Multinomial Regression Tanh Estimator
Multinomial Regression Hyperbolic Tangent (Tanh) Estimator
multinomTanh
fits the overdispersed multinomial regression
model for grouped count data using the hyperbolic tangent (tanh)
estimator. This function is not meant to be called directly by the
user. It is called by multinomRob
, which constructs the
various arguments.
 Keywords
 robust, models, regression
Usage
multinomTanh(Y, Ypos, X, jacstack, xvec, tvec, pop, s2, xvar.labels, choice.labels, print.level = 0)
Arguments
 Y

Matrix (observations by alternatives) of outcome counts.
Values must be nonnegative. Missing data (
NA
values) are not allowed.  Ypos
 Matrix indicating which elements of Y are counts to be analyzed (TRUE) and which are values to be skipped (FALSE). This allows the set of outcome alternatives to vary over observations.
 X
 Array of regressors. dim(X) = c(observations, parameters, alternatives).
 jacstack
 Array of regressors used to facilitate computing the gradient and the hessian matrix. dim(jacstack) = c(observations, unique parameters, alternatives).
 xvec
 Matrix (parameters by alternatives) that represents the model structure. It has a 1 for an estimated parameter, an integer greater than 1 for an estimated parameter constrained equal to another estimated parameter (all parameters constrained to be equal to one another have the same integer value in xvec) and a 0 otherwize.
 tvec
 Starting values for the regression coefficient parameters, as a matrix (parameters by alternatives). Parameters that are involved in equality constraints are repeated in tvec.
 pop

Vector giving the total number of counts for each observation. In general,
pop < apply(Y * ifelse(Ypos,1,0), 1, sum)
.  s2
 Overdispersion value. In multinomRob this is the square of the LQD scale estimate.
 xvar.labels
 Vector of labels for observations.
 choice.labels
 Vector of labels for outcome alternatives.
 print.level
 Specify 0 for minimal printing (error messages only) or 2 to print details about the tanh computations.
Details
The tanh estimator is a redescending Mestimator. Given an estimate of the scale of the overdispersion, the tanh estimator estimates the coefficient parameters of the linear predictors of the multinomial regression model.
Value

multinomTanh returns a list of 5 objects. The returned objects are:
 mtanh

List of tanh estimation results from function
mGNtanh
.  weights

The matrix of tanh weights for the orthogonalized residuals. The matrix
has the same dimensions as the outcome count matrix
Y
. The first column of the matrix has names for the observations, and the remaining columns contain the weights. Each of the latter columns has a name derived from thechoice.labels
vector: columni+1
is namedpaste("weights:",choice.labels[i],sep="")
.Ifsum(Ypos[i,]==FALSE)>0
, then values ofNA
appear inweights[i,]
, withsum(is.na(weights[i,]))==sum(!Ypos[i,])
. TheNA
values will be the last values in the affected row of theweights
matrix, regardless of which outcome alternatives were unavailable for the observation.  Hdiag

The matrix of weights used to fully studentize the orthogonalized
residuals. The matrix has the same dimensions as the outcome count matrix
Y
. The first column of the matrix has names for the observations, and the remaining columns contain the weights. Each of the latter columns has a name derived from thechoice.labels
vector: columni+1
is namedpaste("Hdiag:",choice.labels[i],sep="")
.Ifsum(Ypos[i,]==FALSE)>0
, then values of 0 appear inHdiag[i,]
, withsum(is.na(Hdiag[i,]))==sum(!Ypos[i,])
. The0
values created for this reason will be the last values in the affected row of theHdiag
matrix, regardless of which outcome alternatives were unavailable for the observation.  cr
 List of predicted outcome counts, studentized residuals and standardized residuals.
 tvec

The tanh coefficient estimates in matrix format. The matrix has one
column for each outcome alternative. The label for each row of the matrix
gives the names of the regressors to which the coefficient values in the row
apply. The regressor names in each label are separated by a forward
slash (/), and
NA
is used to denote that no regressor is associated with the corresponding value in the matrix. The value 0 is used in the matrix to fill in for values that do not correspond to a regressor.
References
Walter R. Mebane, Jr. and Jasjeet Singh Sekhon. 2004. ``Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data.'' American Journal of Political Science 48 (April): 391410. http://sekhon.berkeley.edu/multinom.pdf
For additional documentation please visit http://sekhon.berkeley.edu/robust/.