Date: Tue, 16 Apr 1996 15:22:27 GMT
Reply-To: John Hendrickx <J.Hendrickx@MAW.KUN.NL>
Sender: "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From: John Hendrickx <J.Hendrickx@MAW.KUN.NL>
Organization: Nijmegen University
Subject: special constraints in multinomial logistic models
I've placed information on multinomial conditional logistic (MCL)
regression models on my home page
<http://www.socsci.kun.nl/maw/sociologie/J.Hendrickx/mcl/>, together
with macro programs and sample programs. These models can be used to
impose special restrictions on multinomial logistic regression models,
as described below.
A limitation of the multinomial logistic (MNL) regression model is that
it allows only one response function (the type of restriction imposed on
the dependent variable) for all independent variables in the model. If
more flexibility is required in the specification of response functions,
then a conditional logit (ML) model can be used to estimate the MNL
model.The CL model is a more flexible form of the MNL model. It uses
both choices and explanatory variables as independent variables. This
means that the explanatory variables need not affect all choices. If the
explanatory variables do affect all choices, then the CL model yields
identical outcomes to an MNL model.
A special type of nonlinear constraint on the response variable is the
stereotyped ordered regression (SOR) model (Anderson 1984, DiPrete
1990). The SOR model estimates a scaling metric for the dependent
variable and uses this to scale the effects of the covariates in the
model. The effects of the covariates can thus be expressed in a single
parameter, without assuming ordered categories of the dependent
variable. I have written macro programs for estimating the SOR model by
iteratively fitting CL models, using the packages STATA and SAS.
A second application of the CL model is to include models for square
tables such as applied in mobility research (Hout 1983) within MNL
models (Logan 1983, Breen 1994). Sample programs using STATA, SAS, SPSS,
GLIM, and LIMDEP are available.
The nonlinear row and columns model 2 (Goodman 1979) estimates a scaling
metric for the dependent variable and a categorical independent
variable, allowing their association to be expressed in a single
parameter. It can be included in an MNL model using macro programs
written for STATA and SAS.
Anderson, J.A. (1984).
Regression and Ordered Categorical Variables. Journal of the Royal
Statistical Society, Series B 46: 1-30.
Breen, Richard. (1994).
Individual Level Models for Mobility Tables and Other
Cross-Classifications. Sociological Methods & Research 33: 147-173.
DiPrete, Thomas A. (1990).
Adding Covariates to Loglinear Models for the Study of Social Mobility.
American Sociological Review 55: 757-773.
Goodman, Leo A. (1979).
Multiplicative models for the analysis of occupational mobility tables
and other kinds of cross-classification tables. American Journal of
Sociology 84: 804-819.
Hendrickx, John. (1995).
Multinomial Conditional Logit Models for the Analysis of Status
Attainment and Mobility. ICS Working Papers - 1. Available on request.
Hout, Michael. (1983).
Mobility Tables. Beverly Hills: Sage Publications.
Logan, John A. (1983).
A Multivariate Model for Mobility Tables. American Journal of Sociology
89: 324-349.
John Hendrickx
Department of Sociology
Nijmegen University
The Netherlands
