[R-sig-ME] Mixed Models in a very basic replication design

[Peter Claussen]

Tim,

This is more a question of experimental design, but I can answer a bit relevant to mixed models.

In a greenhouse, environmental variation should be negligible and can typically be ignored. In some cases, the variance is so small that it results in a negative estimate from ANOVA. This is most apparent when you have a Location F-ratio less than 1. Briefly, the F-ratio is calculated with an error variance in the denominator, and that same variance plus another source of variance in the numerator, i.e. (EMS + t*Location MS)/EMS. If the ratio is less than 1, then Location MS must be negative.

If this occurs, and you fit the model using lmer and formula  = ~ Treatment A * Treatment B * Time + (1|Location) , you would expect the estimate of Location to be 0, since it would be constrained to be non-negative. If that happens, you can drop location from the model an fit as a CRD using the three-way ANOVA.

However, you also include time in the model. Is this a repeated measures design? If so, then you might want to fit to a mixed model with Pot (or equivalent) as a random effect.

Cheers,

Peter Claussen
Biometrician
Gylling Data Management, Inc.
Brookings, SD 57006-4605 USA
Tel. No.: +1 605 692-4021
Website: www.gdmdata.com <http://www.gdmdata.com/>

> On Dec 18, 2017, at 9:55 AM, Tim Richter-Heitmann <trichter at uni-bremen.de> wrote:
> 
> Dear Group,
> 
> i am to plan a very basic factorial greenhouse experiment, and this time i will first ask for statistical advise before execution :).
> 
> It will encompass two treatment types with two levels each, two sampling dates with five replicates each, resulting in 2 x 2 x 2 x 5 = 40 samples.
> 
> I guess, this is a basic three way ANOVA (~ Treatment A * Treatment B * Time). However, the arrangement of the replicates in the greenhouse will be randomized. I have only a limited understanding of mixed models, obviously, but does the randomized location of the plant also requires the introduction of a random effect (~ Treatment A * Treatment B * Time + (1|Location)?. How do i best code location in this case?
> 
> Thank you!
> 
> -- 
> Tim Richter-Heitmann
> 
> University of Bremen
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