# The form of structural equation models

Structural Equation Modeling - Introductory Overview S tructural Equation Modeling Structural Equation Modeling is a very general, very powerful multivariate analysis technique that includes specialized versions of a number of other analysis methods as special cases. We will assume that you are familiar with the basic logic of statistical reasoning as described in Elementary Concepts. Moreover, we will also assume that you are familiar with the concepts of variance, covariance, and correlation; if not, we advise that you read the Basic Statistics Overview at this point. Although it is not absolutely necessary, it is highly desirable that you have some background in factor analysis before attempting to use structural modeling. Structural Equation Model n this course it was mentioned twice that researchers should not design a complex experiment with too many variables when the knowledge of the subject matter is not well-understood.

Nevertheless, a good architect should build a house rather than just making bricks. As the knowledge of the field accumulates to a degree that a synthesis is needed, researchers should put many variables together to build a coherent model, which specifies causal-effect relationships among those variables.

The importance of model building can be best illustrated by the Keynesian model. Yes, you are not in the wrong class. Let me explain it. The Keynesian model was introduced by John Maynard Keynes, the most well-known British economist in the 20th century.

This model hypothesizes how government spending can trigger more spending in other economic sectors. This idea, "multiplier," originated from another economist instead of John Keynes.

But that economist is virtually unknown while John Keynes has gained world-wide reputation. It is because instead of introducing a piece of concept, John Keynes built a comprehensive model for explaining the relationships among government expenditures, employment, money supply, inflation, interest rate, investment, and gross domestic product.

While dealing with many sets of variables and relationships, inexperienced researchers may perform several separate ANOVA and regression analyses.

Indeed, a structural equation model SEM should be developed to avoid "missing links" among variables. SEM is built upon a measurement model and a structural model. Measurement model A measurement model, as its name implies, is about measurement and data collection.

In the section concerning reliability and Cronbach Alpha, we discussed how researchers develop instrument with high reliability and low measurement error. In factor analysis, researchers extract latent variables from observed variables.

The relationships are indicated in the following figure. The ellipse represents a latent variable such as a mental construct, the rectangles represent observed variables, which are items in a scale.

The circles denote measurement errors. Structural model A structural model specifies how well some variables could predict some other variables. Because prediction involves relationships, it could be viewed as a regression model.

Also, since the relationships form a "chain" or a "path," it is also known as path model. When two models are combined, they form a structural equation model.

The following is an example given by Lomax Assume that based upon literature research, a researcher hypothesizes that "home background" could be a predictor to "school achievement," and "school achievement" could predict "career success", he should define such vague concepts as home background, school achievement, and career success.

The next logical step he should go is to develop instrument and data collection schemes to measure those latent constructs. This example is simplified. A real-life structural equation model is more complicated than that. While applying an input-output model to research on Web-based instruction, researchers may find only one dependent variable and independent variable, namely, test performance and the treatment.

However, while applying the input-process-output structural frameworkbetween the input and output are involved many other observed and latent variables. You can literally draw a model on the program canvas, enter the data, and then test the model. Please use the navigation buttons below the figure to walk through the simulated modeling building process The following simulation may not work on Internet Explorer.

## Reduced form - Wikipedia

Know exactly what you're doing The model shown in the above example contains sets of relationships. How could that researcher formulate those relationships?

Not by taking drugs, of course.Together, the structural model and the measurement model form the entire structural equation model. This model includes everything that has been measured, observed, or otherwise manipulated in the set of variables examined.

Introduction to Structural-Equation Modelling 1 1. Introduction • Structural-equation models (SEMs) are multiple-equation regression models in which the response variable in one regression equation can appear as an explanatory variable in another equation.

Structural equation models are often visualized by a graphical path diagram. The statistical model is usually represented in a set of matrix equations. In the early seventies, when this technique was first introduced in social and (CFA) models.

In structural equation modeling, the confirmatory factor model is imposed on the data. In this. Structural Equation Modeling Kosuke Imai Princeton University POL Quantitative Analysis II Spring Kosuke Imai (Princeton) Structural Equation Modeling POL Spring 1 / This text unifies the principles behind latent variable modeling, which includes multilevel, longitudinal, and structural equation models, as well as generalized mixed models, random coefficient models, item response models, factor models, panel models, repeated-measures models, latent-class models, and frailty models.

A Simultaneous Equation Model (SEM) is a model in the form of a set of linear simultaneous equations. Complete Models and Structural Equation Models. When the total number of endogenous variables is equal to the number of equations, it is called a complete SEM.

Structural equation modeling - Wikipedia