[R] Percentiles/Quantiles with Weighting

[Thomas Lumley]

On Tue, 17 Feb 2009, Brigid Mooney wrote:

> Thanks for pointing me to the quantreg package as a resource.  I was hoping
> to ask be able to address one quick follow-up question...
>
> I get slightly different variants between using the rq funciton with formula
> = mydata ~ 1 as I would if I ran the same data using the quantile function.
>
> Example:
>
> mydata <- (1:10)^2/2
> pctile <- seq(.59, .99, .1)
>
> quantile(mydata, pctile)
> 59%    69%    79%    89%    99%
> 20.015 26.075 32.935 40.595 49.145
>
> rq(mydata~1, tau=pctile)
> Call:
> rq(formula = mydata ~ 1, tau = pctile)
> Coefficients:
>            tau= 0.59 tau= 0.69 tau= 0.79 tau= 0.89 tau= 0.99
> (Intercept)        18      24.5        32      40.5        50
> Degrees of freedom: 10 total; 9 residual
>
> Is it correct to assume this is due to the different accepted methods of
> calculating quantiles?

If you try
  lapply(1:9, function(i)quantile(mydata, pctile,type=i))
the answers from type=1 or 2 agree with rq().

       -thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle