Multinomial Multivariate-T Regressionpackage:multinomRobR Documentation

_M_u_l_t_i_n_o_m_i_a_l _M_u_l_t_i_v_a_r_i_a_t_e-_T _E_s_t_i_m_a_t_i_o_n

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

     'multinomT' fits the multinomial multivariate-t regression for
     grouped count data.  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:

     multinomT(Yp, Xarray, xvec, jacstack, start = NA, nobsvec, fixed.df = NA)

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

      Yp: Matrix (observations by alternatives) of outcome proportions.
          Values must be between 0 and 1.  Missing data ('NA' values)
          are not allowed.

  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).

   start: A list of starting values of three kinds of parameters:
          'start$beta', the values for the regression coefficients;
          'start$Omega', the values for the variance-covariance matrix;
          'start$df', the value for the multivariate-t degrees of
          freedom parameter.

 nobsvec: Vector of the total number of counts for each observation.

fixed.df: The degrees of freedom to be used for the multivariate-t
          distribution.  When this is specified, the DF will not be
          estimated.

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

     The function often provides good starting values for multinomRob's
     LQD estimator, but the standard errors it reports are not correct,
     in part because they ignore heteroscedasticity.

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

    call: Names and values of all of the arguments which were passed to
          the function.  See 'match.call' for further details.

    logL: Log likelihood.

deviance: Deviance.

     par: A list of three kinds of parameter estimates: 'par$beta', the
          estimates for the regression coefficients; 'par$Omega', the
          estimates for the variance-covariance matrix; 'par$df', the
          estimate of the multivariate-t degrees of freedom parameter.

      se: Vector of standard errors for the regression coefficients.
          WARNING: these are not correct in part because the model
          ignores heteroscedasticity.

   optim: Returned by 'optim'.

    pred: A matrix of predicted probabilities with the same dimentions
          as 'Yp'.

_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/>

_S_e_e _A_l_s_o:

     'match.call'.   'optim'.

