[R-sig-eco] Quantile regressions across several predictors
Cade, Brian
cadeb at usgs.gov
Thu May 26 17:12:43 CEST 2016
Peter: Your question is not quite clear to me. I thought at first you
might be talking about quantile regression but then you mentioned the 50%
quantile (which is not the mean) of the predictor and binning. So I'm not
sure exactly what you are after. But under the presumption that you might
really be thinking along the lines of quantile regression (which does not
require binning by predictors), I took your example data and ran it through
a linear quantile regression from quantreg package, where quantiles of the
continuous dependent variable are estimated conditional on an additive
effect of the three predictors provided. Some summary output below for
0.10, 0.25, 0.50, 0.75, and 0.90 quantiles. Here it looks as if only pred2
has a strong nonzero (negative) effect for the upper quantiles (0.50, 0.75,
and 0.90) of the dependent variable based on 95% confidence intervals not
overlapping zero. If this is along the lines of what you were thinking
about, then perhaps you can frame you question in a more focused fashion
and I might be able to provide better advice. There is much more that can
be done with quantile regression. Plotting this sort of summary info is
especially useful.
Brian
example.qr.results <- rq(dependent ~ pred1 + pred2 +
pred3,data=example.data,tau=c(0.10,0.25,0.50,0.75,0.90))
summary(example.qr.results,se="rank",iid=F,alpha=0.05)
Call: rq(formula = dependent ~ pred1 + pred2 + pred3, tau = c(0.1,
0.25, 0.5, 0.75, 0.9), data = example.data)
tau: [1] 0.1
Coefficients:
coefficients lower bd upper bd
(Intercept) 1665.53049 -17.44156 2493.10597
pred1 8.81923 -40.77369 53.37269
pred2 -57.39947 -85.39144 23.59046
pred3 -19.74443 -60.76278 61.19992
Call: rq(formula = dependent ~ pred1 + pred2 + pred3, tau = c(0.1,
0.25, 0.5, 0.75, 0.9), data = example.data)
tau: [1] 0.25
Coefficients:
coefficients lower bd upper bd
(Intercept) 1231.52601 821.28092 1935.37219
pred1 -2.25995 -29.68130 30.79243
pred2 -20.83135 -62.10712 3.75916
pred3 -3.51839 -23.45116 13.38838
Call: rq(formula = dependent ~ pred1 + pred2 + pred3, tau = c(0.1,
0.25, 0.5, 0.75, 0.9), data = example.data)
tau: [1] 0.5
Coefficients:
coefficients lower bd upper bd
(Intercept) 1714.10796 729.52807 2553.46234
pred1 2.02560 -39.70704 29.34070
pred2 -41.81862 -81.38048 -4.06101
pred3 2.90515 -18.68419 21.02118
Call: rq(formula = dependent ~ pred1 + pred2 + pred3, tau = c(0.1,
0.25, 0.5, 0.75, 0.9), data = example.data)
tau: [1] 0.75
Coefficients:
coefficients lower bd upper bd
(Intercept) 2118.28691 1186.20556 3496.67829
pred1 17.75399 -38.41521 32.63466
pred2 -62.43047 -113.90480 -15.35846
pred3 10.53731 -41.48255 35.23541
Call: rq(formula = dependent ~ pred1 + pred2 + pred3, tau = c(0.1,
0.25, 0.5, 0.75, 0.9), data = example.data)
tau: [1] 0.9
Coefficients:
coefficients lower bd upper bd
(Intercept) 2855.31941 1631.16351 4217.13007
pred1 1.31388 -71.21536 65.65507
pred2 -77.54635 -106.11297 -30.33534
pred3 1.74284 -63.49143 56.91477
Warning messages:
1: In rq.fit.br(x, y, tau = tau, ci = TRUE, ...) :
Solution may be nonunique
2: In rq.fit.br(x, y, tau = tau, ci = TRUE, ...) :
Solution may be nonunique
3: In rq.fit.br(x, y, tau = tau, ci = TRUE, ...) :
4.22535211267606 percent fis <=0
4: In rq.fit.br(x, y, tau = tau, ci = TRUE, ...) :
Solution may be nonunique
>
Brian S. Cade, PhD
U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO 80526-8818
email: cadeb at usgs.gov <brian_cade at usgs.gov>
tel: 970 226-9326
On Wed, May 25, 2016 at 4:43 PM, peterhouk1 . <peterhouk at gmail.com> wrote:
> Greetings -
>
> I'm wondering if folks might be able to point out the best approach for
> examining the influence of any particular quantile of many predictor
> variables simultaneously? For instance, the below data show three
> potential predictors of a dependent variable, but in this case, we might
> want to use the 50% quantile (i.e., mean) of each predictor. I'm wondering
> if there Is any standard approach for dealing with multiple predictors,
> that when binned, can no longer be contrasted in a single model.
>
> Thanks for any discussion and guidance,
>
> Peter
>
>
> pred 1 pred 2 pred 3 dependent
> 2 14 4 800.5987
> 2 18 11 414.1341
> 11 15 12 825.5466
> 11 15 12 1143.972
> 11 14 3 904.4725
> 11 18 15 433.1852
> 11 22 14 726.6624
> 11 16 2 1450.15
> 12 20 2 670.4164
> 12 19 7 741.6311
> 12 15 7 1835.707
> 13 18 14 810.5779
> 13 22 5 418.6701
> 13 16 12 1127.189
> 13 20 1 782.0013
> 14 21 4 875.8959
> 14 16 13 1077.747
> 14 11 9 1949.56
> 15 15 14 972.0584
> 16 20 7 1048.716
> 16 11 8 689.4675
> 16 16 11 1523.632
> 16 21 11 816.4746
> 16 14 4 1303.638
> 16 21 13 1270.525
> 16 20 2 1174.816
> 15 13 5 1076.839
> 15 17 10 808.3099
> 15 15 9 1324.503
> 15 19 7 922.1628
> 15 16 6 1644.743
> 14 13 14 864.5559
> 13 19 10 119.296
> 13 19 12 659.5301
> 13 18 5 1214.279
> 13 20 5 1511.839
> 13 14 8 577.8826
> 12 12 2 1242.402
> 12 14 11 1422.48
> 12 19 6 210.9226
> 12 17 14 1982.219
> 11 9 12 1057.788
> 11 18 8 1723.669
> 11 10 3 2188.152
> 11 15 10 1240.588
> 10 16 1 1262.361
> 10 20 15 1092.262
> 10 15 4 813.7531
> 10 16 12 1423.387
> 9 15 10 1621.156
> 8 21 3 1184.342
> 8 21 5 935.7707
> 8 17 2 919.8948
> 8 15 1 960.7185
> 8 16 13 1041.912
> 7 16 8 1633.856
> 7 18 15 1276.876
> 7 18 8 1108.591
> 7 17 9 844.5977
> 7 10 6 1681.484
> 6 18 3 915.3588
> 6 21 11 938.9458
> 6 16 12 1309.535
> 6 20 3 881.339
> 6 17 15 952.1002
> 5 19 6 803.3203
> 5 16 13 826.4538
> 5 20 10 1382.564
> 5 21 2 851.8552
> 5 19 7 1400.708
> 4 19 14 1411.594
>
> --
>
> Peter Houk, PhD
> Assistant Professor
> University of Guam Marine Laboratory
> *http://guammarinelab.org/peterhouk.html
> <http://guammarinelab.org/peterhouk.html>*
>
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>
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