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
- 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
- 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
- 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.