MSE in GLM ANOVA

Question

Experimental Design:

Whole plot: Tree species (Spp) Subplot: Location relative to canopy boundary (In/Out)

Tests: 2-way ANOVA on data collected for several tree species from a transect running through the tree (We'll call this Objective 1); Regression ANOVA comparing whether response variables changed with increasing DBH and distance from tree stem (ie Subplot: Distance from stem) (we'll call this Objective 2)

Based on conversations that I've had with some statistics advisers, Minitab, R, and SAS all use the wrong MSE2 in the denominator instead of MSE1 to calculate GLM ANOVA. As such, he suggested I use this roundabout way of doing it:

Statistical Analysis:

Objective 1

1.) Calculate the average dependent variables (DV) of the samples within the tree canopy for each individual tree sampled

2.) Calculate the average DV of the samples outside the canopy boundary for each individual tree sampled

3.) Subtract in-out to obtain data point for each individual

4.) Use ANOVA to see if difference in differences varies among species

5.) If difference in differences is significant, then interaction is present and look tat simple effects

i.) Use paired t-test comparing response variables of in and out samples for an individual

ii.) Separate t-test for each species

6.) If difference in differences is not significant, then interaction is not present and look at main effects

i.) Species main effect: ANOVA comparing species collapsed over sampling position

ii.) Position main effect: Paired t-test with in and out samples collapsed over all species

Objective 2

1.) Perform regression (sampling distance from stem vs response variables) for each individual tree

2.) Isolate slopes of regressions for each tree

3.) Use ANOVA to see if there is a difference in the slopes among species

4.) If there is a significant difference look at simple effects (because interaction present)

5.) Perform 1-sample t-test on slopes for each species (Ho: m=0)

6.) If no significant difference look at main effects (because no interaction)

i.) Calculate ANOVA comparing species collapsed over position (species main effect)

ii.) Perform 1-sample t-test collapsed over species (position main effect)

Now, I ran the basic GLM on the data and I noticed that the p values I got were not even close to the p values that I got from the procedure above. Now, that could just be because R and Minitab are dumb and use the wrong MSE, but I thought at least the interaction would be similar. This has called into question whether this "modified" GLM actually works. Thoughts?

Answer 1

It's true, general linear model (usually abbreviated as LM, especially in the SAS world) software will not construct correct tests for all terms in a mixed model. Take advantage of "modern" tools (although these tools have been available to us for more than a decade), and switch to general linear mixed model (LMM) software. In SAS, that would be the MIXED (LMM) or GLIMMIX (GLMM) procedures. An excellent reference is

Littell, RC et al., SAS for Mixed Models, 2nd ed., SAS Institute Inc., 2006

The problem with incorrect tests is well-discussed in this book.

In R, the lme4 package (among others) fits GLMMs. (Note that LMMs are a subset of GLMMs, so you can use GLMM software to fit a LMM.)