# Structural Equation Modeling and Cause & Effect

**Structural Equation Modeling**

Structural equation modeling (SEM) is used to describe theoretical
and analytical techniques for examining** cause-and-effect relationships**. It is
used interchangeably with the terms causal modeling, **covariance structure
modeling, and LISREL modeling**.

The theoretical issues are discussed in **“Causal
Modeling.”** A description of the analytical issues when programs such as LISREL
or EQS are used will ensue.

## Use of Modeling

Structural equation modeling techniques are extremely flexible. Most models of cause can be estimated. In some models the causal flow is specified only between the latent variable and its empirical indicators, such as in a factor analysis model.

This is known as confirmatory factor analysis.
In other models, causal paths among the latent variables also are included.

## Benefits with SEM

Conducting a confirmatory factor analysis with SEM has many advantages. With SEM, the analyst can specify exactly which indicators will load on which latent variables (the factors), and the amount of variance in the indicators not explained by the latent variable (due to error in either measurement or model specification) is estimated.

Correlations between latent variables and among errors associated with the indicators can be estimated and examined. Statistics that describe the fit of the model with the data allow the analyst to evaluate the adequacy of the factor structure, make theoretically appropriate modifications to the structure based on empirical evidence, and test the change in fit caused by these modifications.

Thus, confirmatory factor analysis provides a direct test of the hypothesized structure of an instrument's scales. An advantage of using SEM to estimate models containing causal paths among the latent variables is that many of the regression assumptions can be relaxed or estimated.

For example, with multiple regression, the analyst must assume perfect measurement (no measurement error); however, with SEM, measurement error can be specified and the amount estimated.

In addition , constraints can be introduced based on theoretical expectations . For example, equality constraints, setting two or more paths to have equal values , are useful when the model contains cross lagged paths from three or more time points. The path from latent variable A at Time 1 to latent variable B at Time 2 can be set to equal the path from latent variable A at Time 2 to latent variable B at Time 3.

Equality constraints also are used to compare
models for two or more different groups. For example, to compare the models of
effects of maternal employment on preterm and full-term child outcomes, paths
in the preterm model can be constrained to be equal to the corresponding paths
in the** full-term model**.

## Data Requirement for SEM

Data requirements for SEM are similar to those for factor analysis
and multiple regression in level of measurement but not sample size. Exogenous
variables can have indicators that are measured as **interval, near-interval, or
categorical** (dummy, effect, or orthogonally coded) levels, but endogenous
variables must have indicators that are measured at the interval or near interval
level.

The rule of thumb regarding the number of cases needed for SEM, 5 to 10
cases per parameter to be estimated, suggests considerably larger samples than
usually needed for multiple regression; Thus, samples of 100 for a very modest
model to 500 or more for more complex models are often required. Despite the
advantages of SEM, these larger samples can result in complex and costly
studies.

## Stages of SEM

Structural equation modeling is generally a multistage procedure. First, the SEM implied by the theoretical model is tested and the fit of the model to the observed data is evaluated.

A nonsignificant 7 indicates
acceptable fit, but this is difficult to obtain because the value is heavily
influenced (increased) by larger sample sizes. Thus, most analytical programs
provide other measures of fit. A **well-fitting model** is necessary before the
parameter estimates can be evaluated and interpreted.

In most cases, the original theoretical model does not fit the data well, and modifications must be made to the model in order to obtain a well-fitting model. Although deletion of nonsignificant paths (based on t values) is possible, modifications generally focus on the inclusion of omitted paths (causal or correlational).

Any path that is omitted specifies that there is no relationship, implying a parameter of zero; Thus, analysis programs constrain these paths to be zero.

After estimating the specified model, most
programs provide a numerical estimate of the **“strain”** experienced by fixing
parameters to zero or improvement in fit that would result from freeing the
parameters (allowing them to vary). Suggested paths must be theoretically
defensible before adding them to the respecified model.

Because the model specification is based on the data at hand in the light of theoretical evidence and those data are repeatedly tested, the significance level of the x is actually higher than what the program indicates. Thus, other criteria are necessary to evaluate the adequacy of the final model.

First is the theoretical appropriateness of the final model. Comparison of the
original model with the final model will indicate how much **“trimming”** has taken
place. In addition, the values and signs of the parameters are evaluated.

The
signs **(positive or negative)** of the parameters should be in the expected
direction. Parameters on the paths between the latent variable and its
indicators should be 2 50 but ≤ 1.0 in a standardized solution.

The lower the unexplained variance of the endogenous variables, the better the model performed in explaining those endogenous variables (similar to the 1-R value in multiple regression). Results that are consistent with a priori expectations and findings from previous research increase one's confidence in the model.

In
summary, SEM is a powerful and flexible analysis technique for testing models
of cause, investigating specific **cause-and-effect** relationships, and exploring
the hypothesized process by which specific outcomes are produced.

With SEM
programs, the researcher has greater control over the analyzes than with other
factor analysis and multiple regression programs. Model specification is
usually necessary, but the role of theory in selecting appropriate
modifications is crucial.

Give your opinion if have any.