[R-sig-ME] P-values from interaction terms using lme4

[Sam Hardman [sah74]]

Dear all,


I have some data which I would like to analyse using lme4 and I would really appreciate some help deciding what the best method is.


My experiment is as follows:


I tested the responses of urban and rural great tits to playbacks of great tit song from a loud speaker within their territories.


I created three playback song types:

-undegraded

-degraded

-very degraded


I played these to birds in 20 different cities. In each city I tested one bird in the city centre and one bird in a rural location outside of the city (i.e. paired samples). Each bird received all three playback types.


I measured five different responses to these playbacks:

-Time to sing back to playback (in seconds)

-Time to sing back to playback (in seconds)

-Time the bird spent within five metres of the speaker (in seconds)

-Number of times the bird flew over the speaker (count)

-The closest approach the bird made to the speaker (in metres)


For each of these five repsonses I would like to know if there is an interaction between habitat and playback type.


So, I have a model which looks like this:


mod1<-lmer(repsonse ~ Playback*UR + (1|ID))


Where response is one of the five repsonse behaviours, playback is the playback type, UR is habitat type (urban or rural) and ID is the ID of the bird.


This gives me results and P-Values but am not sure these P-values are valid and I think I should compare this model to a null model to get a valid P-values.


So I can use a likelihood ratio tests to test for differences in response by habitat type alone:


mod1<-lmer(approach ~ UR + (1|Location))
mod2<-lmer(approach ~ 1 + (1|Location))
anova(mod1, mod2)

or for differences in response according tom playback type alone:

mod1<-lmer(approach ~ Playback + (1|Location))
mod2<-lmer(approach ~ 1 + (1|Location))
anova(mod1, mod2)

But how should I do this when there is an interaction term? I deally I would like P-values for each playback type in interaction with habitat. e.g.

Undregraded playback * Habitat (urban/rural
Degraded playback * Habitat (urban/rural)
Very degraded playback * Habitat (urban/rural)

This would allow me to say, for example, something like "urban birds approached the speaker more closely than rural birds in response to undegraded playbacks". I would like to do this with each of the five response behaviours.

I would really appreciate any suggestions for the best way forward with this and apologies if this question is too simple for this group.

Best wishes,
Sam


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