Quantile regressions across several predictors

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

Quantile regressions across several predictors

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