Dear all,
I studied in tank prey fish behavior. Using the design described below
(and R code), I want to test the effects of both habitat and predator
(and interaction) on prey fish's vertical distribution, which was
recorded (with repeated measures) as a categorical variable.
I found that package mlogit might fit to my need but I don't know how to
specify my complex design in the formulae (which of my variables are
individual- or alternative-specific?) If this package is the good one, I
would be glad you help me in formulating my full model. If it is not,
any suggestion would be appreciate.
Design:
Factor Habitat (Hab): fixed, 3 levels
Factor Predator (Pre): fixed, 2 levels (abscence vs presence)
Factor subject (Sub): random, nested in Hab X Pre, 4 levels (hence a
total of 24 subjects)
Data collection using repeated measures.
I observed each subject during a 130 min trial but I collected data only
during 3 periods (10 min long separated each other by 50min) --> Factor
period (Per): 3 levels, from 0min to 10min (after trial start), from
60min to 70min, and from 120 to 130min.
Within each period, I recorded subject's positions 21 times (every
30sec). I consider these observations as independent because 30 sec is
large enough so that fish go back-and forth several time in the tank.
--> Postition (Pos) was a categorical variable with 8 levels. Levels are
in reality ordered but I don't need to consider them as such. However, I
would like to compare them 2 by 2, which is more useful as regard to my
ecological hypotheses).
To test putative differences in vertical distribution between habitat
and predator treatments, I thought to use mixed linear modeling with as
response variable the number of time(Nobs) each position was observed
(out of 21 observations for a given combinations of Hab, Pre, Sub and
Per). However, the 8 values of Nobs for a given period are not
independent, by definition (ad up to 21). Hence, I cannot use linear
modeling and dig in the way of model multinomial. However, I appreciate
the boxplot (run R code) as graphical representation and would be able
to assign letters for pairwise comparisons of positions within a
treatment, and also of treatments within a position level.
I hope I have been clear and I thank you in advance,
Best regards,
Pierre THIRIET
Université de Nice
########################### here is R code for exemplifying the
structure of my data set.
#factorial design
hab=c("h1","h2","h3")
pre=c("a","p")
sub=c("s1","s2","s3","s4")
per=c("p1","P2","p3")
tim=paste("t",1:21,sep="")
mydata=expand.grid(tim=tim,per=per,sub=sub,pre=pre,hab=hab)
#random generation of the response variable,with an effect of factor pre
(by adding a vector of probability weights)
require(plyr)
posl=paste("z",1:8,sep="")
mydata$pos=factor(NA,levels=posl)
n=length(mydata$pos[pre=="a"])
mydata$pos[mydata$pre=="a"]=replicate(n,sample(posl,1,prob=c(0.05,0.05,0.05,0.4,0.3,0.05,0.05,0.05)))#strong
preference for z3 and z4
mydata$pos[mydata$pre=="p"]=replicate(n,sample(posl,1,prob=c(0.3,0.4,0.05,0.05,0.05,0.05,0.05,0.05)))#strong
preference for z1 and z2
summary(mydata)
# number of time (out of 21) each position was observed, given hab, pre,
sub and per
mydata2=ddply(mydata,.(hab,pre,sub,per,pos),summarize,nobs=length(pos),.drop=F)
mydata2[,1:5]=catcolwise(function(x)as.factor(x))(mydata2)
summary(mydata2)
# boxplot of frequencies of occpupancy
require(ggplot2)
ggplot(mydata2)+geom_boxplot(aes(pos,I(100*nobs/21)))+facet_grid(pre~hab)
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