Many colleagues have asked me if there was or will be a review of a good program to analyze structural equation models. In particular, they wondered about the performance of the latest version of LISREL, a market leader in this field. In this issue, Professor George Marcoulides gives us the answers. George is a long-time user of this and related products, and has written about structural equation modeling.

A Review of LISREL8 with PRELIS2

by George A. Marcoulides, California State University, Fullerton

Structural equation modeling techniques are considered today to be a major component of applied multivariate analyses. Although the statistical theory that underlies structural equation modeling (SEM) appeared in the early 1970's, a considerable number of years passed before SEM received the widespread attention it holds today. One reason for the recent attention is the availability of specialized SEM computer packages (e.g., Amos, EQS, LISREL, LISCOMP, Mx, SAS PROC-CALIS, STATISTICA-SEPATH). Another reason has been the publication of several introductory and advanced texts on SEM (e.g., Bollen, 1989; Bollen & Long, 1993; Byrne, 1989, 1994; Hoyle, 1995; Marcoulides & Schumacker, 1995), numerous illustrative chapters and articles (e.g., Bentler, 1980; Joresk”g, 1973; Marcoulides & Heck, 1993), and a new journal entitled Structural Equation Modeling: A Multidisciplinary Journal, published by Lawrence Erlbaum Associates, devoted exclusively to SEM.

In its broadest sense SEM is concerned with testing complex models for structure of functional relationships between observed variables and latent (hypothetically existing) variables. The functional relationships are described by parameters that indicate the magnitude of the effect (direct or indirect) that independent variables have on dependent variables. As implemented in most commercial computer packages, SEM includes as special cases such procedures as confirmatory factor analysis, multiple regression, path analysis, models for time-dependent data, recursive and non-recursive models for cross-sectional and longitudinal data, and covariance structure analysis. Although there are currently a number of excellent computer packages available for the analysis of SEM, two stand apart from the rest in terms of popularity and widespread use: EQS (Bentler, 1994) and LISREL (Joresk”g & Sorb”m, 1992). This review will focus on the LInear Structural RELations program (Version 8.12) and its PRELIS (Version 2.12) companion.

Overview of the Product

LISREL8 is a specialized program for analyzing structural equation models and all other models that can be conceptualized as special cases of SEM. LISREL8 is fully compatible with earlier versions of the program. LISREL8 can estimate any number of unknown parameters according to a prespecified model, and can evaluate the fit of the model to some empirical data.

LISREL8 contains seven estimation procedures: Instrumental Variables (IV), Two-Stage Least Squares (TSLS), Generalized Least Squares (GLS), Unweighted Least Squares (ULS), Generally Weighted Least Squares (WLS), Diagonally Weighted Least Squares (DWLS), and Maximum Likelihood (ML). Each of these estimation procedures is based on minimizing the discrepancy between a sample covariance (or correlation) matrix and the theoretical population covariance matrix according to some weighting method. The estimates from each procedure are produced by varying the elements of the weight matrix under various distributional assumptions. For each estimation procedure, a large number (31, to be exact) of goodness-of-fit indices are provided to judge whether the model is consistent with the empirical data. The choice of the estimation procedure depends on the type of data included in the model.

LISREL8 can handle models with variables observed in any scale of measurement. For example, ordinal variables can be included using polychoric correlations and parameter estimates can be obtained using GLS estimation. The calculation of the polychoric correlations with their asymptotic covariance matrix is obtained via PRELIS2 (which is considered a preprocessor program of LISREL) and imported into LISREL8. PRELIS2 can also be used for multivariate data screening, missing value imputation, for constructing bootstrap samples, and for conducting Monte Carlo simulation experiments. A unique feature of LISREL8 is that any number of linear and non-linear models can be tested and compared across multiple samples. In addition, high quality path diagrams can be produced and can be modified interactively by adding or deleting paths in the diagram.

Using the Program

The LISREL8 program begins by asking the user to edit a new or existing command file. The command file must also include a reference to a data file. The data can be formatted as a correlation matrix, a covariance matrix or as raw data. The user is then provided with the option of running either PRELIS or LISREL. At this point, two new buttons appear on the screen "SHOW OUTPUT" and "PATH DIAGRAM." Figure 1 shows the setup box for running LISREL8 and PRELIS2.

LISREL8 uses a matrix oriented command language in which relations among variables are specified in an input file by indicating the particular elements in several parameter matrices that must be estimated. The parameter matrices all have Greek names (making it quite simple to use if you happen to speak Greek) and follow standard matrix notation. For example, Gamma is used to specify the path coefficients relating independent latent variables to dependent latent variables. For those that have trouble with Greek names or matrix notation, the program contains a new command language (SIMPLIS) which is quite easy to use and reduces the possibility of making errors in the problem set up. The SIMPLIS command language requires only the names of the observed and latent variables and a specification of the model to be estimated. The model may be specified either as paths between variables or relationships between variables. As such, to use the LISREL8 program all that is required is for one to formulate the model as a path diagram.

Figure 2 presents a SIMPLIS input file for a model with six observed variables and three latent variables. Figure 3 presents the path diagram for the same model with the parameter estimates displayed in the diagram. As can be seen, the latent variable "SES," measured by the observed variables "Education - EDU" and "Socioeconomic Index ->> SEI", is specified as a relationship by: EDUC SEI = SES. To specify the same model in terms of a path would be: SES - EDU SEI. Of course, the conventional LISREL command language can still be used (especially if you feel more at ease with matrix notation), because SIMPLIS merely translates the model into the standard matrix oriented command language. Figure 4 presents a LISREL command language input file for the same model. Although users can choose between the SIMLIS language and the LISREL language in an input command file, the two cannot be mixed in the same file.

With SIMPLIS language input, one can get an output file either in SIMPLIS format or LISREL format. The main difference between the two formats is that in SIMPLIS the estimated model is given in the form of equations, whereas in LISREL format the model is given in terms of parameter estimates. Unfortunately, some information in the LISREL output is not available in the SIMPLIS output and certain specialized commands like nonlinear constraints cannot be used in SIMPLIS. To generate LISREL format output using the SIMPLIS language one need only specify the command "LISREL OUTPUT" in the input command file.

In LISREL8 it is also possible to omit the specification of the model in the input file and specify the model interactively by adding paths on the screen. To do so, one does not specify the relationships or paths for a model in the input file. Instead, one only specifies which are the independent and the dependent variables. The program produces an "empty" path diagram on the screen and one can then use the arrow keys on the keyboard or the mouse to define paths in the model. Once the model is complete, the program will estimate the model and test the fit. A path diagram can also be interactively modified. Whenever a change is made to a path diagram, LISREL8 instantly generates approximate parameter estimates. Final parameter estimates are obtained by clicking the "Re-estimate" option. When a path diagram is produced on the screen, any part of it may be selected for magnification to achieve better visibility. In addition, any path diagram (excluding enlarged windows) may be printed using a variety of justification and size options.

Figure 5 presents some of the fit statistics generated for the example model. The fit statistics all indicate that the proposed model fairly accurately accounts for the variability observed in the empirical data. For example, the chi-square is a measure of the difference between the sample covariance (or correlation) matrix and the fitted covariance matrix. A small chi-square corresponds to a good fit. Other fit measures include the GFI and the RMR. It is generally recognized that GFI values should be above 0.90 and RMR values should be close to 0.0.

If the fit statistics examined suggest a poor model fit, one might benefit by examining the modification indices provided in the output file. Modification indices are an important feature of LISREL8 and are generally computed for each fixed and constrained parameter in the model. Each computed modification index measures how much the chi-squared goodness-of-fit test is expected to decrease if a particular parameter is set free and the model is re-estimated. As such, modification indices can be used in the process of model evaluation and refinement. Of course, one should not forget that any modification to the proposed model should always make substantive sense.

Ease of Learning and of Use

LISREL8 is quite easy to use. The dialog boxes are straightforward and the output generated is excellent. The problem with LISREL8 (and for that matter with most other commercial SEM packages) lies more in understanding the theory of SEM techniques and being able formulate an SEM model. My advice is to begin defining an SEM model with a simple statement of the verbal theory that makes explicit the hypothesized relationships among a set of observed and latent variables and the links that exist between them. In this manner, at least the structure of an SEM model can be formulated as a path diagram that represents the relationships using arrows going from independent to dependent variables. Once this step is tackled, one can focus on understanding and mastering the nuances of the LISREL8 computer program.

Documentation

LISREL8 and PRELIS2 documentation consists of two user's reference guides and a book that describes the new SIMPLIS command language. The reference guides also provide installation instructions. Although the book on SIMPLIS is quite well-written and up to date, the documentation for LISREL8 and PRELIS2 are just supplements to the older LISREL7 and PRELIS1 user's reference guides. The documentation could benefit from an update. Nevertheless, the users' guides are a good reference source and do an excellent job of explaining the various types of models that can be analyzed in LISREL8.

Support and Pricing

Registered users get free technical support. LISREL8 with PRELIS2 is currently available in three versions: DOS, DOS-Extender, and Windows. DOS and DOS-Extender versions contain HALO graphics drives for display and printing of path diagrams. The DOS-Extender and Windows versions are much faster and better suited for the analysis of complex models. The purchase price for a regular DOS version is $495, or $575 for all three versions combined. Registered users of LISREL may upgrade older versions to the DOS version ($195), or to all three versions combined ($245). Contact Scientific Software International, Lawrence Erlbaum Associates or the European distributor for discounts on multi-user and network licenses.

Conclusions

There is no doubt that LISREL8 with PRELIS2 is one of the flagship SEM programs. The program can be used by both experts and novices alike. The SIMPLIS language is quite easy to use and minimizes potential errors in problem set ups. Of course, for users more comfortable with Greek notation or matrix operations, the LISREL command language is also excellent. Finally, high quality path diagrams can be produced on the screen and interactively modified by adding or deleting paths.

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References

Bentl er, P.M. (1980). Multivariate analysis with latent variables: Causal modeling. Annual Review of Psychology, 31, 419-456.

Bentler, P.M. (1994). EQS structural equations program. Multivariate Software, Inc.

Bollen, K.A. (1989). Structural equations with latent variables. New York: Wiley.

Bollen, K., & Long, J.S. (Editors) (1993). Testing structural equation models. Sage Publications, Inc.

Byrne, B.M. (1989). A primer of LISREL: Basic applications and programming for confirmatory factor analytic models. New York: Springer Verlag.

Byrne, B.M. (1994). Structural equation modeling with EQS and EQS/Windows: Basic concepts, applications, and programming. Sage Publications, Inc.

Hoyle, R.H. (1995). Structural equation modeling: Concepts, issues and applications. Sage Publications, Inc.

Joresk”g, K.G. (1973). A general method for estimating a linear structural equation system. In A.S. Goldberger & O.D. Duncan (Eds.), Structural equation models in the social sciences (pp.85-112). New York: Academic.

Joresk”g, K.G., & Sorb”m, D. (1992). LISREL VIII: A guide to the program and applications. Mooresville, IN: Scientific Software.

Marcoulides, G.A., & Heck, R.H. (1993). Organizational culture and performance: Proposing and testing a model. Organization Science, 4(2), 209-225.

Marcoulides, G.A., & Schumacker, R.E. (Editors) (1995). Advanced structural equation modeling: issues and techniques. Lawrence Earlbaum Associates, Inc.

GEORGE A. MARCOULIDES is Professor of Statistics in the Department of Management Science at California State University - Fullerton and Adjunct Professor in the Graduate School of Management at the University of California - Irvine. He is the recipient of the 1991 UCEA William J. Davis Memorial Award for outstanding scholarship. He is currenly president-elect of the Western Decision Sciences Institute, review editor of Structural Equation Modeling: A Multidisciplinary Journal, associate editor of The International Journal of Educational Management, and on the editorial board of several measurement and statistics journals. His research interests include generalizability theory and structural equation modeling.

If you are interested in writing a software review for a future issue of Decision Line, please contact Professor Jack Yurkiewicz at the address below.

Professor Jack Yurkiewicz
Pace University
212-346-1908
e-mail: yurk@pacevm.dac.pace.edu