Prediction Intervals for Multilevel Models

There are many methods for constructing prediction intervals for differences in observations. This document will explain several of these methods in the context of different models using data from a kiwi yield experiment as an example. 1. KIWI DATA In an experiment (discussed in more detail in class), kiwi yields were measured in a designed experiment. There were three blocks (north, east, and west) at a single site. Each block had four plots. (The plots were arranged in a single column in the east and west blocks, but in a square pattern in the north block.) Due to natural and artificial barriers, each of the four plots was subject to a different shading treatment; no shade from August to December, from December to February, and from February to May. one plot in each block has each shading treatment. Within each plot there were four vines. Kiwi yield was measured at each vine. The following plot shows the data. The third and fourth lines of R code reorder the shade and block factors in order from smallest to largest by mean kiwi yield. We observe that there is no obvious need to transform the response variable, and that there do appear to be both block and shade treatment effects. Perhaps the shade treatment acts differently in the north block than in the east and west blocks. > library(lattice) > kiwi = read.table("kiwi.txt", header = T) > kiwi$shade = with(kiwi, reorder(shade, yield)) > kiwi$block = with(kiwi, reorder(block, yield)) > print(xyplot(yield ~ shade | block, data = kiwi, layout = c(3, + 1), groups = shade))