An essential feature of these applications is that only the dependent variable or the observed response is assumed to be subject to measurement error or other uncontrolled variation. That is, there is only one random variable in the picture. The independent variable or treatment level is assumed to be fixed by the experimenter at known predetermined values. The only exception to this formulation is the empirical prediction problem. For that purpose, the investigator observes certain values of one or more predictor variables and wishes to estimate the mean and variance of the distribution of a criterion variable among respondents with given values of the predictors. Because the prediction is conditional on these known values, they may be considered fixed quantities in the regression model. An example is predicting the height that a child will attain at maturity from his or her current height and the known heights of the parents. Even though all of the heights are measured subject to error, only the childs height at maturity is considered a random variable.

Where ordinary regression methods no longer suffice, and indeed give misleading results, is in purely observational studies in which all variables are subject to measurement error or uncontrolled variation and the purpose of the inquiry is to estimate relationships that account for variation among the variables in question. This is the essential problem of data analysis in those fields where experimentation is impossible or impractical and mere empirical prediction is not the objective of the study. It is typical of almost all research in fields such as sociology, economics, ecology, and even areas of physical science such as geology and meteorology. In these fields, the essential problem of data analysis is the estimation of structural relationships between quantitative observed variables. When the mathematical model that represents these relationships is linear we speak of a linear structural relationship. The various aspects of formulating, fitting, and testing such relationships we refer to as structural equation modeling.

Although structural equation modeling has become a prominent form of data analysis only in the last twenty years (thanks in part to the availability of the LISREL program), the concept was first introduced nearly eighty years ago by the population biologist, Sewell Wright, at the University of Chicago. He showed that linear relationships among observed variables could be represented in the form of so-called path diagrams and associated path coefficients. By tracing causal and associational paths on the diagram according to simple rules, he was able to write down immediately the linear structural relationship between the variables. Wright applied this technique initially to calculate the correlation expected between observed characteristics of related persons on the supposition of Mendelian inheritance. Later, he applied it to more general types of relationships among persons.

Today, however, LISREL for Windows is no longer limited to SEM. The latest LISREL for Windows includes the following statistical applications.

• LISREL for structural equation modeling.
• PRELIS for data manipulations and basic statistical analyses.
• MULTILEV for hierarchical linear and non-linear modeling.
• SURVEYGLIM for generalized linear modeling.
• CATFIRM for formative inference-based recursive modeling for categorical response variables.
• CONFIRM for formative inference-based recursive modeling for continuous response variables.
• MAPGLIM for generalized linear modeling for multilevel data.

The PRELIS, LISREL and SIMPLIS manuals (as PDF) are included with the LISREL program.

New features in LISREL 8.8 for Windows

• Structured latent curve models
  The LISREL CO command has been extended to include the exponential (EXP) and natural logarithm (LOG) operators as well as parentheses. This allows LISREL users to fit, for example, the structured latent curve models outlined in Browne (1993).
  
  
• Factor analysis of ordinal variables
  Classical exploratory factor analysis assumes that the observed variables are continuous. The PRELIS OFA command implements exploratory factor analysis of ordinal variables as described in Jöreskog & Moustaki (2006).
  
  
• Generalized linear models (GLIMs) for multilevel data
  The new statistical application MAPGLIM fits generalized linear models to multilevel data. Users can select from the multinomial, Bernoulli, Poisson, binomial, negative binomial, Normal, Gamma and inverse Gaussian sampling distributions. The corresponding link functions include the log, cumulative logit, cumulative probit, complementary log-log and logit link functions.
  
  
• Observational residuals
  Bollen and Arminger (1991) introduced observational residuals for structural equation models. LISREL 8.8 for Windows allows users to compute observational residuals along with latent variable scores for the latent variables of the model. This implementation is described and illustrated in Jöreskog, Sörbom & Wallentin (2006)
  
  
• Writing parameter estimates, standard error estimates and measures of fit to a PSF
  The PV, SV and GF keywords on the LISREL OU command or the SIMPLIS LISREL output command have been extended to allow users to save the parameter estimates, standard error estimates and measures of fit to a PSF. This is especially useful for Monte Carlo studies.
  
  
• Changes to the graphical user interface (GUI)
  The main window of LISREL 8.8 for Windows is now entitled LISREL for Windows. The revised Export Data option on the File menu of the main window allows users to export data to various data formats such as SPSS, SAS, SYSTAT, Statistica, etc.