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Thread: Question related to Generalized Linear Mixed Model

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    Question related to Generalized Linear Mixed Model




    I'm working with a dataset containing the following:

    Fixed variables: Age, Body Size, Antler Size, Average Age
    Random variable: Animal ID
    Response: Number of Offspring

    My primary goal is to develop a GLMM that will best explain the effects of the fixed variables on numbers of offspring produced

    I first wanted to examine the dataset for collinearity between my fixed variables (since I think age, body size, and antler size are collinear), and did so using VIF. Results from VIF are as follows

    Age=3.5
    Average Age = 1.2
    Body Size = 3.18
    Antler Size = 5.57

    I'm finding conflicting information as to when collinearity is a problem as identified by VIF. Some say above 5 is problematic, some say above 10. Any advice on whether or not VIF scores of this level will cause problems with my GLMM. I don't think any sort of centering, etc. will work to reduce collinearity in my situation, and I can't really drop any of the variables since all are at the heart of my research questions. Any additonal tests, etc? Any insight is appreciated.

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    Re: Question related to Generalized Linear Mixed Model

    If this collinearity does not produce numerical problems (i.e. your fitting algorithm converges) and you are aware of the consequences of collinearity, maybe there is not really a problem: Collinarity (in a random sample) usually does not produce bias, but there are two potential disadvantages: 1.) the estimated regression coefficients/effects are not "pure" but confounded by other correlated predictors, and 2.) the variance of the parameter estimates inflates over-proportionally, since you add predictors but not much additional information. So if your model converges, you are pleased with your significance values and you are aware of the fact that predictors are to some extend exchangable, everything might be fine...

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    Re: Question related to Generalized Linear Mixed Model


    Ok. Thanks for insight. My next question is regarding model selection using AIC. I have two competitive models: model 1 (number of offspring~body size + antler size + Average age + (1|Animal ID)) and model 2 (number of offspring~body size + antler size + Average age + Antler size*Average age + (1|Animal ID). AIC for model 1 is 200 and AIC for model 2 is 199. According to many, a change of 2 AIC units is required before a model is really "better" than another. In this case it appears at first glance to only be a 1 AIC unit change, indicating that the additional parameter is uninformative; however, AIC automatically increases by 2 AIC units with the addition of another parameter as a "penalty". My question is this: is the model with the additional parameter (model 2) superior to model 1 as evident by the lower AIC (really treated like a 3 AIC unit difference due to the penalty for the additional parameter) or is the additional parameter in model 2 uninformative, thereby making the more simple model 1 superior. Hope that makes sense as brain is a bit boggled....

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