[R-sig-eco] Using residuals as dependent variables

[Ivailo]

On Thu, Jun 21, 2012 at 8:06 PM, Chris Mcowen <chrismcowen at gmail.com> wrote:
> Dear List,
>
> I am wondering if the methodological approach I am taking is correct and
> would be very grateful if people could comment and make suggestions, much
> appreciated.
>
> I have developed the best model ( AIC model selection) using oceanographic
> data ( i.e. SST, chlorophyll, NPP...x6) to predict reported fisheries catch
> for 52 countries.
>
> I then extract the residuals from the model and anything positive has a
> higher catch than would be predicted given the level of productivity in the
> country, with the opposite being true.

Dear Chris,

it is difficult to comment without having more details about the model
(i.e. how many samples, variables, etc. you have) you're trying to
fit, but keep in mind that the residuals indicate that some variation
in the dependent variable has not been "explained" by the predictors
included in the model. If you need to explain the unexplained
variation (i.e. the residuals from the model), why don't you include
all the variables of interest just from the beginning?

> What I want to do is:
>
> 1.       Regress a suite of ecological and socioeconomic variables against
> the residuals from the oceanographic model to determine which factors cause
> some countries to be above and some below. I.E as trophic level increase the
> residuals become increasingly negative.
>
> 2.       Ideally ( and I am unsure how or if it is possible) work out for
> each country which variables/s cause the poor fit of that country to the
> oceanographic model.

My feeling is that you might want to perform a multilevel model on
your data, but as I just learn that matter myself I would recommend
you to check some of the wonderful resources on this topic --- either
"Data Analysis Using Regression and Multilevel/Hierarchical Models" by
Gelman & Hill (CUP, 2007) or "Mixed Effects Models and Extensions in
Ecology with R" by Zuur, Ieno, Walker, Saveliev & Smith (Springer,
2009).

> P.S - Below is the type of conclusions I am drawing
>
> There are a number of reasons why some countries have higher / lower catch
> than you would expect.
>
> For example if the target fishery is a high trophic level species then the
> link between primary productivity and catch will be lesser than if the
> species was a lower trophic level ( transfer efficiency etc etc)- resulting
> in a negative residual.  Alternatively it maybe that the area is being
> overfished i.e. the north sea meaning more fish are being caught in that
> region than it can sustain - resulting in a high positive residual (as
> predicted by the model)
>
> In reality it is likely a combination of this plus other, however some
> factors will be relevant to others i.e. Somalia has a really low catch
> compared to its productivity likely due to piracy and poor reporting of
> statistics.

This type of inference could be made by using a hierarchical model
setting where you relate individual catches to both catch-level
variables (as it appears you have already done that) and to
country-level variables (this you still want to do).

HTH,
Ivailo
-- 
UBUNTU: a person is a person through other persons.