[R-sig-eco] question on gls model interpretation

[Zoltan Botta-Dukat]

Dear Iris,

The expected value of any treatment combination can be calculated as sum 
of the coefficients. For example:
E(no comptetitors, no insecticide) = Intercept
E(many competitors, high concentration) =  Intercept + conditionold + 
contaminationhigh + conditionold:contaminationhigh

The non-significant interactions would mean that effects of competition 
and insecticide are simple summed.

You have two interaction parameters that significantly differ from zero. 
For example, conditionold:contaminationhigh=1.2005231. This value can be 
interpreted by two ways. High insecticede concentration has a strong 
negative effect if no competion (contaminationhigh=-1.2825250), but it 
has negligible effect, if competition is stong: 
-1.2825250+1.2005231=-0.0820019. The interaction parameter measures the 
difference between two levels of competition in the effect of insecticide.
Another interpretation is that interaction coefficient measures the 
difference between two levels of insecticide treatment in the effect of 
strong competition (ie. in the decrease of abundance caused by strong 
competition).
 From mathematical point of view these two interpretations are 
equivalent. You can choose either.



Best wishes


Zoltan


2013.01.29. 14:54 keltezéssel, "Iris Kröger" írta:
> Dear R-Sig-Ecology,
>
> I'm analysing an experiment about mosquito larvae beeing treated with 3 conditions (no competitors added = "algae", few competitors added ="new", many competitors added ="old"). After 2 weeks I contaminated all conditions with 3 insecticide concentrations (no treatment = "control", low concentration ="low", medium concentration = "medium", high concentration ="high"). The effect of treatments was observed over a time period of 35 days.
> Now I would like to analyse, if there is a synergistic effect of condition and insecticide treatment. I used a gls model (see below).
> (Important: the mosquito larval abundances differed significantly between conditions when insecticide contamination was applied. I'm not sure if this is a problem for the further analyses....)
>
> Obviously there is a synergistic effect (condition * contamination, p<0.001), but I don't know how to interpret the output. Which treatments did the model compare?Does it mean, that the effect of medium and high contamination increased significantly at old-condition compared with the effect at algae-condition? (This I can hardly believe. Mosquito larval abundances were close to zero even without contamination at condition-old&contamination-control , hence an additional effect of insecticide treatment should be hardly detectable. I would rather expect an effect at condition-new in combination with contamination...)
>
> I used:
> mod1<-gls(log10(mosquito+1) ~condition * contamination , data=MK ,
>   correlation = corAR1(form=~day |bucket),
>   weights=varIdent(form= ~ 1|condition),
>   method="REML")
> summary(mod1)
> anova(mod1)
>
> The output was:
>
>> anova(mod5)
> Denom. DF: 258
>   numDF F-value p-value
> (Intercept) 1 221.04772 <.0001
> condition 2 243.79461 <.0001
> contamination 3 24.71058 <.0001
> condition:contamination 6 23.92481 <.0001
>
> Coefficients:
>   Value Std.Error t-value p-value
> (Intercept) 1.9778939 0.1391071 14.218493 0.0000
> conditionnew -0.7766661 0.1610017 -4.823963 0.0000
> conditionold -1.8958920 0.1461519 -12.972068 0.0000
> contaminationhigh -1.2825250 0.1840214 -6.969433 0.0000
> contaminationlow -0.2044417 0.1840214 -1.110967 0.2676
> contaminationmedium -0.7833268 0.1840214 -4.256715 0.0000
> conditionnew:contaminationhigh 0.1011773 0.2129852 0.475044 0.6352
> conditionold:contaminationhigh 1.2005231 0.1933408 6.209364 0.0000
> conditionnew:contaminationlow -0.1917487 0.2129852 -0.900291 0.3688
> conditionold:contaminationlow 0.1496570 0.1933408 0.774058 0.4396
> conditionnew:contaminationmedium -0.1454105 0.2129852 -0.682726 0.4954
> conditionold:contaminationmedium 0.7940461 0.1933408 4.106978 0.0001
>
> Can anyone help me?
> Many thanks,
> Iris
>
> 	[[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology


-- 
Botta-Dukát Zoltán
--------------------------------
Ökológiai és Botanikai Intézet
Magyar Tudományos Akadémia
Ökológiai Kutatóközpont
--------------------------------
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu


Zoltán BOTTA-Dukát
--------------------------------
Institute of Ecology and Botany
Hungarian Academy of Sciences
Centre for Ecological Research
--------------------------------
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu