table.pvalues {BANOVA} | R Documentation |
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:\theta_{j,k}^{p,q}=0
H_1:\theta_{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(\theta_{j,k}^{p,q}<0),P(\theta_{j,k}^{p,q}>0 ))
which can be estimated from posterior samples. For example, P(\theta_{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_\theta(\theta_{j,k}^{p,q}) = 2*min(P(\theta_{j,k}^{p,q}<0),P(\theta_{j,k}^{p,q}>0 ))
.
If there are \theta_{j,k_1}^{p,q},\theta_{j,k_2}^{p,q},...,\theta_{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:\theta_{j,k_1}^{p,q} = \theta_{j,k_2}^{p,q} = \cdots = \theta_{j,k_J}^{p,q}=0
H_1
: some \theta_{j,k_j}^{p,q} \neq 0
Let \theta_{j,k_{min}}^{p,q}
and \theta_{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_\theta (\theta_{j,k_{min}}^{p,q}), P_\theta(\theta_{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)