[R-sig-eco] error distribution in GLM model

[Peter Solymos]

Mario,

If you can assume that the waiting time between events is constant
through time, you can model your counts per unit time with Poisson glm
(constant waiting time leads to an exponential survival function).
log(Observation time) can be used as an offset:

glm(interactions~covariate, offset=log(obs.time), family=poisson)

Note that diagnostic plots indicate that homogeneous Poisson process
assumption might not hold.

Peter

--
Péter Sólymos, Dept Biol Sci, Univ Alberta, T6G 2E9, Canada AB
solymos at ualberta.ca, Ph 780.492.8534, http://psolymos.github.com
Alberta Biodiversity Monitoring Institute, http://www.abmi.ca
Boreal Avian Modelling Project, http://www.borealbirds.ca


On Sun, Aug 19, 2012 at 10:14 AM, Mario Serrajotto
<mario.serrajotto at gmail.com> wrote:
> Dear R-users,
>
> apologies for the total beginner's question. I have some behavioural
> data expressed in number of interactions measured over a certain
> amount of time (expressed in minutes). I have calculated the number of
> interactions per minute and I would like to model this variable as a
> function of a covariate. I am, however, struggling with the choice of
> the argument family. I have thought to log transform the data and
> model them with a GLM by specifying a Gaussian family. Unfortunately
> for me my data do not seem to follow a normal distribution. I then
> recalled that my response is some kind of proportion and should
> perhaps be modelled with binomial GLM. But the data are not bounded
> from 0 to 1...Any suggestions would be greatly appreciated! Please see
> data and R code at the bottom of the e-mail.
>
> Cheers,
>
> Mario
>
> # number of interactions recorded
> interactions<-c(2,1,2,3,0,0,0,0,1,2,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,3,0,8,7,6,3,5,4,5,7,6,0,0,0,0,2,2,3,4,1,2,5,6,2,4,0,6,0,0,39,46,45,48,11,8,7,8,6,7,13,10,7,9,32,38,39,25,32,30,11,13)
>
> # observation time (in minutes)
> obs.time<-c(9.4666666667,9.7,9.1,9.45,8.8166666667,8.9333333333,8.7166666667,8.85,6,3.85,6.1666666667,6.3166666667,2,2.3833333333,7.95,9.6333333333,9.8166666667,1.5,9.4166666667,9.35,1.2833333333,1.85,1,2.3333333333,6.6,6.3166666667,4.4333333333,2.5,9.35,9.3166666667,6.6,6.3166666667,6.3166666667,6.1666666667,6,9.5166666667,9.1,9.45,8.7333333333,2.5,2.3833333333,2,1.85,1.2833333333,2.3833333333,8.65,8.5333333333,8.5,8,7.6833333333,0.55,2.4,8.5166666667,8.1833333333,7.9166666667,8,9.5833333333,9.6833333333,9.6833333333,9.4833333333,9.5833333333,9.55,9.4833333333,9.45,9.7333333333,9.6833333333,9.6333333333,9.45,9.4833333333,9.6833333333,9.65,9.6166666667,9.5,9.4333333333,9.3166666667,9.3333333333,9.4166666667,9.4666666667)
>
> # covariate
> covariate<-c(15,15,18,18,40,40,45,45,42,42,50,50,200,200,400,400,500,500,200,200,150,150,90,90,45,45,37,37,42,42,37,37,80,80,110,110,150,150,300,300,250,250,85,85,18,18,42,42,15,15,50,50,45,45,200,200,45,45,15,15,115,115,125,125,500,500,550,550,550,550,45,45,37,37,80,80,100,100)
>
> # calculate total number of interaction per minute
> interactions.m<-interactions/obs.time
>
> # fit glm
> glm(log(interactions.m+1)~covariate)
>
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