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

[Tim Richter-Heitmann]

Peter,

thank you very much. That was a very elucidating answer.
If i may elaborate on the issue of time a bit more, because i am also a 
bit clueless here.
Will the selection of appropriate modelling approaches be a matter of if 
we disrupt the plants (e.g. harvesting soil) or not (e.g. measuring 
height or surface areas)? Or is it just to account for possibly 
individual intercepts for individual plants?
The plants will be grown from surface-sterilized seeds in homogenized 
starting soils.

Also, how would i encode the factor "Pot"? Just in as many levels as i 
have pots?

Thank you again very much, Tim


On 18.12.2017 18:31, Peter Claussen wrote:
> 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 <mailto: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
>> Microbial Ecophysiology Group (AG Friedrich)
>> FB02 - Biologie/Chemie
>> Leobener Straße (NW2 A2130)
>> D-28359 Bremen
>> Tel.: 0049(0)421 218-63062
>> Fax: 0049(0)421 218-63069
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org 
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>

-- 
Dr. Tim Richter-Heitmann

University of Bremen
Microbial Ecophysiology Group (AG Friedrich)
FB02 - Biologie/Chemie
Leobener Straße (NW2 A2130)
D-28359 Bremen
Tel.: 0049(0)421 218-63062
Fax: 0049(0)421 218-63069