9. Structural Equation Modeling with Robust Covariances

In the social and behavioural sciences, structural equation modelling has been widely used to test a substantive theory or causal relationship among latent constructs. Cross-validation (CV) is a valuable tool for selecting the best model among competing structural models. Influential cases or outliers are often present in practical data. Therefore, even the correct model for the majority of the data may not cross-validate well. This paper discusses various drawbacks of CV based on sample covariance matrices, and develops a procedure for using robust covariance matrices in the model calibration and validation stages. Examples illustrate that the CV index based on sample covariance matrices is very sensitive to influential cases, and even a single outlier can cause the CV index to support a wrong model. The CV index based on robust covariance matrices is much less sensitive to influential cases and thus leads to a more valid conclusion about the practical value of a model structure.

Objective: The objective of the present study was to develop a structural model for predicting the organizational performance of bank employees in the western Tehran branches based on career path resilience and psychological capital, with the mediating role of professional ethics. Methodology: The research method was descriptive-correlational, with a structural equation modeling approach. The statistical population consisted of all bank employees in the western Tehran branches in 2023. The sampling method was convenience sampling. The sample size was 430 individuals, who were evaluated using questionnaires on organizational performance (Andre de Waal et al., 2017), career path resilience (Morgen Lyon, 2001), psychological capital (Luthans, 2007), and professional ethics (Kadous, 2002). The findings were analyzed using structural equation modeling. Findings: Based on the analysis of the research findings, all fit indices derived from the analysis supported the acceptable fit of the structural model with the collected data. The chi-square to degrees of freedom ratio was 2.21, the Comparative Fit Index (CFI) was 0.959, the Goodness of Fit Index (GFI) was 0.938, the Adjusted Goodness of Fit Index (AGFI) was 0.913, and the Root Mean Square Error of Approximation (RMSEA) was 0.057. Additionally, the results showed that career path resilience, psychological capital, and professional ethics together explained 62% of the variance in organizational performance among bank employees. Conclusion: It can be concluded that professional ethics among bank employees mediates the relationship between psychological capital and career path resilience with organizational performance.

A full structural equation model (SEM) typically consists of both a measurement model (describing relationships between latent variables and observed scale items) and a structural model (describing relationships among latent variables). However, often researchers are primarily interested in testing hypotheses related to the structural model while treating the measurement model as a necessary but not primary focus of the overall model. In this case, researchers often wish to isolate and just evaluate the fit of the structural model. In our research, we examine a two-stage approach that can compute the chi-square statistic and fit indices for evaluating only the fit of the structural model in a full SEM. We call these the structural chi-square statistic and structural fit indices. For structural fit indices, we focused on the root mean square error of approximation (RMSEA), comparative fit index (CFI), and standardized root mean square residual (SRMR). We developed several new versions of the structural chi-square statistic, structural fit indices, and confidence intervals (CIs) of the structural fit indices. Through a simulation study, we demonstrated that several versions of our newly developed structural chi-square statistic yielded the nominal Type-I error rate; and the same versions of the structural fit indices exhibited low bias and their corresponding CIs had high coverage rates. Therefore, we recommend researchers use these versions of the structural chi-square test of fit alongside the structural fit indices when evaluating the fit of the structural model.

The current generation of structural equation modeling (SEM) is loosely split in two divergent groups - covariance-based and variance-based structural equation modeling. The relative newness of variance-based SEM has limited the development of techniques that extend its applicability to non-metric data. This study focuses upon the extension of general linear model techniques within the variance-based platform of partial least squares structural equation modeling (PLS-SEM). This modeling procedure receives it name through the iterative PLS‑SEM algorithm's estimates of the coefficients for the partial ordinary least squares regression models in both the measurement model and the overall structural model. This research addresses the following research questions: (1) What are the appropriate measures for data segmentation within PLS‑SEM? (2) What are the appropriate steps for the analysis of rank-ordered path coefficients within PLS‑SEM? and (3) What is an appropriate model selection index for PLS‑SEM? The limited type of data to which PLS-SEM is applicable suggests an opportunity to extend the method for use with different data and as a result a broader number of applications. This study develops and tests several methodologies that are prevalent in the general linear model (GLM). The proposed data segmentation approaches posited and tested through post hoc analysis of structural model. Monte Carlo simulation allows demonstrating the improvement of the proposed model fit indices in comparison to the established indices found within the SEM literature. These posited PLS methods, that are logical transfers of GLM methods, are tested using examples. These tests enable demonstrating the methods and recommending reporting requirements.

The present study seeks to find the mutual effect of supply chain management (SCM) and customer relationship management (CRM) in a commercial company on the level of marketing and sales. In order to answer the research questions and also to achieve the research objectives, after reviewing the research literature and finding different dimensions of SCM and CRM variables, the research design and method were determined. After operational definitions and creating a questionnaire to measure the dimensions of the aforementioned variables, 220 employees from different agricultural product manufacturing companies were selected and a questionnaire was presented to them in the period of 2023-2024. Using structural equation modeling (LISREL), various structural models were implemented until the best structural model was selected from among the implemented models. After implementing the model, the final research model that had better fit indices than other models was selected. The results obtained show that all the described variables and the relationships between them are direct, and by strengthening and optimizing each of them, the other variable is mutually improved. By increasing the level of trust in SCM, customer retention and care are improved, and also, conversely, improving customer care leads to increased trust in SCM and marketing. Hence, the different dimensions of CRM and SCM synergistically influence and reinforce each other. Also, a positive and significant link of CRM, SCM, and marketing (P > 0.05) was found in our study.

PurposeThe purpose of this paper is to describe and discuss a few principal and crucial steps of “antecedents” and “postcedents” in relation to structural equation modeling (SEM) in social science research.Design/methodology/approachThis paper is based upon a conceptual and reflective discussion of SEM in social sciences research.FindingsSEM is not science per se, but just a tool that is used to extract meaning from the previous steps of research processes in terms of a research phenomenon in focus.Research limitations/implicationsBased upon the steps of validity and reliability discussed in relation to predetermined measurement and structural models in SEM, application implications are provided.Practical implicationsLike many statistical tools, SEM can be misused to manipulate findings and fit of measurement and structural models. Researchers may become more interested in the tool than in the subject matter.Originality/valueUsing SEM does not elevate research to be science or make the researcher a scientist! An area of concern for further debate is whether the widespread and variable applications of SEM in social science (in particular, marketing) research are all science.

Online education, which is centered on the use of the Internet and the World Wide Web, presents a new generation of educational tools. Its ‘anywhere, any time’ concept frees the student from the constraints of time and place. Because there are no barriers to information flow over the Internet, it holds promise for a ‘curriculum without walls’ where intellectual richness is available to all. To take advantage of the huge number of potential students worldwide, many universities and commercial education providers have moved rapidly to introduce online tertiary programs to get a share of this market. Online programs are now commonplace in many learning institutions. However, Internet-based education has not attracted as many students as had been expected. Specifically, online tertiary education has not attracted as many students as had been expected in Singapore (Gagnon, 2002; Tan & Lambe, 2002; Wong, Gerber, & Toh, 2003); Brunei (Leong, 2006); and Malaysia (Alhabshi, 2002). There is still a lack of confiden...

Structural equation modeling (SEM) consists of two parts, the measurement model and the structural model. In this paper, we develop a SEM model that the measurement model is linear and the structural model is nonlinear. Structural model explain about relationship between latent variables. Truncated spline is used for modeling the nonlinear relationship between the latent variables. Trought weighted least squares (WLS) method, It is found that estimation of parameter truncated spline in nonlinear SEM for two exogen and an endogen latent variables is resulted by optimizingminγ{‖Σ−12(ωη−Γξκγ)‖2}and it gave an estimatorγ^=(Γ′ξkΣ−1Γξk)−1Γ′ξkΣ−1ωηThe estimator influenced by the location and some knot points κ1 and κ2.

Structural Equation Model (SEM) is a statistical technique with simultaneous processing involves measurement errors, indicator variables, and latent variables. SEM is used to test hypotheses that state the relationships between latent variables when latent variables have been assessed through each of the indicator variables. Multiple Group SEM is a basic model analysis that uses more than one sample. This analysis aims to determine whether the components or models of measurement and structural models are invariant for the two sample groups. In this study, the data generated by some requirements. First, the data generated with sample size n = 250. The first generated data is homogeneous data where the measurement model is the same as the structural model in group 1 and group 2, while the second data is non-homogeneous data where the measurement model and the structural model in group 1 and group 2 is not the same. The data was analyzed using the help of the lavaan package available in R to obtain SEM estimation results and Goodness of Fit Model from some data that was formed. From the results of the merger of the two groups, it shows that the invariant of the two models with the largest df (63) which is Fit Mean model states the simplest model. However, the smallest df (48) with Fit.configural model states the most complex model.
 Keywords: SEM, Multiple Group, R Program

Using structural equation modeling and intima-media complex texture features to assess cardiovascular disease risk in the common carotid artery

BackgroundHealthy lifestyle habits formed during young adulthood may have a sustaining impact on health across later life. The current study aimed to test the theoretical model of factors (selected demographic variables, knowledge of heart disease, health belief related to cardiovascular disease (CVD), self-efficacy, cues to action, and screening intention) influencing health-promoting behaviours among Malaysian university students.MethodsIn a cross-sectional survey, the undergraduate students in Universiti Sains Malaysia were invited to complete the self-administered questionnaires. Participants were selected using a purposive sampling method. The proposed hypothesised model was analysed using a structural equation modelling with Mplus 7.3 program. A total of 788 (70.7% female) undergraduate students with a mean age of 20.2 (SD = 1.02) participated in the study. The primary outcome of knowledge, health beliefs, and health-promoting behaviours related to CVD were measured by questionnaires namely: Knowledge of Heart Disease, Health Beliefs Related to CVD, and Health Promoting Lifestyle Profiles-II.ResultsThe final hypothetical structural model showed a good fit to the data based on several fit indices: with comparative fit index (CFI) at .921, standardised root mean square residual (SRMR) at .037, and root mean square error of approximation (RMSEA) at .044 (90% CI: .032, .054). The final structural model supported 13 significant path estimates. These variables explained 12% of the total variance in health-promoting behaviours. Through perceived benefits, total knowledge had an indirect effect on health-promoting behaviours.ConclusionThe results suggest that perceived barriers, perceived benefits, family history of CVD, and screening intention enable young adults to engage in health-promoting behaviours.

This study aims to design and empirically test a structural model explaining managerial competencies through a sustainable human resource management approach in public organizations. This applied, descriptive–correlational research adopted a mixed-methods design. In the qualitative phase, 15 academic experts and senior public managers from Ardabil Province participated in developing the conceptual model using Strauss and Corbin’s paradigm model. In the quantitative phase, data were collected from 384 public-sector managers selected via simple random sampling using a researcher-developed questionnaire. Structural equation modeling (SEM) was conducted in AMOS, and convergent validity, Cronbach’s alpha, and composite reliability were confirmed. The results indicated significant positive effects of causal conditions on the core phenomenon, the core phenomenon on strategies, and strategies on outcomes (p<0.001). Contextual and intervening conditions also significantly influenced competency-based strategies. Overall fit indices (CFI, TLI, RMSEA) demonstrated an acceptable to strong model fit. The proposed model provides a valid and integrated framework for developing managerial competencies grounded in sustainable HRM and offers practical implications for enhancing employee and organizational performance sustainability in public organizations.

to validate a model of the reduced version of the Brazilian Scale of Moral Distress in Nurses. methodological study, with a sample of 269 nurses from a public university hospital in southern Brazil. A sociodemographic questionnaire and the Brazilian Moral Distress Scale for Nurses were used. Descriptive statistics, structural equation modeling, and invariance analysis between age groups were used. regarding profile, professionals aged between 31 and 40, women, married, and specialists prevailed. The structural model fitted the data with acceptable fit indices. The proposed model showed excellent internal consistency, convergent validity, and discriminant validity. The analysis of the structural model revealed that the five hypotheses were confirmed, and the invariance between the age groups indicates that the way the variables are conceptualized, measured, and interrelated in the model does not affect the results, regardless of the groups compared. the scale achieved satisfactory psychometric indicators, proving to be suitable for use, maintaining the relevant validation elements per dimension, and offering practical advantages. Further research is suggested to deepen our understanding of the consequences of moral distress and to develop effective strategies for managing it. (1)The reduced version of the EDME-BR consisted of 24 questions and six factors. (2)Analysis of invariance and structural equation modeling were used for validation. (3)Internal consistency and composite reliability values were adequate. (4)The tests indicated sufficient predictive relevance of the proposed model. (5)The reduced scale offers a clear, accessible approach with a shorter response time.

Robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is properly weighted according to its distance, based on first and second order moments, from the structural model. A simple weighting function is adopted because of its flexibility with changing dimensions. The weight matrix is obtained from an adaptive way of using residuals. Test statistic and standard error estimators are given, based on iteratively reweighted least squares. The method reduces to a standard distribution-free methodology if all cases are equally weighted. Examples demonstrate the value of the robust procedure.

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, RMSEAs, SRMRs, and CFIs-, 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, [RMSEAs, .05] failing entirely in this regard. Of the remaining pairings; a) RMSEA-P and CFIs 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 CFIs-manifested sensitivities to model features, incidental to structural misspecification; and c) although, in the main, behaving in a sensible fashion, SRMRs was only sensitive to structural misspecification when it occurred at a relatively high degree.