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I built a linear mixed effect model with nlme with Body length, Habitat and Sex as fixed effects. Body length is added for body size correction while the other two both have two levels. In the random part of the model Population was used as a random effect (with 8 levels). To account for the violation of heterogeneity I used the VarIdent function. The model is:

Model<- lme(A~ Body_length+Sex X Habitat, random= ~ 1|Population, method="REML", weights = varIdent(form = ~1|PopulationSex))*

As populations are clearly linked to habitats each population can only belong to one Habitat level. As a result of the connection between Habitat and Population (I think) the DF in case of Habitat is 6 while in case of Sex it is 500. To my knowledge low DF results in less chance to detect significant result and also increases the inaccuracy of the estimation. The model was followed by a contrast analysis. When visually inspecting the emmeans it seems like the Standard Errors estimated are very high and are almost the same for each Habitat X Sex. Also Sex and Habitat seems to have simiar effect on the response variable. I tried to check the data building an identical GLS model (without the random effect) and Habitat also became significant , had the same DF as Sex and the Standard Errors estimates became lower and differed between groups. Therefore the random effect -due to its few levels (as suggested by some authors)- seems to case this discrepancy. At the same time leaving out Population effect from the model would be incorrect as Populations clearly differ for each other and individuals within a population are more alike. So my questions would be: Is the random effect specified correctly? Is there a way to fix my model? If not could you please recommend other type models to be used with this kind of data?

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It appears that your model is appropriate. But you can't have your cake and eat it too. If you have 8 populations, and those are the sampling units for habitats (I suppose 4 populations per habitat?), then that's exactly like having 8 subjects in your study, 4 per treatment. You don't have much data for discerning differences between habitats, regardless of what your visual impressions might be.

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  • $\begingroup$ So my follow up idea on this would be to apply a gls model instead : Model2<- gls(A~ Body_length+Sex X Population,method="REML", weights = varIdent(form = ~1|PopulationSex)) and then compare the different habitats/ sexes by contrast analysis with p-value correction. Do you think this is an appliable method to overcome such a problem? $\endgroup$
    – Anna
    Commented Mar 27, 2023 at 12:22
  • $\begingroup$ No, I don't think this is a good approach. As I said earlier, your model appears appropriate. The problem is you don't have enough data. If you have only 8 subjects and you measure each subject 1000 times, that doesn't change the fact that you have only 8 subjects. $\endgroup$
    – Russ Lenth
    Commented Mar 27, 2023 at 14:38

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