# Overview

We will learn how to apply the ICC R package introduced in Wolak et al., (2012) (doi) to the beef cattle dataset.

Use the function load() to load the dat4 object we created in class.

load(file = file.choose())
dim(dat4)
library(ICC)

# ICC

The function ICCbare() returns the estimate of intraclass corrleation coeﬃcient (ICC) , i.e., repeatability. It can be used for both balanced and unbalanced designs. Does the estimate of ICC agree with the one we obtained in class?

ICCbare(x = factor(SIRE), y = BWT, data = dat4)

# Optimal k

When the effort level is fixed ($$s \times n$$ or $$s \times k_1$$), the effort() function computes ICC by internally calling the ICCbare() function and then plots a number of records per sire group ($$k$$), one of which produces the smallest conﬁdence interval around the ICC estimate. Check the tradeoff in confidence interval width with varying $$k$$. What is the estimaete of optimal $$k$$ in this dataset?

# par(mar=c(4,4,1,1))
effort(est.type = "pilot", x = factor(SIRE), y = BWT, data = dat4)

# Confidence interval

The ICCest() function performs a one-way ANOVA. It returns 1) the estimate of ICC, 2) the lower confidence interval of ICC, 3) the upper confidence interval of ICC, 4) the number of unique sire groups, 5) the adjusted $$k$$ (or $$k_1$$), 6) the within group variance V(W), and 7) the between group variance V(B). What are the lower and upper confidence limits of the confidence interval for the ICC estimate?

# par(mar=c(4,4,1,1))
my.ICCest <- ICCest(x = factor(SIRE), alpha = 0.05, y = BWT, data = dat4)
my.ICCest

# Number of sire groups needed to achieve a desired CIW

The Nest() function returns the number of sires or sire groups needed to achieve a predefined conﬁdence interval width (CIW). The estimate of CIW in the beef cattle dataset can be computed as follows.

c(my.ICCest$LowerCI, my.ICCest$ICC, my.ICCest$UpperCI) w1 <- my.ICCest$UpperCI - my.ICCest$LowerCI w1 So if we set the argument w equal to w1, the Nest() function produces a value that is very close to the number of unique sires in the dataset. Nest("pilot", w = w1, x = factor(SIRE), y = BWT, data = dat4) length(unique(dat4$SIRE))

Now suppose we would like to obtain a more precise estimate of ICC, e.g., CIW=0.15. What is the required number of sires or sire groups?

w2 <- 0.15
Nest("pilot", w = w2, x = factor(SIRE), y = BWT, data = dat4)

February 23, 2017