table.pvalues: Function to print the table of p-values

In BANOVA: Hierarchical Bayesian ANOVA Models

Function to print the table of p-values

Description

Computes the Baysian p-values for the test concerning all coefficients/parameters:

For p = 1,...,P
H_0:θ_{j,k}^{p,q}=0
H_1:θ_{j,k}^{p,q} \neq 0

The two-sided P-value for the sample outcome is obtained by first finding the one sided P-value, min(P(θ_{j,k}^{p,q}<0),P(θ_{j,k}^{p,q}>0 )) which can be estimated from posterior samples. For example, P(θ_{j,k}^{p,q}>0) = \frac{n_+}{n}, where n_+ is the number of posterior samples that are greater than 0, n is the target sample size. The two sided P-value is P_θ(θ_{j,k}^{p,q}) = 2*min(P(θ_{j,k}^{p,q}<0),P(θ_{j,k}^{p,q}>0 )).

If there are θ_{j,k_1}^{p,q},θ_{j,k_2}^{p,q},...,θ_{j,k_J}^{p,q} representing J levels of a multi-level variable, we use a single P-value to represent the significance of all levels. The two alternatives are:

H_0:θ_{j,k_1}^{p,q} = θ_{j,k_2}^{p,q} = \cdots = θ_{j,k_J}^{p,q}=0
H_1 : some θ_{j,k_j}^{p,q} \neq 0

Let θ_{j,k_{min}}^{p,q} and θ_{j,k_{max}}^{p,q} denote the coefficients with the smallest and largest posterior mean. Then the overall P-value is defined as

min(P_θ (θ_{j,k_{min}}^{p,q}), P_θ(θ_{j,k_{max}}^{p,q})).

Usage

table.pvalues(x)

Arguments

x	the object from BANOVA.*

Source

It borrows the idea of Sheffe F-test for multiple testing: the F-stat for testing the contrast with maximal difference from zero. Thank Dr. P. Lenk of the University of Michigan for this suggestion.

Examples

data(goalstudy)

library(rstan)
# or use BANOVA.run
res1 <- BANOVA.run(bid~progress*prodvar, model_name = "Normal", 
data = goalstudy, id = 'id', iter = 1000, thin = 1, chains = 2) 
table.pvalues(res1)

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