Lisrel

LISREL—an abbreviation of linear structural relationships—is a statistical software package primarily dedicated to estimating structural equation models (SEMs) although it can handle a variety of other statistical models. SEM unifies several estimation methods into one analytic framework. The methodology has received considerable attention in education research where it has been used to develop and validate measurement instruments, estimate the relationship between students’ development over time and various outcomes of interest, and assess the simultaneous independent effect of a program on students’ achievements.

LISREL’s target uses are students, applied researchers, and practitioners interested in SEM. It is commonly used in the areas of education, psychology, and other social science disciplines. This entry discusses the development of LISREL and then provides an overview of the LISREL statistical package and its modeling capabilities.

Designed in the early 1970s by Karl Jöreskog and Dag Sörbom, LISREL was the first dedicated software package developed for SEM. Since then, it has set the standard in SEM software and served as a prototype for many other SEM programs, such as Amos, EQS, and Mplus. LISREL’s name, notation, and modeling approach have become synonymous with SEM methodology itself. Indeed, SEMs are often referred to as LISREL models, and LISREL notation using Greek characters is often used to specify SEMs in a text.

The LISREL model bridged two distinct statistical traditions: psychometrics and econometrics. The psychometric tradition is reflected in the measurement component of SEM, in which a matrix of observed variables are used to estimate a set of latent, or unobserved, variables. These latent variables can also be referred to as factors. Exploratory factor analysis and confirmatory factor analysis are two common measurement techniques in SEM. The econometric tradition is manifested in the structural component of SEM, in which simultaneous regression equations are used to test hypothesized relationships between a set of latent and/or observed variables. Observed variables can also be referred to as items, indicators, [Page 978]or manifest variables. A researcher then determines how tenable the estimated relationships are, given the observed correlations or covariances between the variables.

The most general SEM is defined by three matrix equations specified using LISREL notation: the measurement model for the latent exogenous variables x = ∧xη + δ, the measurement model for the latent endogenous variables y = ∧yη + ε, and the structural model η = Bη + Γξ + ζ, where Λx, Λy B, and Γ are coefficient matrices and δ, ε, and ζ are vectors of latent variables.

The version of the LISREL software package released in 2015 is 9.20. The package is distributed as a 32-bit application for Windows computers. The core of the package is written in FORTRAN, but its vendor—Scientific Software International Inc. (Skokie, IL)—developed a visual interface in C/C++.