GTrms: Generalized test for the total absolute variation in a...

In baolinwu/RAMgt: Statistical tests in a Random-effects ANOVA Model

Description

Given an one-way random-effects ANOVA model, Y_{ij}=μ+u_i+ε_{ij} with u_i\sim N(0,σ_b^2), ε_{ij}\sim N(0,σ_w^2), we want to make inference on the total absolute variation parameter, ρ^2=μ^2+σ_b^2+σ_w^2. A generalized inference method is taken to conduct significance test and calculate CI for ρ.

Usage

GTrms(ng, mus, sse, alpha = NULL, rho0 = NULL, Bmc = 10000)

Arguments

ng	sample sizes for each factor level
mus	sample mean values at each factor level
sse	total error sum of squares (sum of within-group sample variances)
alpha	desired CI coefficient
rho0	the null threshold value to test H_0: ρ≥ ρ_0.
Bmc	number of Monte Carlo simulations to approximate the distribution of generalized test statistics

Value

p.value

generalized test p-value

GCI

computed CI for ρ

Qt

simulated generalized test statistics

References

Tsui,K.-W. and Weerahandi,S. (1989). Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters. Journal of the American Statistical Association 84, 602–607.

Weerahandi,S. (1993). Generalized Confidence Intervals. Journal of the American Statistical Association 88, 899–905.

Bai,Y., Wang,Z., Lystig,T., and Wu,B. (2019) Efficient and powerful equivalency test on combined mean and variance with application to diagnostic device comparison studies. arXiv:1908.07979

Examples

## Simulation example: how to get summary stats from data
A = rep(1:10, 5:14)
Y = 0.5+rnorm(length(A))+rnorm(length(unique(A)))[A]
ng = as.vector(table(A))
sse = sum(tapply(Y, A, var)*(ng-1), na.rm=TRUE)
mus = tapply(Y, A, mean)
ans = GTrms(ng,mus,sse, alpha=0.05,rho0=2.5); ans[1:2]
## Z-test
Zrms(ng,mus,sse, alpha=0.05,rho0=2.5)
## PO comparison study
ng = c(9, 10, 10, 10, 5, 10, 10, 10, 10, 10, 10, 10, 2, 10, 10, 10)
mus = c(-0.026,0.447,0.083,-0.103,-2.587,-0.61,0.04,-0.593, 0.963,0.643,-0.2,-1.337,-4.333,-2.807,0.563,-0.797)
sse = 221.037
set.seed(123)
ans = GTrms(ng,mus,sse, alpha=0.1, rho0=3, Bmc=1e4); ans[1:2]
## Z-test
Zrms(ng,mus,sse, alpha=0.1,rho0=3)

baolinwu/RAMgt documentation built on Nov. 3, 2019, 2:06 p.m.