mnp                   package:MNP                   R Documentation

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

     'mnp' is used to fit the (Bayesian) Multinomial Probit models via
     Markov chain Monte Carlo. Along with the standard Multinomial
     Probit model, it can also fit models with different choice sets
     for each observation, and complete or partial ordering of all the
     available alternatives. The computation uses the efficient
     marginal data augmentation algorithm that is developed by Imai and
     van Dyk (2004).

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

     mnp(formula, data = parent.frame(), choiceX = NULL, cXnames = NULL,
         base = NULL, latent = FALSE, n.draws = 5000, p.var = "Inf",
         p.df = n.dim+1, p.scale = 1, coef.start = 0, cov.start = 1,
         burnin = 0, thin = 0, verbose = FALSE) 

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

 formula: A symbolic description of the model to be fit specifying the
          response variable and covariates. The formula should  not
          include the choice-specific covariates. Details and specific
          examples are given below.  

    data: An optional data frame in which to interpret the variables in
          'formula' and 'choiceX'. The default is the environment in
          which 'mnp' is called. 

 choiceX: An optional list containing a matrix of choice-specific
          covariates for each category. Details and examples are
          provided below. 

 cXnames: A vector of the names for the choice-specific covariates
          specified in 'choiceX'. The details and examples are provided
          below. 

    base: The name of the base category. For the standard Multinomial
          Probit model, the default is the lowest level of the response
          variable. For the Multinomial ordered Probit model, the
          default base category will be the last column in the matrix
          of response variables. 

  latent: logical. If 'TRUE', then the latent variable W will be
          returned. The default is 'FALSE' 

 n.draws: A positive integer. The number of MCMC draws. The default is
          '5000'. 

   p.var: A positive definite matrix. The prior variance of the
          coefficients.  A scalar input can set the prior variance to
          the diagonal matrix whose diagonal element is equal to that
          value. The default is '"Inf"', which represents an improper
          noninformative prior on the coefficients.    

    p.df: A positive integer greater than 'n.dim-1'. The prior degree
          of freedom parameter for the covariance matrix. The default
          is 'n.dim+1', which is equal to the total number of
          alternatives. 

 p.scale: A positive definite matrix whose first diagonal element is
          set to '1'. The prior scale matrix for the covariance matrix.
          The first diagonal element will be set to 1 if it is not
          equal to 1 already. A scalar input can be used to set the
          scale matrix to a diagonal matrix with diagonal elements
          equal to the scalar input value, except that the first
          diagonal element will be set to one. The default is '1'. 

coef.start: A vector. The starting values for the coefficients. A
          scalar input will set the starting values for all the
          coefficients equal to that value.  The default is '0'. 

cov.start: A positive definite matrix whose first diagonal element is
          set to '1'. The starting values for the covariance matrix.
          The first diagonal element will be set to 1 if it is not
          equal to 1 already. A scalar input can be used to set the
          starting value to a diagonal matrix with diagonal elements
          equal to the scalar input value, except that the first
          diagonal element will be set to one. The default is '1'.  

  burnin: A positive integer. The burnin interval for the Markov chain;
          i.e., the number of initial Gibbs draws that should not be
          stored. The default is '0'.  

    thin: A positive integer. The thinning interval for the Markov
          chain; i.e., the number of Gibbs draws between the recorded
          values that are skipped. The default is '0'.  

 verbose: logical. If 'TRUE', helpful messages along with a progress
          report (every 10%) of the Gibbs sampling are printed on the
          screen. The default is 'FALSE'. 

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

     For *the standard Multinomial Probit model* where only the most
     preferred choice is observed, use the syntax, 'y ~ x1 + x2', where
     'y' is a factor variable indicating the most preferred choice and
     'x1' and 'x2' are individual-specific covariates. The interactions
     of individual-specific variables with each of the choice indicator
     variables will be fit.

     To specify *choice specific covariates*, use the syntax,
     'choiceX=list(A=cbind(z1, z2), B=cbind(z3, z4), C=cbind(z5, z6))',
     where 'A', 'B', and 'C' represent the choice names of the response
     variable, and 'z1' and 'z2' are each vectors of length n that
     record the values of the two choice-specific covariates for each
     individual for choice A, likewise for 'z3', ..., 'z6'. The
     corresponding variable names via 'cXnames=c("price", "quantity")'
     need to be specified, where 'price' refers to the coefficient name
     for 'z1', 'z3', and 'z5', and 'quantity' refers to that for 'z2',
     'z4', and 'z6'.

     If *the choice set* varies from one observation to another, use
     the syntax, 'cbind(y1, y2, y3) ~ x1 + x2', in the case of a three
     choice problem, and indicate unavailable alternatives by 'NA'. If
     only the most preferred choice is observed, y1, y2, and y3 are
     indicator variables that take on the value one for individuals who
     prefer that choice and zero otherwise. The last column of the
     response matrix, 'y3' in this particular example syntax, is used
     as the base category.

     For *the Multinomial ordered Probit model* where the complete or
     partial ordering of the available alternatives is recorded, use
     the same syntax as when the choice set varies (i.e., 'cbind(y1,
     y2, y3, y4) ~ x1 + x2'). For each observation, all the available
     alternatives in the response variables should be numerically
     ordered in terms of preferences such as '1 2 2 3'. Ties are
     allowed. The missing values in the response variable should be
     denoted by 'NA'. The software will impute these missing values
     using the specified covariates. The resulting uncertainty
     estimates of the parameters will properly reflect the amount of
     missing data. For example, we expect the standard errors to be
     larger when there is more missing data.

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

     An object of class 'mnp' containing the following elements: 

   param: A matrix of the Gibbs draws for each parameter; i.e., the
          coefficients and covariance matrix. For the covariance
          matrix, the elements on or above the diagonal are returned. 

    call: The matched call.

       x: The matrix of covariates.

       y: The vector or matrix of the response variable.

       w: The three dimensional array of the latent variable, W. The
          first dimension represents the alternatives, and the second
          dimension indexes the observations. The third dimension
          represents the Gibbs draws. Note that the latent variable for
          the base category is set to 0, and therefore omitted from the
          output.

   n.alt: The total number of alternatives.

   p.var: The prior variance for the coefficients.

    p.df: The prior degrees of freedom parameter for the covariance
          matrix.

 p.scale: The prior scale matrix for the covariance matrix.

  burnin: The number of initial burnin draws.

    thin: The thinning interval.

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

     Kosuke Imai, Department of Politics, Princeton University
     kimai@Princeton.Edu, <URL: http://www.princeton.edu/~kimai>;
     Jordan R. Vance, Princeton University; David A. van Dyk,
     Department of Statistics, University of California, Irvine
     dvd@uci.edu, <URL: http://www.ics.uci.edu/~dvd>.

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

     Imai, Kosuke and David A. van Dyk. (2004) "A Bayesian Analysis of
     the Multinomial Probit Model Using the Marginal Data
     Augmentation," _Journal of Econometrics_, Forthcoming. <URL:
     http://www.princeton.edu/~kimai/research/mnp.html>

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

     'summary.mnp'; MNP home page at <URL:
     http://www.princeton.edu/~kimai/research/MNP.html>

_E_x_a_m_p_l_e_s:

     ## load the detergent data
     data(detergent)
     ## run the standard Multinomial Probit model with intercepts and the price
     res1 <- mnp(choice ~ 1, choiceX = list(Surf=Surf, Tide=Tide, Wisk=Wisk,
                                            EraPlus=EraPlus, Solo=Solo, All=All),
                 cXnames = "price", data = detergent, n.draws = 500, burnin = 100,
                 thin = 3, verbose = TRUE) 
     summary(res1)

     ## load the Japanese election data
     data(japan)
     ## run the Multinomial ordered Probit model
     res2 <- mnp(cbind(LDP, NFP, SKG, JCP) ~ sex + education + age, data = japan,
                 verbose = TRUE)
     summary(res2)

