### Step 5 of 5 -- Manipulating the SEM Model

This article covers the last of fives steps in the Structural Equation Modeling process, and is adapted from the book by R. H. Hoyle (ed.) 1995. *Structural Equation Modeling*. SAGE Publications, Inc. courtesy of Google Books, from the skillful writing by Ricka Stoelting -- a graduate student at San Francisco State University at the time she wrote about SEM -- from *StatSoft* (the electronic statistics textbook by the creators of *STATISTICA* data analysis and software services), and *Statistics Solutions*.

This is the fifth step in the process of using Structural Equation Models. The fifth step addresses model manipulation and builds on the SEM steps 1 through 4.

### A Quick Review of the Five Steps to SEM

Let's recap the five steps to Structural Equation Modeling. Remember, the ultimate goal is to determine if a set of variances and covariances in a matrix fit a specific structure, about which the market researcher already has some ideas.

### The Five Steps Summarized

- Show with a path diagram how the variables are believed to be related
- Using complex rules, figure out the implications for the variances and the covariances of the variables.
- Test whether the variances and covariances fit the model of them that has been built.
- Run statistical tests, parameter estimates, and standard errors for the numerical coefficients in the linear equations.
- Using the reported statistics, decide if the model generated is a good fit to the data.

### How Is the Last SEM Step Accomplished?

The last step in the SEM process entails examining the structural model validity. Three measures are used to determine the validity of the structural model: Chi-Square, an incremental fit index, and a "badness" of fit index. If the value of the Chi-Square test is not significant, the model is believed to be a good fit. Also important are that at least one incremental fit index (like CFI, GFI, TLI, AGFI, etc.) and one badness of fit index (like RMR, RMSEA, SRMR, etc.) meet criteria that have been predetermined. Examples of the two indexes are listed here, but they are beyond the scope of this article.

The individual estimates of the free parameters are assessed in the final step. This is accomplisehd by comparing the free parameters to a null value by using a z-distribution. To get the z-statistic, the market researcher divides the estimate of the parameter by the standard error of that estimate. To be significant, the answer -- which will be a ratio -- must be larger than +/-1.96. Once the individual relationships in the model have been examined, it is necessary to standardize the parameter estimates. This allows the market researcher to interpret the parameter estimates in reference to other parameters in the model. In this way, it becomes possible to compare the relative strength of the pathways within the model.

Structural Equation Modeling (SEM) is a very useful tool for market researchers because it tests the expected casual relationships among variables. As with any statistical model, there are certain underlying assumptions that -- if violated -- call the data into question with regard to validity and reliability. Also there are both advantages and disadvantages to using Structural Equation Modeling.

### Benefits and Limitations of SEM

The directionality in relationships between variables cannot be tested with SEM. Although direction of arrows (by other common names: edges, wires, arcs) are often shown in a Structural Equation Model, the direction represents the hypothesis that the market researcher has generated regarding causality in the system she is exploring.

Also, importantly, the choice of variables and pathways that a market researcher has used will limit the ability of the Structural Equation Model to recreate the sample covariance and variance patterns that have been observed. What this means practically, is that any one of several models might fit the data just as well. Regardless, SEM is a useful technique for understanding the relational data of multivariate systems. Structural Equation Modeling is really very good at distinguishing between the direct and indirect relationships between variables. SEM is also an excellent approach for analyzing the relationships between latent variables without random error.

This is the concluding article on the five steps of Structural Equation Modeling. You may wish to read about the more contemporary version of this computer modeling process that capitalizes on Bayesian Belief Networks (BBN). It is called Probabilistic Structural Equation Modeling. Bayesian Networks is an exciting new trend in market research which can be used to deep-dive into consumer behavior and provide shopper insights.

- Specify the Model
- Identify the Model
- Estimate the Model
- Test the Model Fit
**Manipulate the Model**