GCIsv: Generalized confidence interval for the total variance in a...

In baolinwu/IPAM: Inference problems in various ANOVA models

Description

Consider a random-effects ANOVA model, Y_{ij}=μ+u_i+ε_{ij}, where the random-effects u_i\sim N(0,σ_a^2) and the random error components ε_{ij}\sim N(0,σ^2). We want to compute CI for the total variance parameter σ_a^2+σ^2. We adopt the generalized pivotal test approach to computing the CI, based on sequentially “calculating" the within-group variance parameter σ^2 and the between-group variance parameter σ_a^2.

Usage

GCIsv(Y, A, alpha = 0.1, Nmax = 2000)

Arguments

Y	observed outcomes in an ANOVA model
A	factor level
alpha	desired significance level for the confidence interval
Nmax	total number of generalized pivotal statistics to be generated

Value

GCI

generalized CI

Qt

generated generalized pivotal statistics for the total variance

References

Bai,X., Bai,Y. and Wu,B. (2019) Generalized confidence interval calculation for the total variance in a single-factor random-effects ANOVA model with application to medical device comparison problems. tech report.

Examples

A = rep(1:10, times=5:14)
s2a = 0.05; s2 = 0.95
Y = rnorm(10)[A]*sqrt(s2a) + rnorm(length(A))*sqrt(s2)
BGPsv(Y,A)
aa = GCIsv(Y,A); aa$GCI

baolinwu/IPAM documentation built on May 9, 2019, 2:21 a.m.