Cause and Effect Examining by Structural Equation Modeling

 Structural Equation Modeling and Cause & Effect

Structural Equation Modeling,Use of Modeling,Benefits with SEM,Data Requirement for SEM,Stages of SEM

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.