BANOVA.Multinomial: Estimation of BANOVA with a Multinomial dependent variable

In BANOVA: Hierarchical Bayesian ANOVA Models

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, γ), 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(η_{i\ell})}{∑_{\ell=1}^L exp(η_{i\ell})}
where η_{i\ell} = ∑_{p = 0}^{P}∑_{j=1}^{J_p}X_{i,j}^{k,p} β_{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)

BANOVA documentation built on June 21, 2022, 9:05 a.m.