Random effect for the split plot design analysis

Question

I have question about the random effect for the split plot design analysis, hope someone can help to explain it.
Let me use JMP sample data, "Animals.jmp" for example.
If we consider subject[species] as random effect, the REML variance Component estimates report, as "Repeated Measures Model" script in attachment's script area show subject factor is not a significant effect factor for miles.
However, if we consider the model is basic regression model, as the "basic model" script in script area of attached file.
The result show subject factor effect miles is significant. 
What is the reason that make different conclusion between those two models?

Animals.jmp

Phil_Kay · Accepted Answer

Hi @Eric_Wang ,

The two models are very different, so you should expect different conclusions. They are based on different assumptions about the processes that generate the data.  They make different assumptions about where variance comes from.

One big difference is that Subject is not nested within Species in the basic regression model. That implies that there are only 3 subjects. There are actually 6 subjects: 3 for each of the 2 species. I suspect that is a big part of the reason for the difference. But it is certainly not the only reason.

This illustrates the need for mixed models in cases where a standard fixed effects model is not appropriate. The conclusions will be misleading if an inappropriate model is used.

I am sure the JMP for Mixed Models book would provide more explanation about this.

I hope this helps,

Phil

DonMcCormack · Accepted Answer

In addition to @Phil_Kay's response, the purpose of the subject term is merely to capture the within species variation so it can be used to test for a statistical difference, not to look for subject to subject differences. On top of this, treating subject as a fixed effect not only assumes there are only three (treatment levels) but, that subject 1 for FOX is the same (treatment) as subject 1 for COYOTE.

jiancao · Accepted Answer

I agree with both  @Phil_Kay  and @DonMcCormack . I just wanted to point out that Joint Factor Tests from the basic model show that the subject is not significant .

Looking  at the results, species is a significant factor in both random effect model and basic model. This might explain why,  after controlling for species and season,  Subject[species] is not a significant source of random variability.