[R-sig-eco] logistic regression and spatial autocorrelation

[Tim Seipel]

Thank you for the replies.

To clarify, the points are generally ordered by geogrpahic distance and 
increasing elevation (they are a converted GPS track- spaced evenly 
every 200 m), though there are some ups and downs in elevation. The 
order of points become more difficult at high elevation. The sampling 
followed river valleys which merge to form the Rhine river in 
Switzerland. My grouping factor reflects this, my random factor consists 
of three groups, 'chur'- which is the primary valley, then the valley 
splits to form two secondary tributaries 'vord' and 'hint'.

Given that my points become less well order toward high elevation should 
I use form= ~1|group?



On 25.08.11 11:21, Dunbar, Michael J. wrote:
> Hi Tim
>
> You haven't really explained where your group variable in the glmm has come from. Moving from glm to glmm you've changed two things, adding the grouping and the autocorrelation as well.
>
> You have to be very careful when using the autocorrelation function. As it stands the model will assume that the points on your gradient are evenly spaced and sorted in order.
>
> Regards
> Mike
>
>
> -----Original Message-----
> From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Tim Seipel
> Sent: 25 August 2011 10:04
> To: r-sig-ecology at r-project.org
> Subject: [R-sig-eco] logistic regression and spatial autocorrelation
>
>
> Dear List,
> I am trying to determine the best environmental predictors of the
> presence of a species along an elevational gradient.
> Elevation ranges from 400 to 2050 m a.s.l. and the ratio of presences to
> absences is low (132 presences out 2800 samples)
>
> So to start I fit the full model of with the variable of interest.
>
> sc.m<-glm(PA~sp.max+su.mmin+su.max+fa.mmin+fa.max+Slope+Haupt4+Pop_density+Dist_G+Growi_sea+,data=sc.pa,'binomial')
>
> First, I performed univariate and backward selection using Akaike
> Information Criteria, and the fit was good and realistic given my
> knowledge of the environment though the D^2 was low 0.08. My final model
> was:
> ---------------------------------
> glm(formula = PA ~ Slope + sp.mmin + su.max + fa.mmin + Haupt4,
>       family = "binomial", data = sc.pa)
>
> Deviance Residuals:
>       Min       1Q   Median       3Q      Max
> -0.5415  -0.3506  -0.2608  -0.1762   3.0768
>
> Coefficients:
>                Estimate Std. Error z value Pr(>|z|)
> (Intercept) -73.45212   23.13842  -3.174  0.00150 **
> Slope        -0.03834    0.01174  -3.265  0.00109 **
> sp.mmin     -15.34594    5.30360  -2.893  0.00381 **
> su.max        5.09712    1.70332   2.992  0.00277 **
> fa.mmin      13.52262    4.64021   2.914  0.00357 **
> Haupt42      -0.72237    0.27710  -2.607  0.00914 **
> Haupt43      -0.95730    0.37762  -2.535  0.01124 *
> Haupt44      -0.25357    0.24330  -1.042  0.29731
> ---
>       Null deviance: 958.21  on 2784  degrees of freedom
> Residual deviance: 896.10  on 2777  degrees of freedom
> AIC: 912.1
>
> ----------------------
>
> I then realized that my residuals were all highly correlated (0.8-0.6)
> when I plotted them using acf() function.
>
> So to account for this I used glmmPQL to fit the full model:
>
> model.sc.c<- glmmPQL(PA ~
> sp.mmin+su.mmin+su.max+fa.mmin+Slope+Haupt4+Pop_density+Dist_G+Growi_sea, random=
> ~1|group.sc, data=sc.dat, family=binomial, correlation=corAR1())
>
> However, the algorithm failed to converge and all the p-vaules were
> either 0 or 1 and coefficient estimates approached infinity.
> Additionally the grouping factor of the random effect is slightly
> arbitrary and accounts a tiny amount of variation.
>
> ---
> So know I feel stuck between a rock and a hard place, on the one hand I
> know I have a lot of autocorrelation and on the other hand I don't have
> a clear way to include it in the model.
>
> I would appreciate any advice on the matter.
>
> Sincerely,
>
> Tim
>
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>
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