Methods and Rule-of-Thumbs in The Determination of Minimum Sample Size When Appling Structural Equation Modelling: A Review (original) (raw)
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An Application of Structural Equation Modelling – A Tutorial
covariance structure analysis remains a niche area in statistics. As such SEM is not very well known to most statisticians. This is somewhat surprising because the primary building blocks of SEM-common factor analysis (common factors are by definition latent variables) and linear regression-are all too well known to the statisticians! The primary use of SEM is to test
A SYSTEMATIC REVIEW OF STRUCTURAL EQUATION MODEL (SEM
Open Journal Nigeria, 2020
Structural Equation Model (SEM) is a multivariate statistical technique that has been explored to test relationships between variables. The use of SEM to analyze relationship between variables is premised on the weak assumption of path analysis, regression analysis and so on; that variables are measured without error. This review thus sheds light on the meaning of SEM, its assumptions, steps and some of the terms used in SEM. The importance of item parcelling to SEM and its methods were briefly examined. It also dealt on the stages involved in SEM, similarities and differences between SEM and conventional statistical methods, software packages that can be used for SEM. This article employed systematic literature review method because it critically synthesized research studies and findings on structural equation modeling (SEM). It could be concluded that SEM is useful in analyzing a set of relationships between variables using diagrams. SEM can also be useful in minimizing measurement errors and in enhancing reliability of constructs. Based on this, it is recommended that SEM should be employed to test relationship between variables since it can explore complex relationships among variables such as direct, indirect, spurious, hierarchical and non-hierarchical.
Sample size determination and power estimation in structural equation modeling
Applications of structural equation modeling (SEM) can be found within many influential journals in sport and exercise science. For example, in Exercise and Sport Sciences Reviews, Duncan, Duncan, Strycker, and Chaumeton (2004) provided preliminary findings from a longitudinal study of youth physical activity. In Medicine and Science in Sports and Exercise, Motl, Dishman, Felton, and Pate (2003) investigated self-motivation and physical activity among black and white adolescent girls.
A Handbook on SEM Overview of Structural Equation Modeling (SEM
Academicians, researchers, as well as postgraduate students are developing theories concerning the relationships among certain hypothetical constructs. They are modeling their theorized relationships with the intention to test their theoretical model with the empirical data from the field. The example of a Theoretical Framework is given in Figure A. Figure A: The Schematic Diagram Showing the Theoretical Framework of a Study. The schematic diagram in Figure A is converted into Amos Graphic and analyzed using empirical data. In Amos Graphic, the rectangles represent the directly observed variables while the ellipses represent the unobserved variables or latent constructs. The schematic diagram of theoretical framework in Figure A is converted into Amos Graphic as shown in Figure B. The schematic diagram of the model for the study is developed based on debates in theory and literature. One needs to come out with a theoretical framework for the study.
The Basics of Structural Equation Modeling
Structural equation modeling (SEM) is a methodology for representing, estimating, and testing a network of relationships between variables (measured variables and latent constructs). This tutorial provides an introduction to SEM including comparisons between " traditional statistical " and SEM analyses. Examples include path analysis/ regression, repeated measures analysis/latent growth curve modeling, and confirmatory factor analysis. Participants will learn basic skills to analyze data with structural equation modeling. Rationale Analyzing research data and interpreting results can be complex and confusing. Traditional statistical approaches to data analysis specify default models, assume measurement occurs without error, and are somewhat inflexible. However, structural equation modeling requires specification of a model based on theory and research, is a multivariate technique incorporating measured variables and latent constructs, and explicitly specifies measurement error. A model (diagram) allows for specification of relationships between variables. Purpose The purpose of this tutorial is to provide participants with basic knowledge of structural equation modeling methodology. The goals are to present a powerful, flexible and comprehensive technique for investigating relationships between measured variables and latent constructs and to challenge participants to design and plan research where SEM is an appropriate analysis tool. Structural equation modeling (SEM) • is a comprehensive statistical approach to testing hypotheses about relations among observed and latent variables (Hoyle, 1995). • is a methodology for representing, estimating, and testing a theoretical network of (mostly) linear relations between variables (Rigdon, 1998). • tests hypothesized patterns of directional and nondirectional relationships among a set of observed (measured) and unobserved (latent) variables (MacCallum & Austin, 2000). Two goals in SEM are 1) to understand the patterns of correlation/covariance among a set of variables and 2) to explain as much of their variance as possible with the model specified (Kline, 1998). The purpose of the model, in the most common form of SEM, is to account for variation and covariation of the measured variables (MVs). Path analysis (e.g., regression) tests models and relationships among MVs. Confirmatory factor analysis tests models of relationships between latent variables (LVs or common factors) and MVs which are indicators of common factors. Latent growth curve models (LGM) estimate initial level (intercept), rate of change (slope), structural slopes, and variance. Special cases of SEM are regression, canonical correlation, confirmatory factor analysis, and repeated measures analysis of variance (Kline, 1998). Similarities between Traditional Statistical Methods and SEM SEM is similar to traditional methods like correlation, regression and analysis of variance in many ways. First, both traditional methods and SEM are based on linear statistical models. Second, statistical tests associated with both methods are valid if certain assumptions are met. Traditional methods assume a normal distribution and SEM assumes multivariate normality. Third, neither approach offers a test of causality. Differences Between Traditional and SEM Methods Traditional approaches differ from the SEM approach in several areas. First, SEM is a highly flexible and comprehensive methodology. This methodology is appropriate for investigating achievement, economic trends, health issues, family and peer dynamics, self-concept, exercise, self-efficacy, depression, psychotherapy, and other phenomenon. Second, traditional methods specify a default model whereas SEM requires formal specification of a model to be estimated and tested. SEM offers no default model and places few limitations on what types of relations can be specified. SEM model specification requires researchers to support hypothesis with theory or research and specify relations a priori. Third, SEM is a multivariate technique incorporating observed (measured) and unobserved variables (latent constructs) while traditional techniques analyze only measured variables. Multiple, related equations are solved simultaneously to determine parameter estimates with SEM methodology. Fourth, SEM allows researchers to recognize the imperfect nature of their measures. SEM explicitly specifies error while traditional methods assume measurement occurs without error. Fifth, traditional analysis provides straightforward significance tests to determine group differences, relationships between variables, or the amount of variance explained. SEM provides no straightforward tests to determine model fit. Instead, the best strategy for
2007
Structural equation modeling (SEM) is a versatile statistical modeling tool. Its estimation techniques, modeling capacities, and breadth of applications are expanding rapidly. This module introduces some common terminologies. General steps of SEM are discussed along with important considerations in each step. Simple examples are provided to illustrate some of the ideas for beginners. In addition, several popular specialized SEM software programs are briefly discussed with regard to their features and availability. The intent of this module is to focus on foundational issues to inform readers of the potentials as well as the limitations of SEM. Interested readers are encouraged to consult additional references for advanced model types and more application examples.
STRUCTURAL EQUATION MODEL (SEM
This paper critically examined a broad view of Structural Equation Model (SEM) with a view of pointing out direction on how researchers can employ this model to future researches, with specific focus on several traditional multivariate procedures like factor analysis, discriminant analysis, path analysis. This study employed a descriptive survey and historical research design. Data was computed viaDescriptive Statistics, Correlation Coefficient, Reliability. The study concluded that Novice researchers must take care of assumptions and concepts of Structure Equation Modeling, while building a model to check the proposed hypothesis. SEM is more or less an evolving technique in the research, which is expanding to new fields. Moreover, it is providing new insights to researchers for conducting longitudinal investigations. .
Book Review of Basics of Structural Equation Modeling, by Geoffrey M. Maruyama
Structural Equation Modeling, 2000
The rate of publication of books on structural equation modeling (SEM) has shown an almost exponential growth over the last decade, reflecting the popularity of this type of statistical analysis more than its apparent usefulness. Basics of Structural Equation Modeling is yet another book with the goal "to provide readers a good basic understanding of how and why structural equation approaches have come to be used" and "to learn about the logic underlying the use of these approaches, about how they relate to techniques such as regression and factor analysis, about their strengths and shortcomings as compared to alternative methodologies, and about the various methodologies for analyzing structural equation data" (p. 11f.). By and large, that goal is accomplished. The book has four parts, the contents of which will be discussed briefly, followed by a more general evaluation. PART I. BACKGROUND This part includes two chapters: an introductory chapter on "Causal Processes," and one on the "History and Logic of Structural Equation Modeling." In this part of the book Maruyama tries to express the usefulness and essence of causal modeling. Almost by definition, causal modeling is seen as an "alternative and complementary methodology to experimentation for examining plausibility of hypothesized models" (p. 7), which is partly remarkable: SEM can hardly ever be a substitute for experimentation. The issue of causality in SEM is not treated with great rigor. In fact, the author's position is often ambiguous and vague. For example, on the one hand structural equation modeling is presented as similar to causal modeling, and yet, on the other hand already in the first 10 pages a small impression is given of
Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach
In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed. Substantive use of structural equation modeling has been growing in psychology and the social sciences. One reason for this is that these confirmatory methods (e.g., Bentler, 1983; Browne, 1984; Joreskog, 1978)provide researchers withacom-prehensive means for assessing and modifying theoretical models. As such, they offer great potential for furthering theory development. Because of their relative sophistication, however, a number of problems and pitfalls in their application can hinder this potential from being realized. The purpose of this article is to provide some guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that provides a basis for making meaningful inferences about theoretical constructs and their interrelations, as well as avoiding some specious inferences. The model-building task can be thought of as the analysis of two conceptually distinct models (Anderson & Gerbing, 1982; Joreskog & Sorbom, 1984). A confirmatory measurement, or factor analysis, model specifies the relations of the observed measures to their posited underlying constructs, with the constructs allowed to intercorrelate freely. A confirmatory structural model then specifies the causal relations of the constructs to one another, as posited by some theory. With full-information estimation methods, such as those provided in the EQS (Bentler, 1985) or LISREL (Joreskog & Sorbom, 1984) programs, the measurement and structural submodels can be estimated simultaneously. The ability to do this in a one-step analysis ap