Selecting scaling indicators in structural equation models (sems).

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 Role of Providers in Mental Health Services Offered to American-Indian Youths

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.

Drawing upon recent developments in structural equation modeling, the current study presents an analytical framework for addressing research questions in which, rather than focusing on means, it is intraindividual (or intragroup) variability that is of direct research interest. Beyond merely serving as an alternative to existing multilevel modeling approaches, this framework allows for extensions to accommodate a variety of complex research scenarios by parameterizing variability as a latent variable that can in turn be embedded within a broader covariance and mean structure involving other observed and/or latent variables. The estimation procedures and parameter interpretation for the latent random variability models are discussed. The versatility of the proposed methods is demonstrated through four empirical examples. The Mplus, BUGS, and Stan model syntax for the illustrative examples are supplied to facilitate the application of the methods. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Structural equation model (SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM (QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood (BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.

Often quantities of interest in psychology cannot be observed directly. These unobservable quantities, known as latent variables, tend to be complex, often multidimensional, constructs. In many cases these constructs are categorical, such that individuals belong to mutually exclusive and exhaustive unobservable subgroups. Latent class analysis (LCA) is a statistical approach to modeling a discrete latent variable using multiple, discrete observed variables as indicators. Examples of latent class variables that appear in the psychology literature include temperament type, substance use behavior, teaching style, stages of change in the transtheoretical model, and latent classes of risk. The first section of this chapter provides a conceptual introduction to the concept of a latent class followed by a technical introduction to the mathematical model, including multiple-groups LCA and LCA with covariates. This is followed by a discussion of parameter restrictions, model selection, and goodness-of-fit. The second section demonstrates LCA using the empirical example of depression subtypes in adolescence. Five latent classes were identified based on responses to eight questionnaire items assessing depression symptoms: Non-depressed (characterized by a low probability of reporting all eight depression symptoms), sad, disliked, sad + disliked, and depressed (characterized by a high probability of reporting all eight depression symptoms). The third section presents longitudinal extensions of the model, including repeated-measures LCA and latent transition analysis (LTA). The empirical example is extended to examine change in depression subtypes over time. The final sections describe recent extensions to the latent class model and areas that merit additional research in the future. Keywords: latent class analysis; latent transition analysis; latent variable model; categorical data

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 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 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

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.

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.

In this chapter, two structural equation models are presented. The first one refers to a model that integrates two technical variables and two benefits, while the second model is an integrator, since it integrates the Human factor independent latent variable where the independent Operating factor and Benefits latent variables intervene in the total productive maintenance programs implementing process. In addition, each of the latent variables is validated and the model is evaluated through the partial least squares technique. Also, the direct effects, indirect effect, and total effects between the variables are measured. Similarly, a series of industrial implications from the results obtained are displayed.

This study aims to reveal the Al Washliyah community's preference for sharia insurance in North Sumatra, which is focused on aspects: How far do the cultural and personality significantly affect their preference for sharia insurance in North Sumatra. This study uses a quantitative approach by looking at latent variables and manifest variables together against Al Washliyah's community preferences for sharia insurance. Data were collected using a Likert scale model questionnaire taken from a sample of 374 peoples. Data analysis using Structural Equation Modelling (combined factor analysis with regression analysis) with the help of Lisrel Program. The results revealed that variable factors culture, subculture, and social class are valid and reliable in shaping latent Culture variables. Life cycle factors, economic environment, self-concept, and lifestyle are valid and reliable in forming latent variables of Personality. Preference is significantly related to Culture by 0.67, while the influence / coefficient of determination (R 2 ) is = 0.45 and Contribution by 45%. Preference is significantly related to Personality of 0.33, the influence/coefficient of determination (R 2 ) of = 0.11 and its contribution of 11%. Based on these findings, it is expected that institutions that have sharia insurance products in order to be able to pay attention to factors that make people choose sharia insurance products such as: culture and personality so that sharia insurance products can be in demand, especially for the peoples/residents of Al Washliyah. Keywords : Al Washliyah Community, Islamic insurance

Several studies have stressed the importance of simultaneously estimating interaction and quadratic effects in multiple regression analyses, even if theory only suggests an interaction effect should be present. Specifically, past studies suggested that failing to simultaneously include quadratic effects when testing for interaction effects could result in Type I errors, Type II errors, or misleading interactions. Research investigating this issue has been limited to multiple regression models. Contrarily, structural equation modeling is a more appropriate analysis when hypotheses include latent variables. The current study utilized Monte Carlo simulation to investigate whether quadratic effects should be included in the latent variable interaction model. Consistent with previous research, it was found that including latent variable quadratic effects in the model successfully reduced the frequency of spurious interaction effects but at a cost of low power to detect true interaction effects, inaccurate parameter estimates, inaccurate standard error estimates, and reduced convergence rates. Based on findings from the current study, we recommend that researchers hypothesizing interactions between latent variables should test for these relations using the latent variable interaction model rather than the interaction quadratic model. If researchers are concerned about spurious interactions, then they may want to consider including quadratic effects in the model, provided that they have sample sizes of at least 500 and high indicator reliability. We caution all researchers to base higher order effects models on theory.

Fixed and random effects models for longitudinal data are common in sociology. Their primary advantage is that they control for time-invariant omitted variables. However, analysts face several issues when they employ these models. One is the uncertainty of whether to apply the fixed effects (FEM) versus the random effects (REM) models. Another less discussed issue is that the FEM and REM models as usually implemented might be insufficiently flexible. For instance, the effects of variables, including the latent time-invariant variable, might change over time rather than be constant as in the usual FEM and REM. The latent time-invariant variable might correlate with some variables and not others. Lagged endogenous variables might be necessary. Alternatives that move beyond the classic FEM and REM models are known, but they involve different estimators and software that make these extended models difficult to implement and to compare. This paper presents a general panel model that includes the standard FEM and REM as special cases. In addition, it provides a sequence of nested models that provide a richer range of models that researchers can easily compare with likelihood ratio tests and fit statistics. Furthermore, researchers can implement our general panel model and its special cases in widely available structural equation models (SEMs) software. The paper is oriented towards applied researchers with most technical details given in the appendix and footnotes. An extended empirical example illustrates our results.