Bayesian empirical likelihood estimation of quantile structural equation models

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Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.

The random errors in the measurement process, called measurement error or misclassification, are inevitable and cause bias and inconsistent parameter estimates. Misclassification Simulation Extrapolation (MC-SIMEX) is a simulation based measurement error estimation method to obtain reduced parameter bias under misclassification. The main purpose of this study is an adaptation of MC-SIMEX method on Structural Equation Modeling (SEM). The effects of misclassification on the parameter estimates of a binary explanatory variables in SEM and the performance of MC-SIMEX method investigated with both Monte Carlo and an empirical study. According to the main results, finding the best extrapolant function is just as important as estimating the misclassification matrix although MC-SIMEX corrected a part of the bias.

One of the major challenges for epidemiologists is to understand causal relationships between risk factors and health outcomes by analysing data from observational studies. Epidemiologists know too well that correlations, such as those in regression analysis, rarely mean causation, and it would be very desirable if there is a methodology for observational studies, analogous to randomization in experimental studies, which can discover causes and effects amongst variables or at least confirm or refute the proposed causal relationships. Randomized controlled trials (RCTs) are certainly the ‘gold standard’ of establishing causes and effects, but quite often it is either unethical or unfeasible to conduct RCTs to test causal relations in epidemiological research. Epidemiologists need a methodology, which is sort of a combination of the directed acyclic graphs (DAGs) for conceptual construction of causal models and regression analysis for testing those models. It is therefore surprising that structural equation modelling (SEM) has not been so frequently used in epidemiology as in the social sciences, given that both epidemiologists and social scientists want to delineate causes and effects from observational data. The difference between DAGs and path diagrams in SEM is almost trivial to epidemiologists: the path between two variables can only have one direction in DAGs. 1,2 An individual path in SEM is tested in the same way the regression coefficient is in regression analysis, and model fit indices provided by SEM software packages help the analysts to assess the adequacy of the proposed causal model compared with the observed associations in the sample data. 3,4 Why then is SEM still under-utilized in epidemiology? This is a question posed by a commentary 5 in this journal a few years ago. The answers cited included unfamiliar terminology (SEM theory is formulated in Greek), restriction in the assumptions of variables (outcome variables need to be continuous), difficulties in testing interaction and non-linear relationship (it can be quite tedious to set up SEM models to do these), and equivalent models (two different causal models imply the same correlation structure and consequently, it is impossible to tell which is better). 6 Recent advances in SEM theory and software development has resolved some of these issues: new estimation methods do not require the strict assumption of multivariate normality, 7 and the outcome variables can be binary, ordinal or counts. 7–9 The basic rationale behind SEM is rather simple: multiple linear equations are used to specify causal relationship between variables some of which are manifest variables (i.e. observed and collected by the researchers), whilst others are latent variables (i.e. derived from the observed variables by specifying their relations using equations), such as those in factor analysis. The multiple equations in each causal model entail a certain structure of correlational relationships between observed variables which is usually given as a correlation (or covariance) matrix . The estimation procedure is to minimize the difference between and the observed correlation/covariance matrix S formulated by a likelihood function. The 2 -test is then used to evaluate the difference between these two matrices by taking into account the number of the estimated parameters in the proposed model. When the 2 -value is large (i.e. the difference between the two matrices is large) relative to the model’s degree of freedom, the proposed model is rejected, i.e. something in the causal relationships specified by the proposed model is not quite right and require a second thought. When the 2 -value is small, we fail to reject the model or tentatively accept the model as adequate. Because of the possibility of equivalent models, our model may still be wrong in terms of the causal relations amongst variables but happen to entail the same correlation structure (the same S) of the ‘true’ model. So SEM seems to be an endeavour to search for the truth by approximation, and in this aspect, doing SEM is quite similar to the process of ‘Conjectures and Refutations’ as described by the great philosopher

The use of structural equation modelling has become increasingly common in the social and behavioural sciences. Based on a stochastic analysis of the multivariate density function of indicator variables, latent moderated structural Equations (LMS) implements iterative maximum likelihood estimation for the model parameters. K. A. Bollen developed a general method that makes use of the two stage least squares for structural equation models with nonlinear functions of latent variables. In structural equation modelling, the latent variables in the equation are usually linearly related. But in some cases, theory suggests that in addition to the linear effects a product of the latent predictor variables may have an additional effect on a latent criterion variable. In view of non-normality problems with latent interaction models, a stochastic analysis of the density functions involved by interaction models could provide a theoretical background for the development of efficient estimation methods and a better understanding of the major problems associated with latent interaction.

Structural equation modeling (SEM) is a very general and flexible multivariate technique that allows relationships among variables to be examined. The roots of SEM are in the social sciences. In writing this textbook, the authors look to make SEM accessible to a wider audience of researchers across many disciplines, addressing issues unique to health and medicine. SEM is often used in practice to model and test hypothesized causal relationships among observed and latent (unobserved) variables, including in analysis across time and groups. It can be viewed as the merging of a conceptual model, path diagram, confirmatory factor analysis, and path analysis. In this textbook the authors also discuss techniques, such as mixture modeling, that expand the capacity of SEM using a combination of both continuous and categorical latent variables. Features: Basic, intermediate, and advanced SEM topics Detailed applications, particularly relevant for health and medical scientists Topics and examples that are pertinent to both new and experienced SEM researchers Substantive issues in health and medicine in the context of SEM Both methodological and applied examples Numerous figures and diagrams to illustrate the examples As SEM experts situated among clinicians and multidisciplinary researchers in medical settings, the authors provide a broad, current, on the ground understanding of the issues faced by clinical and health services researchers and decision scientists. This book gives health and medical researchers the tools to apply SEM approaches to study complex relationships between clinical measurements, individual and community-level characteristics, and patient-reported scales.

Purpose: Since oxidative stress involves a variety of cellular changes, no single biomarker can serve as a complete measure of this complex biological process. The analytic technique of structural equation modeling (SEM) provides a possible solution to this problem by modelling a latent (unobserved) variable constructed from the covariance of multiple biomarkers.Methods: Using three pooled datasets, we modelled a latent oxidative stress variable from five biomarkers related to oxidative stress: F2-isoprostanes (FIP), fluorescent oxidation products, mitochondrial DNA copy number, γ-tocopherol (Gtoc) and C-reactive protein (CRP, an inflammation marker closely linked to oxidative stress). We validated the latent variable by assessing its relation to pro- and anti-oxidant exposures.Results: FIP, Gtoc and CRP characterized the latent oxidative stress variable. Obesity, smoking, aspirin use and β-carotene were statistically significantly associated with oxidative stress in the theorized directions; the same exposures were weakly and inconsistently associated with the individual biomarkers.Conclusions: Our results suggest that using SEM with latent variables decreases the biomarker-specific variability, and may produce a better measure of oxidative stress than do single variables. This methodology can be applied to similar areas of research in which a single biomarker is not sufficient to fully describe a complex biological phenomenon.

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects of fixed covariate in its various components. Methods for computing the ML estimates, and the Bayesian information criterion (BIC) for model comparison are established on the basis of powerful tools in statistical computing such as the Monte Carlo EM algorithm, Gibbs sampler, Metropolis–Hastings algorithm, conditional maximization, bridge sampling, and path sampling. The newly developed procedures are illustrated by results obtained from a simulation study and analysis of a real data set in education.

The paper proposes a time series generalisation of the structural equation model with latent variables (SEM). An instrumental variable estimator is considered and its asymptotic properties are analysed. Special emphases are placed on the potential use of the lagged observed variables as instruments and consistency of such estimation is established under some general assumptions about the stochastic properties of the modelled variables. In addition, an identification procedure suitable both for static and dynamic structural equation models is described. The methods are illustrated in an empirical application to dynamic panel estimation of a consumption function using UK household data.

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

Multicollinearity is a very common problem in studies that employ path analysis in agronomic crops, which generates unrealistic results and erroneous interpretations. This study was aimed at assessing the path analysis in data obtained from guava tree full-sib based on modelling multiple regressions applying latent variables to neutralize the effects of multicollinearity. Seven explanatory variables were measured – fruit mass (FM), fruit length (FL), fruit diameter (FD), mesocarp thickness (MT), peel thickness (PT), pulp mass (PM), total number of fruits (NTF) –, plus the main dependent variable, total yield per plant (YIELD). In accordance with the multicollinearity scenario, eleven values were tested with the addition of the constant K to the diagonal of the correlation matrix X’X. Path analysis was applied in two models: all the explanatory variables with direct effect on the dependent one and another model with multiple regression with more than one chain and the presence of latent variables. The path analysis in the multivariate methodology of structural equation modelling (SEM), which uses latent variable prediction, provided better results than the traditional and ridge path analyses.

This study was aimed to explore the application of Structural Equation Modeling (SEM) in the researches relevant with the field of athletic conducted from 2004 to 2010. Through the analysis and conclusion based on the latent growth curve model (LGM), it was hoped to better comprehend all these papers from 2004 to 2010 with SEM application. It was shown that a total of 192 SEM-applied athletic papers were produced during this certain period of time. There were only six SEM papers in 2004. Within these six years, it was increased to 50 papers a year in 2010. This was a tremendous growth in the quantities of papers SEM-applied in athletic fields, averagely increasing 0.3 paper year by year. SEM-applied papers had exceeding reliability and validity compared to those with conventional statistical methods. Moreover, the estimation of latent variables was the other strength of SEM. Many reference books related to SEM were continuously published. With a rapid increase in the theories underlying SEM, it was proved that SEM is a sophistically-developed statistical methodology. The findings and suggestions of this research can be referenced by other athletic related researches in research design and the application of SEM.

It is common practice for psychologists to specify models with latent variables to represent concepts that are difficult to directly measure. Each latent variable needs a scale, and the most popular method of scaling as well as the default in most structural equation modeling (SEM) software uses a scaling or reference indicator. Much of the time, the choice of which indicator to use for this purpose receives little attention, and many analysts use the first indicator without considering whether there are better choices. When all indicators of the latent variable have essentially the same properties, then the choice matters less. But when this is not true, we could benefit from scaling indicator guidelines. Our article first demonstrates why latent variables need a scale. We then propose a set of criteria and accompanying diagnostic tools that can assist researchers in making informed decisions about scaling indicators. The criteria for a good scaling indicator include high face validity, high correlation with the latent variable, factor complexity of one, no correlated errors, no direct effects with other indicators, a minimal number of significant overidentification equation tests and modification indices, and invariance across groups and time. We demonstrate these criteria and diagnostics using two empirical examples and provide guidance on navigating conflicting results among criteria. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Examinations of the relationships between environmental variables and ordination results often give little consideration to the complex relationships among environmental factors. In this chapter I consider the utility of structural equation modeling (SEM) with latent variables for evaluating the relationships among environmental variables and ordination axis scores. Using an example data set, I compare the efficiency of three approaches – (1) multiple regression, (2) principle component analysis, and (3) SEM – as methods for extracting information from multivariate data. All three approaches were found to be equivalent in their ability to explain variance in response variables but differ in their ability to explain the covariation among predictor variables. In general, when sufficient theoretical knowledge exists to permit the formulation of hypotheses about the relationships among variables, structural equation modeling can provide for a more comprehensive analysis. It is suggested that the analysis of latent variables using SEM may advance our understanding of environmental effects on vegetation data in many cases.

Local influence analysis of nonlinear structural equation models with nonignorable missing outcomes from reproductive dispersion models