Help establishing mixed model equation for split, plot design

Hi Samuel,


first of all thanks a lot for the quick and clear response.


As you state, all models give the same results once they are 
established following your examples. Now I have a clear view about 
what is really doing the command and how to continue.


Just one quick comment. The line:

*lmemodel <- lme(Plantsurvival ~ salinityF*immersionF*SpecTF, random= 
~**1|rep:salinityF, data=sp.datos)*


Throws the following error:

*Error in getGroups.data.frame(dataMix, groups) : **invalid formula 
for groups*

I leave it here in case is interesting for you. I've decided to use 
the lmer package because I have other variables that are not balanced, 
so I prefer to use the same model in all cases, and that package is 
working fine.

Just one final question. Is there any consideration I should have when 
working with variables without equal number of samples? I mean, 
something specific in the command of the lmer I should be careful with 
or investigate further on. Or does the function itself has all 
considerations included. i see from the *anova(fit.okay3, 
ddf="Kenward-Roger") *that the anova is made using the type III SS so 
I wouldn't have to change that part. *
*

Also, fyi,? the aov function in the case of not grouping by rep throws 
the same result as the lmer.

Again, I really appreciate your help, it has been a lifesaver.

Best regards,

*Felipe Calleja Ap?stegui*

*Predoctoral researcher*

*
*

*Instituto de Hidr?ulica Ambiental "IH Cantabria"*

C/ Isabel Torres, N? 15

Parque Cient?fico y Tecnol?gico de Cantabria

39011 Santander (Espa?a)

www.ihcantabria.es <http://www.ihcantabria.es/>

Tel:? +34 942 20 16 16 Ext. 1153

Fax: +34 942 26 63 61

e-mail: f*elipe-francisco.calleja at alumnos.unican.es*


------------------------------------------------------------------------
*De:* Samuel Knapp <samuel.knapp at tum.de>
*Enviado:* martes, 3 de abril de 2018 21:26:31
*Para:* r-sig-mixed-models at r-project.org; CALLEJA APESTEGUI, FELIPE 
FRANCISCO
*Asunto:* Re: Help establishing mixed model equation for split, plot 
design
Hi Felipe,

if I understand the design correctly, it is a split-plot design with
salinityF as the whole-plot. Only, if you have arranged the boxes in a
way that replicate blocks are formed, you should include the rep effect
in a model. These replicate blocks could be, that you always have three
boxes with the three different salinity levels grouped together, e.g. on
one shelf. If you have simply replicated each box 5 times and they are
set up fully randomly, you should not include a repliate block.

If you have no missing values, and you specify the right model, both
aov() and lme() should give you the same results. I would suggest the
following models:


# with replicate blocks

aovmodel <- aov(Plantsurvival ~ salinityF*immersionF*SpecTF +
Error(rep/salinityF), data=sp.datos)

lmemodel <- lme(Plantsurvival ~ salinityF*immersionF*SpecTF, random=
~1|rep/salinityF, data=sp.datos)

# or with lmer from lme4 package (library (lme4)

lmermodel <- lmer(Plantsurvival ~ salinityF*immersionF*SpecTF
+(1|rep/salinityF), data=sp.datos)

# without replicate blocks (I'm not completely sure, if aov will report
the exact same results here)

aovmodel <- aov(Plantsurvival ~ salinityF*immersionF*SpecTF +
Error(rep:salinityF), data=sp.datos)

lmemodel <- lme(Plantsurvival ~ salinityF*immersionF*SpecTF, random=
~1|rep:salinityF, data=sp.datos)

lmermodel <- lmer(Plantsurvival ~ salinityF*immersionF*SpecTF
+(1|rep:salinityF), data=sp.datos)


As rep/salinityF is simply a short form for rep+rep:salinityF the
difference will be that you have no rep block effect in the models
without replicate blocks.


If you have no missing values, the point about using a mixed model here
is less about variance estimation through a random effect, but
automatically getting the right F-Test of the main-plot effect in ANOVA
(which is the main part of doing a proper split-plot analysis!!!).

My experience is that the anova() function from the lmerTest package
will give you the right denominator df when using the Kenward-Roger
method. You need to use lmer for this:

library(lmerTest)

anova(lmermodel,ddf="Kenward-Roger")

For proper mean comparisons, I suggest to use the emmeans package, with
the Tukey test and letter display from the cld() function:

library(emmeans)

cld(emmeans(lmermodel,"salinityF") #replace salinityF by the factor you
are interested


Finally, if you have one or more missing values, aov() will return
strange anova tables, thus better use a mixed model!


Best regards,

Samuel

-- 
Samuel Knapp

Lehrstuhl f?r Pflanzenern?hrung
Technische Universit?t M?nchen
(Chair of Plant Nutrition
Technical University of Munich)

Emil-Ramann-Strasse 2
D-85354 Freising

Tel. +49 8161 71-3578
samuel.knapp at tum.de
www.researchgate.net/profile/Samuel_Knapp 
<http://www.researchgate.net/profile/Samuel_Knapp>



On 03/04/18 19:16, r-sig-mixed-models-request at r-project.org wrote:

Message: 1
Date: Tue, 3 Apr 2018 07:53:15 +0000
From: "CALLEJA APESTEGUI, FELIPE FRANCISCO"
<felipe-francisco.calleja at alumnos.unican.es>
To: "r-sig-mixed-models at r-project.org"
??????? <r-sig-mixed-models at r-project.org>
Subject: [R-sig-ME] Help establishing mixed model equation for split
??????? plot design
Message-ID:

<DB6P191MB0088D09AF911107B33C1DE5C87A50 at DB6P191MB0088.EURP191.PROD.OUTLOOK.COM>

Content-Type: text/plain; charset="iso-8859-1"

Hello,


I'm looking for some help establishing a mixed model ANOVA using R, 

for a split plot design I've made for an experiment of saltmarsh 
germination. I'll explain as clear as possible the experimental design 
and afterwards what I've done and my doubts. Hope you can help me. I 
haven't worked very much with R so many of my doubts are about what 
I'm "telling" it to do with one or other command.

The experiment consists in meassuring the germination percentage of 

one species in variable conditions of salinity, immersion time and 
presence of other species. I sow seeds in soil core's, that are inside 
plastic boxes that are filled periodically with saline water. There 
are three factors: salinity (3 levels: 0, 5 and 18), immersion time (3 
levels: 0, 20, 40%), species treatment (2 levels: Baccharis, Baccharis 
+ Juncus). Inside each box there are 6 cores that combine in a 
complete random design the factors of immersion and species treatment. 
The box is filled with water at one of the levels of salinity. Thus, 
I'm using a split plot design with salinity as the whole plot factor, 
and immersion and species treatment as the subplot factors. All 
factors are considered fixed. Each box is repeated 5 times. Thus, 
there are 15 boxes and 90 soil cores. The dependent variable is the 
percentage of germination of the species Baccharis in each core.

I have several doubts about how to analyze the array.


1 - As far as I understand, although I'm treating all my factors as 

fixed, this is a mixed model because of the interaction between 
subjects (the boxes I believe), and the "split plot nature" of the 
array, right? In that sense, which function would be better to analyze 
this, the aov of the stats package, the lme of the nlme package, the 
lmer of lme4?

?? 2 - I've had trouble calculating the degrees of freedom for the 

residuals. The only reference I have is that the error of the whole 
plot part should have 12 df's, and the within error should have 60 
df's. With that reference I've established two possible R commands:

fit.aov2 <- aov(Plantsurvival ~ salinityF*immersionF*SpecTF + 

Error(rep:salinityF/immersionF:SpecTF), data=sp.datos)

With rep being the number of repetition. This last one gives the 12 

and 60 df's for the error terms.

The other option is:

fit.okay <- lme(Plantsurvival ~ salinityF*immersionF*SpecTF, random= 

~1|rep/salinityF, data=sp.datos)

But in this last case, the df's are 8 and 60, which makes me suspect 

maybe there is something wrong. But as I said, I haven't cleared my 
head on which should be the correct df's.

Questions: Is the aov line solving a mixed model adequate for my 

design?,

?????????????????????? Is the lme line considering salinityF as a 

random factor? If it is, how can I tell it to consider all factors as 
fixed, but put salinity at the "higher level" of the whole plot and 
the other ones in the "lower level" of the subplot?

I hope the questions and the experimental array are clear. If there 

is any doubt or need more information please let me know. I attach a 
csv file with the data in case you want to see it.

Finally, if is not too much to ask, I'm fairly new to the splitplot 

anova's and R, so I would really appreciate if you could answer be 
with as much detail as possible, to fully understand what's going on 
and where to continue.

Thanks a lot,


Felipe Calleja Ap?stegui

Predoctoral researcher


Instituto de Hidr?ulica Ambiental "IH Cantabria"

C/ Isabel Torres, N? 15

Parque Cient?fico y Tecnol?gico de Cantabria

39011 Santander (Espa?a)

www.ihcantabria.es<http://www.ihcantabria.es/>

Tel:? +34 942 20 16 16 Ext. 1153

Fax: +34 942 26 63 61

e-mail: felipe-francisco.calleja at alumnos.unican.es