Use of offset variable when analysing rates in lme4

Dear Caroli,

Your model is
visits ~ Pois(lamba)
log(lambda) = mu = beta_i * treat + beta_j * timecat + log(infl)

which can be rewritten to

log(lambda) - log(infl) = mu - log(infl) = beta_i * treat + beta_j * timecat
log(lambda) - log(infl) = log(lambda / infl) = log(visitation rate)

hence beta_i and beta_j are effects in log(visitation rate). Exponentiating the results from glht should give you the relative effects on the visitation rate.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be

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-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] Namens De Waal, C, Mej <caroli at sun.ac.za>
Verzonden: woensdag 2 april 2014 11:50
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] Use of offset variable when analysing rates in lme4

Dear all,

This is my first post to the list as I have been unsuccessful in getting an answer elsewhere. I am also quite new to R.

I am investigating variation in pollinator visitation rate (number of visits per inflorescence) with treatment and time category as fixed factors. Block is a random factor. Following Zuur et al (2009), I used the number of visits as response variable with the log(number of inflorescences) as offset variable. A poisson model was overdispersed, and therefore I opted for a negative binomial model in lme4, as follows:

model1 = glmer.nb(visits ~ treat + timecat + offset(log(infl)) + (1|block))


I am specifically interested in differences in visitation rates between treatments. I therefore performed a post hoc test:

OPexp1 =  glht(model1,mcp(treat = "Tukey"))
plot(cld(OPexp1))

When I plot these results, I get number of visits on the y axis. But what I want is visitation rate (visits per inflorescence). How do I specifiy that the post hoc test should be performed using visitation rate?

I assume what is happening is that fitted values are currently expressed as ? ? V, but how to I specify that they should be expressed as ? (visits per inflorescence) only? On p 240, Zuur et al (2009) mentions that this is possible, but I have not been able to find an example.

Any advice would be much appreciated.

Kind regards,

Caroli de Waal

PhD Student
University of Stellenbosch, South Africa The integrity and confidentiality of this email is governed by these terms / Hierdie terme bepaal die integriteit en vertroulikheid van hierdie epos. http://www.sun.ac.za/emaildisclaimer


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