Extra exercises for VHM 881: Statistical Analysis of Generalized, Linear, and Mixed Models - Fall Semester 2004

• Example 3.1:
  Analyze the data from Figure 3.1 in MS (with data values read off the figure) by a linear regression model and by a generalised linear model (in both cases ignoring the weeks), and by a linear mixed model taking the weeks into account.
• Example 4.7:
  Go through the calculations of Section 4.7 using the R software.
• Extra for Chapter 6 of VR:
  For the Whiteside data, fit simple linear regressions and check the normality of standardized residuals using Shapiro-Wilks test (shapiro.test). By simulation, compute a P-value that takes into account the dependence between residuals. Use n=1000 simulated datasets with normal errors. (solution)
• Extra for Chapter 2 of PB:
  Consider the textbook example of simulation for testing fm1Machine against fm2Machine, and restrict attention to ML estimation.
  1. Choose a seed, and run 1000 simulations. Extract the two sets of logL values from the object, and compute the value of -2logL for each of the 1000 simulations. (Hint: read carefully the description of the simulation.lme object in the nlme help pages.)
  2. Carry out a descriptive analysis of those simulated values. Do all the values seem reasonable? - if not, try to give an explanation. Compute the proportion of values equal to zero, and interpret that value.
  3. Sort the -2logL values, and compare them by a plot to the percentiles of a chi-square(1) distribution. What does the plot show? Then make the comparison on probability scale, by plotting the cumulative distribution function of the chi-square(1) against the -2logL values. Make a final adjustment to achieve the same plot as in Figure 2.4.
  4. Repeat the steps of 3. for a reference distribution which is a 0.5:0.5 mixture of chi-squares (0) and (1).
  (solution)
• Extra for Chapter 10 of VR:
  Analyse the bacteria dataset in the MASS library by a random effects generalised linear model using the following methods:
  • glmmPQL function in the MASS library
  • glmmML user-contributed package
  Study the documentation to determine which estimation procedure is used. Export the dataset to Stata and run the same model using the gllamm macro.
  Other options in R are a glmmGIBBS package not currently listed at CRAN but apparently it has been in the past, and packages developed by Jim Lindsey, accessible from http://popgen0146uns50.unimaas.nl/~jlindsey/rcode.html.