Analysis of Ordinal Variables Part 5: Covariates
Karl G. Joreskog
June 3, 2002
Because of the mathematical content and length of this contribution to Karl's Corner, we are only making
it available as a PDF file. It can be printed using Adobe's Acrobat Reader (version 4 and higher).
The zip file ordinal5.zip contains both the PDF
file and examples (input files and datasets). Note that you need version 8.52 of LISREL to run the examples.
The contents of this column are briefly described below.
This is the fifth note in a sequence of notes on the analysis of ordinal variables with LISREL. Karl refers
to these notes as Note 1, Note 2, etc. In all previous notes he assumed that all observed variables were ordinal.
Thus, in Note 2, he described the analysis of ordinal variables in cross-sectional studies; in Note 3, he described
the analysis of ordinal variables in longitudinal studies; and in Note 4, the analysis of ordinal variables observed
in several groups was discussed.
In this note, he considers the case when one or more ordinal variables are observed jointly with a set of possible
explanatory variables, so-called covariates. These covariates can be dummy-coded categorical variables or
measured variables on an interval scale. They are assumed not to contain measurement error. With PRELIS one can
estimate the effect of the covariates on the probability of response in various categories of the ordinal variables
using either the probit or logit model. PRELIS can also estimate the joint covariance matrix of the covariates
and the variables underlying the ordinal variables. This can be used for further modeling in LISREL.
Continuing his analysis of the Efficacy variables from the Political Action Survey, Karl illustrates the analysis
of the six Efficacy variables using four covariates: Gender, Age, Education, and a Left-Right Scale. For information
about the Political Action Survey and the Efficacy variables, see Note 1. As in Notes 2 and 4, only the data from
the USA sample is used.
Since probit and logit regression have not been well documented in the LISREL literature, a rather technical
description is given in Sections 1 to 5 of this note. Readers who are merely interested in how to do it with LISREL
can skip this and proceed to Section 6. New examples and data files are included in the downloadable ordinal5.zip