# [R] multinomial logistic regression with equality constraints?

Walter Mebane wrm1 at macht.arts.cornell.edu
Sun Feb 4 02:17:36 CET 2007

Roger,

summary(multinomRob(list(y1 ~ x1 + x2,y2 ~ x1 + x2, y3 ~ 0),data=d,
print.level=1))

Walter Mebane

Roger Levy writes:
> Many thanks for pointing this out to me!
>
> I'm still a bit confused, however, as to how to use multinomRob.  For
> example I tried to translate the following example using nnet:
>
>
> x1 <- c(1,1,1,1,0,0,0,0,0,0,0,0)
> x2 <- c(0,0,0,0,1,1,1,1,0,0,0,0)
> y <- factor(c("a","b","b","c","a","b","c","c","a","a","b","c"))
> library(nnet)
> d <- data.frame(x1,x2,y)
> summary(multinom(y ~ x1 + x2, data=d))
>
>
> into multinomRob as follows:
>
>
> x1 <- c(1,1,1,1,0,0,0,0,0,0,0,0)
> x2 <- c(0,0,0,0,1,1,1,1,0,0,0,0)
> y <- factor(c("a","b","b","c","a","b","c","c","a","a","b","c"))
> y1 <- ifelse(y=="a",1, 0)
> y2 <- ifelse(y=="b", 1, 0)
> y3 <- ifelse(y=="c", 1, 0)
> d <- data.frame(x1,x2,y,y1,y2,y3)
> summary(multinomRob(list(y1 ~ x1 + x2,y2 ~ x1 + x2, y3 ~ x1 + x2),data=d))
>
> but the last command gives me the error message:
>
>
> [1] "multinomMLE: Hessian is not positive definite"
> Error in obsformation %*% opg : non-conformable arguments
>
>
> though it's not obvious to me why.  I also tried a couple other variants:
>
>
>  > summary(multinomRob(list(y1 ~ 0,y2 ~ x1 + x2,y3 ~ x1 + x2),data=d))
> Error in multinomT(Yp = Yp, Xarray = X, xvec = xvec, jacstack =
> jacstack,  :
>          (multinomT): invalid specification of Xarray (regressors not
> allowed for last category
>  > summary(multinomRob(list(y1 ~ 0,y2 ~ x1 ,y3 ~ x2),data=d))
> Error in multinomT(Yp = Yp, Xarray = X, xvec = xvec, jacstack =
> jacstack,  :
>          (multinomT): invalid specification of Xarray (regressors not
> allowed for last category
>
>
> Any advice would be much appreciated!
>
>
> Many thanks,
>
> Roger
>
> Walter Mebane wrote:
> > By default, with print.level=0 or greater, the multinomRob program
> > prints the maximum likelihood estimates with conventional standard
> > errors before going on to compute the robust estimates.
> >
> > Walter Mebane
> >
> > Jasjeet Singh Sekhon writes:
> >  >
> >  > Hi Roger,
> >  >
> >  > Yes, multinomRob can handle equality constraints of this type---see
> >  > the 'equality' option.  But the function assumes that the outcomes are
> >  > multinomial counts and it estimates overdispersed multinomial logistic
> >  > models via MLE, a robust redescending-M estimator, and LQD which is
> >  > another high breakdown point estimator.  It would be a simple matter
> >  > to edit the 'multinomMLE' function to work without counts and to do
> >  > straight MNL instead, but right now it estimates an overdispersed MNL
> >  > model.
> >  >
> >  > Cheers,
> >  > Jas.
> >  >
> >  > =======================================
> >  > Jasjeet S. Sekhon
> >  >
> >  > Associate Professor
> >  > Travers Department of Political Science
> >  > Survey Research Center
> >  > UC Berkeley
> >  >
> >  > http://sekhon.berkeley.edu/
> >  > V: 510-642-9974  F: 617-507-5524
> >  > =======================================
> >  >
> >  >
> >  >
> >  > Roger Levy writes:
> >  >  > I'm interested in doing multinomial logistic regression with equality
> >  >  > constraints on some of the parameter values.  For example, with
> >  >  > categorical outcomes Y_1 (baseline), Y_2, and Y_3, and covariates X_1
> >  >  > and X_2, I might want to impose the equality constraint that
> >  >  >
> >  >  >    \beta_{2,1} = \beta_{3,2}
> >  >  >
> >  >  > that is, that the effect of X_1 on the logit of Y_2 is the same as the
> >  >  > effect of X_2 on the logit of Y_3.
> >  >  >
> >  >  > Is there an existing facility or package in R for doing this?  Would
> >  >  > multinomRob fit the bill?
> >  >  >
> >  >  > Many thanks,
> >  >  >
> >  >  > Roger
> >  >  >
> >  >  >
> >  >  > --
> >  >  >
> >  >  > Roger Levy                      Email: rlevy at ucsd.edu
> >  >  > Assistant Professor             Phone: 858-534-7219
> >  >  > Department of Linguistics       Fax:   858-534-4789
> >  >  > UC San Diego                    Web:   http://ling.ucsd.edu/~rlevy
> >  >  >
> >  >  >
> >

--
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Walter R. Mebane, Jr.                        email:  wrm1 at cornell.edu
Professor                             office voice:  607/255-3868
Department of Government                      cell:  607/592-0546
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