[R] multinomial logistic regression with equality constraints?

[Walter Mebane]

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
 > >  >  > 
 > >  >  > 
 > > 

-- 
* - * - * - * - * - * - * - * - * - * - * - * - * - * - * - * - * - *
Walter R. Mebane, Jr.                        email:  wrm1 at cornell.edu
Professor                             office voice:  607/255-3868    
Department of Government                      cell:  607/592-0546
Cornell University                             fax:  607/255-4530    
217 White Hall              WWW:  http://macht.arts.cornell.edu/wrm1/
Ithaca, NY 14853-7901
* - * - * - * - * - * - * - * - * - * - * - * - * - * - * - * - * - *