# Problems plotting GLM data of binomial proportional data

This might be a question for the programmers, but I thought I would ask here first. Im comparing browsing pressure on plants between sites. Ive a value to indicate Browsing Pressure and count data of trees that have been damaged between locations. Ive been using Crawleys R example (page 574) regarding sex ratios and my issue is with the lines command to plot the information. I can't get a fitted regression line to the points to show up for my data. At least not using the commands Crawley suggested. Ive included Crawley's script for quick reference:

density = c(1,4,10,22,55,121,210,444)
females=c(1,3,7,18,22,41,52,79)
males=c(0,1,3,4,33,80,158,365)
numbers=as.data.frame(cbind(density,females,males))
attach(numbers)
par(mfrow=c(1,2))
p<-males/(males+females)
plot(log(density),p,ylab="Proportion male")
y<-cbind(males,females)
model<-glm(y~log(density),binomial)
xv<-seq(0,6,0.1)
plot(log(density),p,ylab="Proportion male")
lines(xv,predict(model,list(density=exp(xv)),type="response"))


My Script:

data<-####see the dput() data below to insert here
attach(data)
p1<-MS1/(MS1+M1)
y<-cbind(MS1,M1)
GM1<-glm(y~BPT,family=binomial (logit),data=data)
summary(GM1)
plot(BPT,p1,col="black",pch=1,main="Relationship a",xlab="Browsing pressure",
ylab="Moose Damage Survey")


This is where I am having difficulties interpreting Crawley's lines command. I can create a sequence for my data like his xv values - mine go from 0 to 0.7.
xv<-seq(0,0.7,0.01) But as Im not sure what is happening in the command line, blindly inserting my data results in no line showing on my graph. I have some success with regLine from the car library, but its not a line fit to my data. Any help explaining why this works for Crawleys but not my data would be appreciated

My DATA:

structure(list(S = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,
46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60),
BPT = c(0.195778643105884, 0.0651216427326909, 0.0199432997190648,
0.255717971810655, 0.21031730503132, 0.0380060076389563,
0.0592940237882193, 0.00425756881206537, 0.107351336677244,
0.353626952501855, 0.134358354834345, 0.0774003112699534,
0.0571275803730281, 0.102480049705623, 0.506048974065245,
0.637795327349053, 0, 0.00825369912299262, 0.123063816485164,
0.244214078077056, 0, 0.231982659809539, 0.0265824936284919,
0, 0, 0, 0.197470272555566, 0, 0.0481572367104686, 0.339072491473947,
0.0640004726042278, 0.099465609734403, 0, 0.153951519788959,
0.103791449528225, 0.22066571012681, 0.101286659375451, 0.0210055739071239,
0, 0, 0.00811999120846242, 0.0576334384710714, 0.0514027186783361,
0.00907843357263548, 0.0785740169740806, 0.0801612249152947,
0.0439884643248279, 0.189608233745472, 0.434349352638054,
0.188190501082836, 0.016381369054353, 0.215189432724754,
0.0948563822493123, 0, 0.0111745795351048, 0.0289751701436048,
0.0962515835377456, 0.199970627051051, 0.0306277369169669,
0), M1 = c(51, 123, 137, 23, 69, 98, 80, 59, 84, 87, 63,
88, 64, 75, 30, 19, 86, 152, 55, 22, 115, 66, 75, 124, 87,
179, 39, 66, 117, 37, 59, 103, 57, 65, 83, 68, 87, 104, 134,
89, 52, 61, 65, 75, 71, 97, 45, 37, 86, 82, 36, 139, 40,
56, 63, 64, 37, 79, 70, 121), M2 = c(108, 195, 255, 31, 104,
157, 135, 88, 117, 152, 96, 124, 102, 118, 37, 25, 135, 277,
97, 47, 174, 121, 134, 196, 163, 270, 75, 123, 214, 46, 109,
156, 92, 118, 127, 112, 134, 152, 194, 132, 107, 101, 105,
140, 107, 163, 87, 60, 122, 122, 66, 237, 66, 95, 108, 95,
50, 128, 128, 189)), .Names = c("S", "BPT", "M1", "M2"), row.names = c(NA,
-60L), class = "data.frame")

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This is probably more appropriate for the R section of Stackoverflow. Thanks for providing the data; however, it looks like your data column names might be slightly inconsistent. you have p1 <- MS1/(MS1+M2), but I'm not seeing MS1 in the dataframe. Should that be M2? –  N Brouwer Sep 28 '12 at 16:49

Here is a solution.

First, I replaced MS1 with M2 since there is no varibale with the name MS1 in your example data.

attach(data)
p1<-M2/(M2+M1)
y<-cbind(M2,M1)


The model:

GM1<-glm(y~BPT,family=binomial (logit),data=data)


Note that there is one important difference between your model and Crawley's. His predictor varibale was log-transformed, your predictor variable BPT is used untransformed. By the way: Since BPT does include zeros, log-transformation would result in -Inf values.

Now the main plot:

plot(BPT,p1,col="black",pch=1,main="Relationship a",xlab="Browsing pressure",
ylab="Moose Damage Survey")


Now the important differences. Crawley created a sequence xv containg values corresponding to his log-transformed predictor variable density. Note that the lengths of density and xv must be identical. Compare:

range(log(density))
#[1] 0.000000 6.095825
xv<-seq(0,6,0.1)
range(xv)
#[1] 0 6


Since your predictor variable is untransformed, you don't need this kind of sequence but can use the original variable BPT.

lines(BPT,predict(GM1,type="response"))


This is the plot:

If you would like to use your own sequence of values for the prediction, use this:

xv<-seq(0,0.7,length.out = length(BPT))
lines(xv,predict(GM1, list(BPT = xv), type="response"))

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It looks like your data object y and the vector of predicted values you created (xv) are different length. If you do dim(y) it will show that you have 60 rows, but if you do length(xv) the vector is 71 elements long. If you just run predict(GM1,list(density=exp(xv)),type="response") you get 60 predicted points.

You can manually shorten your xv vector, or try this (which I cribbed from the seq help file:

xv<-seq(0,0.7,by = ((0.7 - 0)/(60 - 1)))


This should make xv have 60 elements.

Books by Alain Zuur et al. are excellent introductions for ecologists to GLMs and mixed models for R.

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