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