[R-sig-ME] Fwd: linear model selection analysis

[Jarrod Hadfield]

Hi,

If your traits don't appear as interactions (or quadratics) then the 
coefficients associated with the traits are Lande-Arnold standardised 
selection gradients if you fit a log-link glm (i.e. the standard with 
Poisson models).  If you do have interactions, then its a bit more 
complicated.

Cheers,

Jarrod


On 11/05/2016 08:54, Harriet Jamieson wrote:
> Hello list,
>
> I am attempting a selection analysis sensu Lande and Arnold (1983), where
> the basic premise is to model relative fitness of individuals as a function
> of standardised trait values, where the relative fitness is relative to the
> mean (by dividing fitness values by the mean fitness value, so centred
> around 1) and the standardised trait values are calculated as z scores,
> i.e. = (trait - mean) / SD, so they are centred around zero. The idea is
> that, in its simplest form with a single trait of interest, the results of
> the model 'fitness ~ trait’ should give a coefficient for ‘trait’ that is a
> selection gradient. My problem is that my ‘trait’ in this case is count
> data, and it doesn’t seem appropriate to transform Poisson data into the
> standardised trait variable as above. So my first question is whether this
> is an appropriate way to treat count data?
>
> I have considered three alternatives to work round this:
> 1. Plough ahead and transform the count data into the standardised trait
> scores and do the analysis.
> 2. Use the raw count data as the trait variable, unstandardised - this
> might be fine as a general linear model, but doesn’t give me sensible
> estimates for selection gradients on the traits.
> 3. I tried looking for published work where count data was used in a
> selection analysis - I’m sure I can’t be doing something that strange, but
> I could only find one other example, and here they did something different,
> where they actually turned the model around and modelled the trait as a
> function of fitness, so trait ~ fitness, where fitness was relativised but
> the trait was kept as count data and a Poisson distribution was specified.
>
> I suppose if anyone has any specific experience of selection analysis, this
> would be extremely helpful. More generally, however, I think I would like
> some thoughts on the following questions:
> 1. Is it appropriate to z score transform count data? Why/why not?
> 2. If the basic model Y ~ X gives a coefficient for X that is the gradient,
> then how is this interpretation of the coefficient affected if X is raw
> count data?
> 3. Does the example I found where the model was flipped round give the same
> information?
>
> I realise the problem is rather specific to a certain application of linear
> models, but I would be grateful for any insight anyone could offer on how
> these alternatives change the interpretation of the models.
>
> Thanks very much in advance,
> Harriet
>
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>
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