providing subsidies to the decision-making process of agricultural establishments. The research methodological approach was quantitative, applying techniques of normality statistics, hypothesis and multivariate analysis without statistical significance (P <0,05). A path diagram model was developed that presented structural quality adjustment and its validated explanatory equations, obtaining relevant R2. The results demonstrate that the Equation 1 (IBCcane = 0.02Rcane - 0.75ICcane – 0.46ISVO + 0.35ISPS + error) is explained in 73.7% of its variance (R2), in the Equation 2 (ICcane = 0.59ISVO – 0.45ISPS + 0.35SizeEstablis + error) successor vocation affects 42% on production costs and in the Equation 3 (Rcane = -0.40 AgroDistance – 0.16ISPS + error) the distance between farm and agribusiness influences 72% on the proposed revenue mix. The SEM analysis verified that social factors influence the economic factors that compose the sugarcane production system studied. The path diagram proved that the influence track relative to the costs in the proposed model is more representative than revenue for the economic results of rural sugarcane establishments.

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Estimation of nonlinear structural equation models with dichotomous indicator variables: a Monte Carlo comparison of methods

International Journal of Quantitative Research in Education ◽

10.1504/ijqre.2020.106565 ◽

2020 ◽

Vol 5 (1) ◽

pp. 39

Author(s):

W. Holmes Finch

Keyword(s):

Monte Carlo ◽

Structural Equation ◽

Structural Equation Models ◽

Comparison Of Methods ◽

Nonlinear Structural ◽

Indicator Variables ◽

Nonlinear Structural Equation ◽

Dichotomous Indicator

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Efeito da gamificação na intenção de uso de treinamentos on-line: uma adaptação do modelo UTAUT aplicado no TRT-2

Revista de Administração da UFSM ◽

10.5902/1983465921624 ◽

2019 ◽

Vol 12 (3) ◽

pp. 472

Author(s):

Ludmilla Cavarzere de Oliveira ◽

Luis Hernan Contreras Pinochet ◽

Ricardo Luiz Pereira Bueno ◽

Mauri Aparecido de Oliveira

Keyword(s):

Structural Equation ◽

Statistical Significance ◽

Learning By Doing ◽

Equation Modeling ◽

Intention To Use ◽

Cross Sectional Survey ◽

Cross Sectional ◽

Regional Labor ◽

On Line ◽

Facilitating Conditions

The objective of this research was to analyze the effect of gamification on intention to use online training from the partial validation of the UTAUT model for qualification of members and servers of the Regional Labor Court of the 2nd Region (TRT-2). The study analyzed the relationship between constructs performance expectancy, effort expectancy, facilitating conditions, and familiarity with the intention to use gaming in distance media. This was conducted through an empirical application, which used the Structural Equation Modeling (SEM) for data analysis. The research was a single cross-sectional survey, carried out with TRT-2 members and servers who participated in the distance-feeding course ‘Healthy Living’ in 2015. Of the four hypotheses, only familiarity (F) was not significant as it did not serve as a behavioral intentions (BI) predictor of gamification for distance learning courses. Some explanations for such phenomenon may be career promotion and additional qualifications, learning by doing and sample size. The results confirmed that most hypotheses have a high statistical significance of the structural paths and have demonstrated that the model proposed in this study is consistent and can be applied in future studies with appropriate adjustments.

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

10.2337/figshare.13645727.v1 ◽

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

OBJECTIVE 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. RESEARCH DESIGN AND METHODS 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. RESULTS 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%). CONCLUSIONS 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.

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