Stat 210B: Homework Assignment 4
Consider an experiment to compare five methods for predicting the shear
strength for steel girders.
Data for seven girders are given. Each of the five
methods are used to predict the strength of each of the seven girders.
This is a complete randomized block design, where each girder forms
a block.
I. Fit a mixed effects model.
1. Write down the model and report the estimates (with REML method).
2. Test whether five methods are different. Write down the null and
alternative hypotheses. Report your conclusion.
3. Test whether there is a girder effect. Write down the null and alternative
hypotheses. Report your conclusion.
II. Fit a fixed effects model.
1. Write down the model.
2. Test whether five methods are different. Write down the null and
alternative hypotheses. Report your conclusion.
3. Test whether there is a girder effect. Write down the null and alternative
hypotheses. Report your conclusion.
III. Compare the results from I and II.
Note: The function logLik() returns the log-likelihood of an object of lm()
and lme().