**LISREL (LInear Structural RELations modeling)** was one of the first statistical computer packages used for structural equation modeling. Created by Karl Joreskog and Dag Sorbom, it remains one of the most popular programs for such analyses, although numerous other programs exist, including EQS, Proc Calis within SAS, and Amos. As with all structural modeling programs, LISREL provides an extremely powerful and flexible way to analyze complex data.

LISREL essentially assesses the extent to which theorized relations between variables are consistent with observed relations between those variables. The researcher begins by theorizing how a set of variables should be related to each other. For example, he or she might theorize that many measured variables (e.g., a verbal test, math test, reaction time test) all relate to a single underlying construct of generalized intelligence (IQ). This is an example of a “latent variable model.” IQ is not measured directly; rather, its existence is inferred because a variety of measured or “observed” variables (the various tests) are themselves highly related to each other. If the researcher collects the data and the measured tests are not all highly related to each other, a model that assumes a single latent variable may not “fit” the observed data. LISREL provides the researcher with specific, quantitative estimates of the extent to which the theorized model fits the observed data.

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Popular uses of LISREL include tests for the presence of a single latent variable, multiple latent variables, and even latent variables that are nested hierarchically. A model that tests only for the presence of latent variables is often referred to as a “confirmatory factor model.” Other common uses of LISREL include tests of models in which the researcher theorizes a chain of direct and indirect influences among variables. The variables included in such a “path” model can be either observed or latent variables or a mixture of the two. They may all be measured at a sin-gle point in time or involve multiple time-points. Indeed, structural modeling programs like LISREL are often used to analyze longitudinal data.

When analyzing data using LISREL, the researcher is provided a variety of statistics that are useful in determining how well or poorly the model fits the observed data. These include statistics for individually theorized associations among variables as well as statistics that assess the model as a whole. In addition, the researcher is provided statistics that pinpoint sources of ill fit. Armed with these statistics, the researcher is often tempted to modify the originally theorized model in an attempt to provide a better fitting model. Although such modifications will improve fit, they run the risk of capitalizing on chance fluctuations in the data and should be replicated in a separate sample before they are trusted.

LISREL and other structural equation modeling programs provide powerful tools for testing complex models of psychological phenomena. At the same time, they require a fair amount of mathematical ability and statistical sophistication to use properly.

### References:

- Byrne, B. (1998). Structural equation modeling with LISREL, PRELIS, and SIMPLIS: Basic concepts, applications, and programming. Mahwah, NJ: Erlbaum.
- Byrne, B. (2006). Structural equation modeling with EQS: Basic concepts, applications, and programming. Mahwah, NJ: Erlbaum.
- du Toit, M., & du Toit, S. (2001). Interactive LISREL: User’s Guide. Lincolnwood, IL: Scientific Software.
- Kline, R. B. (2004). Principles and practice of structural equation modeling (2nd ed.). New York: Guilford Press.

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