Ordered Logit Models – Page 1
Ordered Logit Models - Overview
This is adapted heavily from Menard’s Applied Logistic Regression analysis; also, Borooah’s
Logit and Probit: Ordered and Multinomial Models; Also, Hamilton’s Statistics with Stata,
Updated for Version 7.
We have talked about the analysis of dependent variables that have only two possible values, e.g.
lives or dies, wins or loses, gets an A or doesn’t get an A. Of course, many dependent variables
of interest will have more than two possible categories. These categories might be unordered
(doesn’t move, moves South, moves East) or ordered (high, medium, low; favors more
immigration, thinks the level of immigration is about right, favors less immigration). We will
briefly discuss techniques for handling each of these.
Ordinal Regression
As Menard notes, when dependent variables are measured on an ordinal scale, there are many
options for their analysis. These include
Treating the variable as though it were continuous. In this case, just use OLS regression
or the other techniques we have discussed for continuous variables. Certainly, this is
widely done, particularly when the DV has 5 or more categories. Since this is probably
the easiest approach for readers to understand, sometimes the other approaches are tried
just to confirm that the use of OLS does not seriously distort the findings.
Ignoring the ordinality of the variable and treating it as nominal. i.e. use multinomial
logit techniques like those we will discuss later. The key problem here is a loss of
efficiency. By ignoring the fact that the categories are ordered, you fail to use some of the
information available to you, and you may estimate many more parameters than is
necessary. This increases the risk of getting insignificant results. But, your parameter
estimates still should be unbiased.
Treating the variable as though it were measured on a true ordinal scale. For example, the
professorial ranks of Full Professor, Associate Professor, and Assistance Professor are
ordered but you may or may not think they reflect crude measurement of some
underlying continuous variable. Stereotype logistic regression models (estimated by
slogit
in Stata) might be used in such cases.
Treating the variable as though it were measured on an ordinal scale, but the ordinal scale
represented crude measurement of an underlying interval/ratio scale. For example, the
categories “High, Medium, Low” might be rough measures for Socio-economic status or
intelligence. Ordered logit models can be used in such cases, and they are the primary
focus of this handout.