Multinomial Regression      package:multinomRob      R Documentation

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

     'multinomMLE' estimates the coefficients of the multinomial
     regression model for grouped count data by maximum likelihood,
     then computes a moment estimator for overdispersion and reports
     standard errors for the coefficients that take overdispersion into
     account. 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:

     multinomMLE(Y, Ypos, Xarray, xvec, jacstack, itmax=100, xvar.labels,
                        choice.labels, print.level)

_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.

  Xarray: Array of regressors.  dim(Xarray) = c(observations,
          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.

jacstack: Array of regressors used to facilitate computing the gradient
          and the hessian matrix. dim(jacstack) = c(observations,
          unique parameters, alternatives).

   itmax: The maximum number of iterations to be done in the
          Gauss-Newton optimization.

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 3
          to print details about the MLE computations.

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

     Following the generalized linear models approach, the coefficient
     parameters in an overdispersed multinomial regression model may be
     estimated using the likelihood for a standard multinomial
     regression model.  A moment estimator may be used for the
     dispersion parameter, given the coefficient estimates, with little
     efficiency loss.

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

     multinomMLE returns a list of 20 objects.  The returned objects
     are:

coefficients: The maximum likelihood coefficient estimates in matrix
          format.  The value 0 is used in the matrix to fill in for
          values that do not correspond to a regressor.

coeffvec: A vector containing the maximum likelihood coefficient
          estimates.

dispersion: Moment estimate of the dispersion:  mean sum of squared
          orthogonalized residuals (adjusted for degrees of freedom
          lost to estimated coefficients).

      se: The tanh coefficient estimate standard errors in matrix
          format.  The format and labelling used for the matrix is the
          same as is used for the 'coefficients'.  The standard errors
          are derived from the estimated asymptotic sandwich covariance
          estimate.

  se.opg: The tanh coefficient estimate standard errors derived from
          the asymptotic covariance estimated using the outer product
          of the gradient (expected information) divided by the moment
          estimate of the dispersion.

  se.hes: The tanh coefficient estimate standard errors derived from
          the asymptotic covariance estimated using the hessian matrix
          (observed information).

  se.vec: A vector containing the tanh coefficient sandwich estimate
          standard errors.

se.opg.vec: A vector containing the tanh coefficient OPG estimate
          standard errors.

       A: The outer product of the gradient (expected information)
          divided by the moment estimate of the dispersion.

       B: The inverse of the hessian matrix (observed formation).

  covmat: Sandwich estimate of the asymptotic covariance of the maximum
          likelihood coefficient estimates.

   iters: Number of Gauss-Newton iterations.

   error: Exit error code.

  GNlist: List reporting final results of the Gauss-Newton
          optimization.  Elements: 'coefficients', vector of
          coefficient parameters (same as 'coeffvec' value in list
          returned by multinomMLE);  'tvec', matrix of coefficient
          parameters (same as 'coefficients' value in list returned by
          multinomMLE); 'formation', inverse Hessian matrix;  'score',
          score (or gradient element) matrix;  'LLvals', list
          containing log-likelihood value; 'convflag', TRUE/FALSE
          convergence flag;  'iters', number of iterations done in
          final Gauss-Newton stage;  'posdef', TRUE if Hessian is
          positive definite.

  sigma2: Moment estimate of the dispersion:  mean sum of squared
          orthogonalized residuals (adjusted for degrees of freedom
          lost to estimated coefficients).

       Y: The same 'Y' matrix that was supplied as input, except
          modified by  having done 'Y[!Ypos] <- 0'.

    Ypos: The same 'Ypos' matrix that was supplied as input.

fitted.prob: The matrix of predicted probabilities for each category
          for each observation based on the coefficient estimates.

jacstack: The same 'jacstack' that was supplied as an input argument.

_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/>

