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LISREL
LISREL, which is an acronym for linear structural relations, is a statistical program package particularly designed to estimate structural equation models (SEMs). It can also been used for several other types of analysis, such as data manipulation, exploratory data analyses, and regression, as well as factor analytic procedures. In the past few decades, SEM has become an increasingly popular technique for the analysis of nonexperimental data in the social sciences. Among programs from which researchers wishing to apply SEM might choose, such as AMOS, EQS, Mplus, SAS CALIS, and RAMONA among many others, LISREL is arguably the most longstanding and widely used tool. Notably, LISREL has been the prototype for many later developed SEM programs. After a brief history, this entry discusses the LISREL model and its execution.
Background and Brief History
The LISREL model and computer program was developed in the 1970s by Karl G. Jöreskog and Dag Sörbom, who were both professors at Uppsala University, Sweden. In 1973, Jöreskog discovered a “maximum likelihood estimation” computational procedure and created a computer program for fitting factor models to data based on this estimation. A few years later, he, together with Sörbom, developed a program called LISREL, which incorporates maximum likelihood estimation procedures for both confirmatory factor analysis and the linear structural model among factors. To date, LISREL has undergone a few revisions. LISREL is available on a variety of operation systems such as Microsoft Windows, Macintosh, Mainframe, and UNIX. The most current version as of December 2008 is LISREL 8.8.
The General LISREL Model
In general, LISREL estimates the unknown coefficients of a set of linear structural equations. A full LISREL model consists of two submodels: the measurement model and the structural equation model. These models can be described by the following three equations:
Types of Variables
In specifying structural equation models, one needs to be familiar with several types of variables. LISREL distinguishes variables between latent variables and observed variables. Latent variables are variables that are not observed or measured directly. They are theoretical concepts that can only be indexed by observed behaviors. Of the two types of latent variables, exogenous variables are variables that are not influenced by other variables in the model, whereas endogenous variables are the ones influenced by other variables. In other words, exogenous latent variables are independent variables and endogenous variables are dependent variables, which are influenced by the exogenous variables in the model.
The Measurement Model
The measurement model (also known as the CFA model) specifies how latent variables or hypothetical constructs are indicated by the observed variables. It is designed particularly to describe the measurement properties of the observed variables. It can be specified as X variables or Y variables.
The Structural Equation Model
The structural model describes the causal relations among latent variables, or how the latent variables are linked to each other. In addition, it assigns the explained and unexplained variance.
Greek Notation and Matrices in LISREL
The command language of LISREL is based on a matrix representation of the confirmatory factor analysis or full structural equation model. Prior to version 8, LISREL required the use of Greek letters to specify models. Later on, LISREL used Greek as well as English, which was made possible by the SIMPLIS command language. However, familiarity with LISREL matrices and their Greek representation is helpful to master this program fully.
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