[R-sig-eco] Factors in partial RDA part 2

[Andrew Halford]

Hi Listers,

Further to my last post I am seeking more insights into how to interpret
effects of Factors in a RDA analysis.

I think of a factor as a single variable whose influence on observed fish
distribution patterns I would like to quantify, along with a bunch of other
numerical variables.

To do the analyses this Factor (called 'geom') is turned into a number of
dummy variables (seven actually).

The conceptual problem I am having is that when I do a call to vif.cca to
check on collinearity for example, the output suggests I should remove some
of the dummy variables making up the levels of my Factor. Doing this would
leave me with only 3 of the dummy variables out of the original 8 to put
into the RDA. I then don't see that I am actually testing the Factor 'geom'
anymore but rather just individual variables representing a couple of the
different levels of the original Factor. How do I proceed with this?

The same conundrum for me is seen when I run the forward.sel command to
look at the most efficient number of explanatory variables to have in the
final model. The process selects only some of the dummy variables to
include in the model. Again I struggle to see how I am testing or including
the full effects of the Factor 'geom' if only a few of the dummy variables
are actually included in the model.

# here is the model run with all the potential explanatory variables
('geom' is the FACTOR with 7 levels)

> fish.env <-
rda(fish.h~coral_cover+macroalgae+turf_algae_sqrt+ccc_4thrt+rubble_sqrt+reef_slope_sqrt+rugosity

+exposure+min_d_sqrt+d_range+chl_a_log+popn_density_4throot+fp+protection
                +geom,data=env.factor)

# collinearity assessment - the results favour dropping 3 of the 'geo'
dummy variables leaving only 2 for the model.
> vif.cca(fish.env)

coral_cover           macroalgae      turf_algae_sqrt
ccc_4thrt          rubble_sqrt      reef_slope_sqrt
2.688656             3.099972             2.849219
1.771637             2.411291             2.418953
rugosity             exposure           min_d_sqrt
d_range            chl_a_log         popn_density_4throot
2.967752             3.433961             2.587696
2.643991             3.626107             4.571781
fp                  protection           geomgeo_bl
geomgeo_cbrc        geomgeo_isefr        geomgeo_isprc
4.059624             3.195210             4.329852
12.657270             9.570015            12.052385
geomgeo_lefr         geomgeo_oefr
7.347812            17.090731

# here I have kept all the 'geom' dummy variables to submit to forward
selection and it only selects 3 of them, hence it doesnt feel that I am
actually including a Factor 'geom' in the model but rather just a few
individual dummy variables?


> forward.sel(fish.h,env.dummy3,adjR2thresh=R2a.all_fish_env)

Testing variable 1
Testing variable 2
Testing variable 3
Testing variable 4
Testing variable 5
Testing variable 6
Testing variable 7
Testing variable 8
Procedure stopped (alpha criteria): pvalue for variable 8 is 0.092000
(superior to 0.050000)
        variables order         R2     R2Cum   AdjR2Cum        F  pval
1        exposure     8 0.07086240 0.0708624 0.04925455 3.279475 0.001
2              fp    13 0.04756799 0.1184304 0.07645089 2.266248 0.002
3       geo_isefr    16 0.04571706 0.1641474 0.10298750 2.242500 0.003
4       chl_a_log    11 0.03812686 0.2022743 0.12250174 1.911778 0.009
5          geo_bl    17 0.03423972 0.2365140 0.13863121 1.749016 0.008
6       geo_isprc    21 0.03384005 0.2703541 0.15514682 1.762391 0.012
7 reef_slope_sqrt     6 0.03466752 0.3050216 0.17353919 1.845666 0.007


Any advice appreciated

cheers

Andy






-- 
Andrew Halford Ph.D
Research Scientist (Kimberley Marine Parks)
Dept. Parks and Wildlife
Western Australia

Ph: +61 8 9219 9795
Mobile: +61 (0) 468 419 473

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