Robust Structural Equation Modeling with Missing Data and Auxiliary Variables

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a familiar function while being only marginally less efficient than the full information ML (FIML) approach. Additional advantages of the TS approach include that it allows for easy incorporation of auxiliary variables and that it is more stable in smaller samples. The main disadvantage is that the standard errors and test statistics provided by the complete data routine will not be correct. Empirical approaches to finding the right corrections for the TS approach have failed to provide unequivocal solutions. In this article, correct standard errors and test statistics for the TS approach with missing completely at random and missing at random normally distributed data are developed and studied. The new TS approach performs well in all conditions, is only marginally less efficient than the FIML approach (and is sometimes more efficient), and has good coverage. Additionally, the residual-based TS statistic outperforms the FIML test statistic in smaller samples. The TS method is thus a viable alternative to FIML, especially in small samples, and its further study is encouraged.

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the combined correlations, called meta-analytical SEM (MASEM), is a powerful tool for examining the relationship among latent constructs as well as those between the latent constructs and the manifest variables. Three classes of methods have been proposed for MASEM: (1) generalized least squares (GLS) in combining correlations and in estimating the structural model, (2) normal-distribution-based maximum likelihood (ML) in combining the correlations and then GLS in estimating the structural model (ML-GLS), and (3) ML in combining correlations and in estimating the structural model (ML). The current article shows that these three methods are equivalent. In particular, (a) the GLS method for combining correlation matrices in meta-analysis is asymptotically equivalent to ML, (b) the three methods (GLS, ML-GLS, ML) for MASEM with correlation matrices are asymptotically equivalent, (c) they also perform equally well empirically, and (d) the GLS method for SEM with the sample correlation matrix in a single study is asymptotically equivalent to ML, which has being discussed extensively in the SEM literature regarding whether the analysis of a correlation matrix yields consistent standard errors and asymptotically valid test statistics. The results and analysis suggest that a sample-size weighted GLS method is preferred for combining correlations and for MASEM.

Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.

Existing methods for structural equation modeling involve fitting the ordinary sample covariance matrix by a proposed structural model. Since a sample covariance is easily influenced by a few outlying cases, the standard practice of modeling sample covariances can lead to inefficient estimates as well as inflated fit indices. By giving a proper weight to each individual case, a robust covariance will have a bounded influence function as well as a nonzero breakdown point. These robust properties of the covariance estimators will be carried over to the parameter estimators in the structural model if a technically appropriate procedure is used. We study such a procedure in which robust covariances replace ordinary sample covariances in the context of the Wishart likelihood function. This procedure is easy to implement in practice. Statistical properties of this procedure are investigated. A fit index is given based on sampling from an elliptical distribution. An estimating equation approach is used to develop a variety of robust covariances, and consistent covariances of these robust estimators, needed for standard errors and test statistics, follow from this approach. Examples illustrate the inflated statistics and distorted parameter estimates obtained by using sample covariances when compared with those obtained by using robust covariances. The merits of each method and its relevance to specific types of data are discussed.

While much literature has examined the independent effect of perceived neighbourhood disorder on criminal behaviour and/or mental disorder, comparatively little is known about the role of depressive symptoms on these associations over time. Our aim was to examine whether depressive symptoms mediate association between perceived neighbourhood disorder, future criminal justice contact, and future suicidal ideation. We grounded this research in primary arguments derived from General Strain Theory (GST). Data were drawn from structured self-reports in surveys of over 2000 young adult participants from the Children of the National Longitudinal Survey of Youth, who are the offspring born to the women from the National Longitudinal Survey of Youth 1979. Information on neighbourhood disorder and depressive symptoms were used from the 2012 data collection period, while information on criminal justice contact and suicidal ideation were drawn from the 2014 period. Structural equation modelling was used to examine both direct and indirect pathways between neighbourhood disorder, depression, contact with the justice system, and suicidal ideation from 2012 to 2014. Depressive symptoms were found to partially mediate the effect of perceived neighbourhood disorder on future criminal justice contact, with the strength of this effect varying across categories of race/ethnicity. The association between perceived neighbourhood disorder and suicidal ideation was fully mediated by depressive symptoms. Our findings are consistent with an ecological stress framework integrated with arguments from GST to understand the associations between neighbourhood disorder, criminal justice contact, and severe mental illness. Future research is needed on gender and racial/ethnic pathways. The reported findings suggest that, in addition to neighbourhood improvements, ready access to mental health services could not only reduce the risk of suicide but support safer communities.

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.

Even though data sets in psychology are seldom normal, the statistics used to evaluate covariance structure models are typically based on the assumption of multivariate normality. Consequently, many conclusions based on normal theory methods are suspect. In this paper, we develop test statistics that can be correctly applied to the normal theory maximum likelihood estimator. We propose three new asymptotically distribution-free (ADF) test statistics that technically must yield improved behaviour in samples of realistic size, and use Monte Carlo methods to study their actual finite sample behaviour. Results indicate that there exists an ADF test statistic that also performs quite well in finite sample situations. Our analysis shows that various forms of ADF test statistics are sensitive to model degrees of freedom rather than to model complexity. A new index is proposed for evaluating whether a rescaled statistic will be robust. Recommendations are given regarding the application of each test statistic.

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.

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

Self-determination theory has proven to be a useful theoretical explanation of the occurrence of ill-being on a variety of accounts. Self-determination theory may also provide a useful explanation of the occurrence of athlete burnout. To date, limited evidence exists to support links between motivation and burnout. To examine relationships and potential causal directions among burnout and types of motivation differing in degree of self-determination. Data were collected on burnout using the Athlete Burnout Questionnaire and Sport Motivation Scale from 392 top amateur male rugby players. Structural equation modeling procedures were employed to evaluate a measurement model and three conceptually grounded structural models. One conceptual model specified concomitant (noncausal) relationships between burnout and motivations varying in self-determination. The other conceptual models specified causal pathways between burnout and the three motivation variables considered in the investigation (i.e., intrinsic motivation, external regulation, and amotivation). Within the models, amotivation, the least self-determined type of motivation, had a large positive association with burnout. Externally regulated motivation had trivial and nonsignificant relationships with burnout. Self-determined forms of motivation (i.e., intrinsic motivation) exhibited significant negative associations with burnout. Overall the results support the potential utility of a self-determination theory explanation of burnout. As all models displayed reasonable and comparable fits, further research is required to establish the nature (concomitant vs directional causal vs reciprocal causal) of the relationship between burnout and motivation.

Background and AimsThe simultaneous role of self‐care and self‐efficacy in improving the quality of life (QoL) of diabetic patients has been less considered in previous studies. This study was aimed to investigate the path association between self‐care and self‐efficacy with QoL using the structural equation model (SEM).MethodsThis cross‐sectional study was conducted with 496 individuals of type 2 diabetic patients aged 35–75 years that were selected consequently from outpatients' clinic, in Babol, the north of Iran. The data collection instruments were demographic, self‐care, self‐efficacy, and QoL scales. The conceptual hypothesized model was designed based on previous evidence and tested by confirmatory factor analysis using SEM and path coefficients were estimated by the maximum likelihood method.ResultsSelf‐care had a significant relationship with employment status, level of education, and body mass index. QoL was significantly associated with economic status and place of residence. Self‐efficacy beliefs had a positive and a direct effect on both self‐care and QoL. But self‐care and self‐efficacy tended to have a nonsignificant positive relationship with QoL. The postulated conceptual path model was acceptable through the SEM goodness of fit criteria.ConclusionThe findings show the fitness of the framework hypothesized structural model in the QoL of diabetic patients and this SEM makes this study unique from others. The results showed that the role of self‐efficacy and self‐care could be considered on the QoL. Therefore, nonpharmacological and supportive methods, such as strengthening self‐efficacy and self‐care, could be recommended as an effective method to enhance the QoL of diabetic patients.

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.

Objective To analyze correlations between personality traits, life events and depressive symptoms based on structural equation model and to identify risky factors of depressive symptoms. Methods Using stratified random cluster sampling method, industrial workers recruited from Shougang Qianan corporation received questionnaire survey consisted of LES, NEO-FFI and CES-D.Maximum likelihood method was applied to calculate parameters of structural equation model, then the final model was confirmed based on modification indices. Results Depressive symptom(CES-D≥16) prevalence was 41.05% among industrial workers in current study.Neuroticism, extraversion, agreeableness and negative life events were significantly predictive to depressive symptoms(r=0.356, -0.304, -0.135, 0.227). Positive and negative life events, neuroticism and extraversion, extraversion and conscientiousness, neuroticism and agreeableness presented high correlation, with coefficients 0.614, -0.469, 0.432 and 0.402 respectively. The regression weight of affective symptoms, somatic symptoms and interpersonal relationship in measurement model were 0.779, 0.678, 0.464. Conclusion The onset of depressive symptoms among industrial workers is remarkably related to neuroticism, extraversion, agreeableness and negative life events. Certain measures are supposed to be conducted for mental nursing and intervention in order to strengthen depression prevention. Key words: Industrial workers; Depressive symptoms; Personality traits; Life events; Structural equation model

This study investigated the relationships among managerial leadership, transformational leadership, and performance of school administrators of Northern Iloilo Polytechnic State College (NIPSC) through Structural Equation Modeling (SEM). Covariance-Based SEM (CB-SEM), Confirmatory Factor Analysis (CFA) with its default Maximum Likelihood Estimation (MLE) were used to test the hypothesized model that managerial leadership covary transformational leadership which were both related to the school administrators’ performance. Results revealed that of the eight alternative models, two equivalent models, one model generates every probability distribution that can be generated by another model, Model B3 and Model D3 were generated, got the smallest Alkaike Information Criterion (AIC) and Bayes Information Criterion (BIC) indicating that both models had relatively better fit. Model B3 and Model D3 have the same degrees of freedom but feature a different configuration of paths among the same variables. However, of the two equivalent models, model B3 was rejected due to discriminant validity concerns while model D3 passed both measurement model and structural model, model D3 was confirmed and retained. As contribution to the fields of education, management and leadership, the researcher confirmed and recommends, through CB-SEM using CFA with its default MLE, the Managerial Leadership and Performance as fully mediated by Transformational Leadership Model.