Analysis of Ordinal Variables Part 2: Cross-Sectional Data
Karl G. Joreskog
October 18, 2001
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 then be printed using
Adobe's Acrobat Reader (version 4 and higher). This document is hard to read on screen, because it uses the Computer
Modern fonts from the LaTeX typesetting system that were designed for printing.
Note that there is a patch file available to upgrade
LISREL 8.50 to LISREL 8.51. This patch includes the data and examples referred to in this
contribution. Once this patch is applied, a subfolder named ordinal will be created in your LISREL folder.
The data and example files will be automatically installed to this folder. If you wish to download only the input
files and datasets, you can alternatively download the the ordinal2.zip.
The contents of this column are briefly described below.
"This is the second note of a sequence of notes on the analysis of ordinal variables with LISREL. Since
the release of LISREL 8.50 in June 2001 we have added some new features in PRELIS to improve data screening and
other procedures. To explain the differences between the two versions, I will refer to this as PRELIS 2.51 in this
In the previous note I introduced
a small data set of six variables from the cross-sectional USA sample of the Political Action Survey. After imputation
of some missing values and listwise deletion after imputation I ended up with 1589 cases with complete data on
all six variables.
The six variables are the responses to the following six questionnaire items:
- NOSAY: People like me have no say in what the government does
- VOTING: Voting is the only way that people like me can have any say about how the government runs things.
- COMPLEX: Sometimes politics and government seem so complicated that a person like me cannot really understand
what is going on.
- NOCARE: I don't think that public officials care much about what people like me think.
- TOUCH: Generally speaking, those we elect to Congress in Washington lose touch with the people pretty quickly.
- INTEREST: Parties are only interested in people's votes but not in their opinions.
The responses to these statements were agree strongly (AS), agree (A), disagree (D), and disagree strongly (DS).
These responses were coded 1, 2, 3, 4, respectively.
Political scientists assume that these items measure a uni-dimensional trait called political efficacy which
has been defined as the feeling that individual political action does have, or can have, an impact upon the political
process (Campbell, et al, 1954). In this note I will demonstrate how the assumption of uni-dimensionality can be
tested. I will also describe the statistical model used in PRELIS and LISREL for this purpose and discuss the assumptions
of this model."