# [R] Fitting quantile (or cdf?) function to data with specified percentiles

Vito Michele Rosario Muggeo vito.muggeo at unipa.it
Fri May 27 17:54:39 CEST 2016

```A possible (simple) solution is to use a binomial GLM which guarantees
fitted values (percentiles) in (0,1):

plot(percentile, score)
o<-glm(percentile~sc, family=binomial)
points(fitted(o), sc, col=2)

You can "predict" percentiles given score via predict.glm()
best,
vito

Franco Danilo Roca Landaveri <fradarola at hotmail.com> ha scritto:

> Hello,
>
> I hope you can help me. In class, we were given an Excel worksheet
> with specified formulas that take the total score from a survey (or
> from a specific section) and convert it to a percentage, according
> to a table that assigns scores to a percentile. Since the formulas
> are too long and complicated (some have been input by hand) I
> figured we could fit the data with a function with some parameters.
> I plotted the table and sure it resembled a more-or-less symmetrical
> quantile function, and I wanted to use R to find a curve that
> fittted the data. Here it is:
>
> percentile <- c(0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.05, 0.05, 0.05,
> 0.05, 0.05, 0.10, 0.10, 0.15, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50,
> 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.90, 0.95, 0.95, 0.99, 0.99, 0.99, 0.99,
> 0.99, 0.99, 0.99, 0.99, 0.99)
>
> score <- c(10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
> 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
> 42, 43, 44,
> 45, 46, 47, 48, 49, 50)
>
> I looked up the quantreg package, but I didn't know how to use it
> properly since I don't have the raw data, only the percentiles, and
> also because what I'm trying to get is the percentile based on the
> score, not the other way around. Then I tried to fit it using a
> sigmoid curve (similar to a cdf), using the following code:
>
> require(drc)
> model1 <- drm(percentile ~ score, fct = LL.4())
> summary(model1)
>
> But I found another problem, the fitted curve apparently went over 1
> on the y axis, something not possible for a cdf. I'd like to know
> what would be the most appropiate way to do this, and also if it is
> possible to fit a quantile function with this data, apart from the
> cdf.
>
> Thank you very much for your help
>
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