BANOVA.Multinomial {BANOVA}

Estimation of BANOVA with a Multinomial dependent variable

Description

BANOVA.Multinomial implements a Hierarchical Bayesian ANOVA for multinomial response variable using a logit link and a normal heterogeneity distribution.

Usage

BANOVA.Multinomial(l1_formula = "NA", l2_formula = "NA",
  dataX, dataZ, y, id, l2_hyper = c(1, 1, 0.0001), burnin = 5000, sample = 2000, 
  thin = 10, adapt = 0, conv_speedup = F, jags = runjags.getOption('jagspath'))
## S3 method for class 'BANOVA.Multinomial'
summary(object, ...)
## S3 method for class 'BANOVA.Multinomial'
predict(object, Xsamples = NULL, Zsamples = NULL,...)
## S3 method for class 'BANOVA.Multinomial'
print(x, ...)

Arguments

l1_formula

formula for level 1 e.g. '~X1+X2', response variable must not be included

l2_formula

formula for level 2 e.g. '~Z1+Z2', response variable must not be included

dataX

a list of data frames(each corresponds to the choice set of each observation) that includes all covariates and factors

dataZ

a data frame(long format) that includes all level 2 covariates and factors

y

choice responses, 1,2,3...

id

subject id

l2_hyper

level 2 hyperparameters, c(a, b, \gamma), default c(1,1,0.0001)

burnin

the number of burn in draws in the MCMC algorithm, default 5000

sample

target samples in the MCMC algorithm after thinning, default 2000

thin

the number of samples in the MCMC algorithm that needs to be thinned, default 10

adapt

the number of adaptive iterations, default 0 (see run.jags)

conv_speedup

whether to speedup convergence, default F

jags

the system call or path for activating 'JAGS'. Default calls findjags() to attempt to locate 'JAGS' on your system

object

object of class BANOVA.Multinomial(returned by BANOVA.Multinomial)

Xsamples

new data samples in level one, must be a list( the same format with the traning data), numeric variables must be mean centered.

Zsamples

new data samples in level two( the same format with the traning data), numeric variables must be mean centered.

x

object of class BANOVA.Multinomial (returned by BANOVA.Multinomial)

...

additional arguments,currently ignored

Details

Level 1 model:
P(y_i = \ell) = \frac{exp(\eta_{i\ell})}{\sum_{\ell=1}^L exp(\eta_{i\ell})}
where \eta_{i\ell} = \sum_{p = 0}^{P}\sum_{j=1}^{J_p}X_{i,j}^{k,p} \beta_{j,s_i}^p, s_i is the subject id of response i, see BANOVA-package. X_{i,j}^{k,p} is the design matrix corresponding to each class \ell(\ell=1,.,L) of y_i. The first level of the response is the base level, thus the intercept corresponding to this level will not be included.

Value

BANOVA.Multinomial returns an object of class "BANOVA.Multinomial". The returned object is a list containing:

anova.table

table of effect sizes BAnova

coef.tables

table of estimated coefficients

pvalue.table

table of p-values table.pvalues

dMatrice

design matrices at level 1 and level 2

samples_l2_param

posterior samples of level 2 parameters

dataX

original dataX

dataZ

original dataZ

mf1

model.frame of level 1

mf2

model.frame of level 2

n_categories

the number of categories of the response

JAGSmodel

'JAGS' model

Examples

# see 'choicedata'
data(choicedata)
# generate dataX(convert the within-subject variables to a list)
dataX <- list()
for (i in 1:nrow(choicedata)){
  logP <- as.numeric(log(choicedata[i,3:8]))
  # all numeric variables must be mean centered
  dataX[[i]] <- as.data.frame(logP) - mean(logP)
}
dataZ <- choicedata[,9:13]

res <- BANOVA.Multinomial(~ logP, ~ college, dataX, dataZ, 
  choicedata$choice, choicedata$hhid, burnin = 100, sample = 100, thin = 10)
# or use BANOVA.run based on 'Stan'
require(rstan)
res <- BANOVA.run(~ logP, ~ college, dataX = dataX, dataZ = dataZ, 
                    model_name = 'Multinomial', y_value = choicedata$choice, 
                    id = choicedata$hhid, iter = 100, thin = 1, chains = 2)