Supplemental material for STAT 8052

1. R reference card by Tom Short, 2004-11-07

2. Linear hypotheses and contrasts

• with package multcomp by Torsten Hothorn, 11 Jan 2012
• with package contrast by Kuhn, Weston, Wing, Forester, 23 Dec 2011

3. Mixed effect models, testing for fixed effects, denominator dfs for F- and t-tests

There are several methods for estimating the dfs of the denominator when using F-tests or t-tests for fixed effects. An short overview of methods used in SAS proc mixed is given in West BT, Welch KB, Galecki AT, "Linear mixed models: a practical guide using statistical software", Chapman and Hall, 2007; p.110-111.

• The method used in lme{nlme} in R was described in Pinheiro and Bates (2000), page 91.
  
  
• lmer{lme4} in R does not provide denominator dfs (and no p-values). Douglas Bates explains in
  https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html
  
  
• SAS proc mixed gives the option to select a method; the default method varies depending on whether you use a RANDOM statement or not. The Kenward-Roger method can be called by the option ddfm=kr. (Source: West, Welch, Galecki (2007); p.110-111, see above for complete citation).

4. Model selection in GEE

• The R package geepack contains the method anova(.) for comparing nested models fitted with geeglm{geepack}. The package is documented here; anova{geepack} uses the Wald test.
  
• The usual AIC does not work in GEE because we don't have likelihood function, but a quasi-likelihood. This paper by Wei Pan (2001) introduces a QIC for GEE, a modification of the AIC. And here is R code for the QIC by Daniel Hocking for Poisson GEE -- use at your own risk. This code requires that the GEE model was fit with geeglm{geepack}.

5. Response surface methods

• The R package rsm by R. V. Lenth contains methods for fitting first and second order response surfaces, and for generating central composite and Box-Behnken designs. The package is documented here.