mnp  R Documentation 
mnp
is used to fit (Bayesian) multinomial probit model via Markov
chain Monte Carlo. mnp
can also fit the model 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 (2005a).
mnp(formula, data = parent.frame(), choiceX = NULL, cXnames = NULL, base = NULL, latent = FALSE, invcdf = FALSE, trace = TRUE, 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)
formula 
A symbolic description of the model to be fit specifying the response variable and covariates. The formula should not include the choicespecific covariates. Details and specific examples are given below. 
data 
An optional data frame in which to interpret the variables in

choiceX 
An optional list containing a matrix of choicespecific covariates for each category. Details and examples are provided below. 
cXnames 
A vector of the names for the choicespecific covariates
specified in 
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 probit model with ordered preferences, the default base category is the last column in the matrix of response variables. 
latent 
logical. If 
invcdf 
logical. If 
trace 
logical. If 
n.draws 
A positive integer. The number of MCMC draws. The default is

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

p.df 
A positive integer greater than 
p.scale 
A positive definite matrix. When 
coef.start 
A vector. The starting values for the coefficients. A
scalar input sets the starting values for all the coefficients equal to that
value. The default is 
cov.start 
A positive definite matrix. When 
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 
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 
verbose 
logical. If 
To fit the multinomial probit model when only the most preferred choice is
observed, use the syntax for the formula, y ~ x1 + x2
, where y
is a factor variable indicating the most preferred choice and x1
and
x2
are individualspecific covariates. The interactions of
individualspecific variables with each of the choice indicator variables
will be fit.
To specify choicespecific 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 choicespecific 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.
To fit the multinomial probit model when 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.
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. 
alt 
The names of alternatives. 
n.alt 
The total number of alternatives. 
base 
The base category used for fitting. 
invcdf 
The value of

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. 
Kosuke Imai, Department of Politics, Princeton University kimai@Princeton.Edu, http://imai.princeton.edu; David A. van Dyk, Statistics Section, Department of Mathematics, Imperial College London.
Imai, Kosuke and David A. van Dyk. (2005a) “A Bayesian Analysis of the Multinomial Probit Model Using the Marginal Data Augmentation,” Journal of Econometrics, Vol. 124, No. 2 (February), pp.311334.
Imai, Kosuke and David A. van Dyk. (2005b) “MNP: R Package for Fitting the Multinomial Probit Models,” Journal of Statistical Software, Vol. 14, No. 3 (May), pp.132.
Burgette, L.F. and E.V. Nordheim. (2009). “An alternate identifying restriction for the Bayesian multinomial probit model,” Technical report, Department of Statistics, University of Wisconsin, Madison.
coef.mnp
, cov.mnp
, predict.mnp
,
summary.mnp
;
### ### NOTE: this example is not fully analyzed. In particular, the ### convergence has not been assessed. A full analysis of these data ### sets appear in Imai and van Dyk (2005b). ### ## load the detergent data data(detergent) ## run the standard multinomial probit model with intercepts and the price res1 < mnp(choice ~ 1, choiceX = list(Surf=SurfPrice, Tide=TidePrice, Wisk=WiskPrice, EraPlus=EraPlusPrice, Solo=SoloPrice, All=AllPrice), cXnames = "price", data = detergent, n.draws = 100, burnin = 10, thin = 3, verbose = TRUE) ## summarize the results summary(res1) ## calculate the quantities of interest for the first 3 observations pre1 < predict(res1, newdata = detergent[1:3,]) ## load the Japanese election data data(japan) ## run the multinomial probit model with ordered preferences res2 < mnp(cbind(LDP, NFP, SKG, JCP) ~ gender + education + age, data = japan, verbose = TRUE) ## summarize the results summary(res2) ## calculate the predicted probabilities for the 10th observation ## averaging over 100 additional Monte Carlo draws given each of MCMC draw. pre2 < predict(res2, newdata = japan[10,], type = "prob", n.draws = 100, verbose = TRUE)
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