Multinomial Regression Tanh Estimatorpackage:multinomRobR Documentation

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_D_e_s_c_r_i_p_t_i_o_n:

     '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.

_U_s_a_g_e:

     multinomTanh(Y, Ypos, X, jacstack, xvec, tvec, pop, s2,
                         xvar.labels, choice.labels, print.level = 0)

_A_r_g_u_m_e_n_t_s:

       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.

_D_e_t_a_i_l_s:

     The tanh estimator is a redescending M-estimator.  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.

_V_a_l_u_e:

     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 the
          'choice.labels' vector:  column 'i+1' is named
          'paste("weights:",choice.labels[i],sep="")'.

          If 'sum(Ypos[i,]==FALSE)>0', then values of 'NA' appear in
          'weights[i,]', with
          'sum(is.na(weights[i,]))==sum(!Ypos[i,])'. The 'NA' values
          will be the last values in the affected row of the 'weights'
          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 the 'choice.labels' vector:  column 'i+1'
          is named 'paste("Hdiag:",choice.labels[i],sep="")'.

          If 'sum(Ypos[i,]==FALSE)>0', then values of 0 appear in
          'Hdiag[i,]', with 'sum(is.na(Hdiag[i,]))==sum(!Ypos[i,])'.
          The '0' values created for this reason will be the last
          values in the affected row of the 'Hdiag' 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.

_A_u_t_h_o_r(_s):

     Walter R. Mebane, Jr., Cornell University, wrm1@cornell.edu, <URL:
     http://macht.arts.cornell.edu/wrm1/> 

     Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu, <URL:
     http://sekhon.polisci.berkeley.edu/>

_R_e_f_e_r_e_n_c_e_s:

     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): 391-410 . <URL:
     http://macht.arts.cornell.edu/wrm1/multinom.pdf>

     For the most current code and related material see <URL:
     http://sekhon.polisci.berkeley.edu/robust/>

