Covariance Structure and Structural Equation Modelling in Research: A Conceptual Overview of Lisrel Modelling

Abstract

The principal objective of this paper is to demonstrate conceptually the relationship between various modelling techniques commonly employed in data analysis in social and behavioral research. The paper focuses on the commonalities between such multivariate techniques as path analysis, regression analysis, panel models, longitudinal models, common factor analysis, higher order factor analysis, factorial models (eg multitrait-multimethod models), test score models, error structure analysis models and the ANOVA model.

It shows how the covariance structure model which underlies the
LISREL model can be employed to reconceptualise and parameterise
each of the above models in terms of a more general framework. In
particular, these models can be conceptualised as a specific
configuration of the sub-models which comprise the LISREL model.
The measurement and structural models of the general covariance
model are employed as the basic building blocks to reconceptualise
the specific models on which each of the various techniques are based. The LISREL model has been chosen as the vehicle for demonstrating these conceptual commonalities because it is the most widely used general covariance structure model. Although other models such as COASN (McDonald, 1978) EQS (Bentler, 1982) and LACCI (Muthen, 1983) are similar to the LISREL model and will thus also allow for the parameterisation of the models discussed in this paper, the associated computer programs for estimating them are not as yet widely used as the LISREL model. 

Significant advances have been incorporated into the recently released version V of the LISREL program. In particular, the
program now includes a procedure which automatically estimates a
set of initial start values for the iteration process in the
maximum liklihood method of estimation. The provision of these
start values by the user had been a major obstacle to the use of.
the program in previous versions. Version V also provides a wider
range of statistics for judging the fit of the model, in addition
to an option for estimating relationships between 'discrete'
variables and another for using a least squares estimation
procedure where the assumptions underlying the maximum liklihood
model are not met by the data and model under investigation.

Further, the LISRJEL program is soon to be interfaced to one of the most widely used packages available in the social, behavioral
and medical sciences. It is expected that this will mean a much
wider availability and use of the program than has been the case
hitherto.

The paper is written and presented in a schematic and didactic
style suited to novice modellers in social and behavioral research.
The only requirement is that readers have an idea of and some
previous experience with at least one or two of the multivariate
techniques mentioned in the opening paragraph above. They are not
required to have an understanding of matrix algebra or statistics
in general. Path diagrams are employed as visual representations
of the conceptual models.