BANOVA.run {BANOVA}

Estimation of BANOVA models

Description

BANOVA.run implements Hierarchical Bayesian ANOVA models using 'Stan'

Usage

BANOVA.run(l1_formula = "NA", l2_formula = "NA", fit = NULL, model_name = 'NA', 
dataX = NULL, dataZ = NULL, data = NULL, y_value = NULL, id, iter = 2000, 
num_trials = 1, contrast = NULL, y_lowerBound = -Inf, y_upperBound = Inf, ...)
## S3 method for class 'BANOVA'
summary(object, ...)
## S3 method for class 'BANOVA'
predict(object, newdata = NULL, Xsamples = NULL, Zsamples = 
                        NULL, ...)
## S3 method for class 'BANOVA'
print(x, ...)

Arguments

l1_formula

formula for level 1 e.g. 'Y~X1+X2'

l2_formula

formula for level 2 e.g. '~Z1+Z2', response variable must not be included. If NULL, the single-level model is used

fit

a fitted BANOVA models, an object of class "BANOVA.build", default NULL which needs compilation

model_name

a character string in c('Normal', 'T', 'Bernoulli', 'Binomial', 'Poisson', 'ordMultinomial', 'Multinomial', 'multiNormal', 'truncNormal')

dataX

a list of data frames (each corresponds to the choice set of each observation) that includes all covariates and factors, for the Multinomial model only, default NULL

dataZ

a data frame (long format) that includes all level 2 covariates and factors, for the Multinomial model only, default NULL

data

a data.frame in a long format including all features in level 1 and level 2 (covariates and categorical factors) and responses, default NULL. For the Multivariate Normal model the data must be specially prepared: first, combine the set of dependent variables in a single matrix; next, add this matrix to an original data frame used in the analysis. For an example of the specification of the data, please, see below.

id

subject ID (string) of each response unit

y_value

choice responses, 1,2,3..., for the Multinomial model only, default NULL

iter

target samples in the 'Stan' algorithm after thinning, default 2000

num_trials

the number of trials of each observation(=1, if it is Bernoulli), the type is forced to be 'integer', for the Binomial model only, default 0

contrast

a list of contrasts for planned comparisons, default: effect coding (NULL value)

y_lowerBound

lower bound of the dependent variable, for the Truncated Normal model only, default -Inf.

y_upperBound

upper bound of the dependent variable, for the Truncated Normal model only, default Inf.

object

an object of class BANOVA (returned by BANOVA.run)

x

an object of class BANOVA (returned by BANOVA.run)

newdata

test data, either a matrix, vector or a data frame. It must have the same format as the original data (the same column number)

Xsamples

a list of sample data frames(each corresponds to the choice set of each observation) that includes all covariates and factors, for the Multinomial model only, default NULL

Zsamples

a data frame(long format) that includes all level 2 covariates and factors, for the Multinomial model only, default NULL

...

additional arguments, for BANOVA.run, it can include standard 'Stan' arguments, e.g. warmup, thin, chains, etc., see sampling for more details, for other functions, ignored currently

Value

BANOVA.run returns an object of class "BANOVA". 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_l1_param

posterior samples of level 1 parameters

samples_l2_param

posterior samples of level 2 parameters

samples_l2_sigma_param

posterior samples of level 2 standard deviations

samples_cutp_param

posterior samples of cutpoints

data

original data.frame

mf1

model.frame of level 1

mf2

model.frame of level 2

model_code

'Stan' code

single_level

if this is a single level model

stan_fit

fitted samples

model_name

the name of the model

contrast

contrasts for planned comparisons

new_id

id values coded in 1,2,3,...

old_id

original id values

Examples

# Analysis of a single-level Normal dependent variable
# Use the ipadstudy data set
data(ipadstudy)
library(rstan)
# build the BANOVA model first so that it can be reused
model <- BANOVA.model('Normal', single_level = TRUE)
banova_model <- BANOVA.build(model)
res_1 <- BANOVA.run(attitude~owner + age + gender + selfbrand*conspic, 
fit = banova_model, data = ipadstudy, id = 'id', iter = 2000, chains = 2)
summary(res_1)
# or call the function directly without specifying the fit argument
# but it needs compilation
res_1 <- BANOVA.run(attitude~owner + age + gender + selfbrand*conspic,
model_name = 'Normal', data = ipadstudy, id = 'id', iter = 2000, chains = 2)

# Hierarchical analysis of multiple dependent variables (Multivariate Normal distribution)
# Use the colorad data set
data(colorad)
# Prepare dependent variables to be analyzed
colorad$blur_squared <- (colorad$blur)^2
dv <- cbind(colorad$blur, colorad$blur_squared)
colnames(dv) <- c("blur", "blur_squared")
colorad$dv <- dv
# Build and analyze the model for the dependent variables
model <- BANOVA.model('multiNormal')
banova_multi_norm_model <- BANOVA.build(model)
res_2 <- BANOVA.run(dv ~ typic, ~ color, fit = banova_multi_norm_model,
                    data = colorad, id = 'id', iter = 2000, thin = 1, chains = 2)