Mixed Models in a very basic replication design
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 Stra?e (NW2 A2130) D-28359 Bremen Tel.: 0049(0)421 218-63062 Fax: 0049(0)421 218-63069
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Dr. Tim Richter-Heitmann University of Bremen Microbial Ecophysiology Group (AG Friedrich) FB02 - Biologie/Chemie Leobener Stra?e (NW2 A2130) D-28359 Bremen Tel.: 0049(0)421 218-63062 Fax: 0049(0)421 218-63069