P spline smoother

Question

Hi I am trying to find a non-parametric regression smoother to the difference between the control and treatment groups so as to determine the effectiveness of the appetite suppressant over time. then I need to use my model to estimate the difference between the treatment and control group at t=0 and t=50.

I want to use P-spline smoother ,but I do not have enough background about it This is my data :

t

0 1 3 7 8 10 14 15 17 21 22 24 28 29 31 35 36 38 42 43 45 49 50 52 56 57 59 63 64 70 73 77 80 84 87 91 94 98 105 

con

20.5 19.399 22.25 17.949 19.899 21.449 16.899 21.5 22.8 24.699 26.2 28.5 24.35 24.399 26.6 26.2 26.649 29.25 27.55 29.6 24.899 27.6 28.1 27.85 26.899 27.8 30.25 27.6 27.449 27.199 27.8 28.199 28 27.3 27.899 28.699 27.6 28.6 27.5  

trt

21.3 16.35 19.25 16.6 14.75 18.149 14.649 16.7 15.05 15.5 13.949 16.949 15.6 14.699 14.15 14.899 12.449 14.85 16.75 14.3 16 16.85 15.65 17.149 18.05 15.699 18.25 18.149 16.149 16.899 18.95 22 23.6 23.75 27.149 28.449 25.85 29.7  29.449

where:

t - the time in days since the experiment started.
con - the median food intake of the control group.
trt - the median food intake of the treatment group.

Can anybody help please?

Answer 1

Only to give you a start. mgcv package implements various regression spline basis, including P-splines (penalized B-splines with difference penalty).

First, you need to set up your data:

dat <- data.frame(time = rep(t, 2), y = c(con, trt), 
                  grp = gl(2, 39, labels = c("con", "trt")))

Then call gam for non-parametric regression:

library(mgcv)  # no need to install; it comes with R
fit <- gam(y ~ s(time, bs = 'ps', by = grp) + grp, data = dat)

Read mgcv: how to specify interaction between smooth and factor? for specification of interaction. bs = 'ps' sets P-spline basis. By default, 10 (evenly spaced interior) knots are chosen. You can change k if you want.

More about P-splines in mgcv, read mgcv: how to extract knots, basis, coefficients and predictions for P-splines in adaptive smooth?.