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I have a time series of binomial data $y_i$ with a time dependent $p(t)$. The data is generated iteratively, hence $t \in 1,...,T$. Any suggestions on how to estimate $p(t)$? I feel that the naive approach would be to use some sort of smoothing method (e.g. smoothing splines) to the raw data, but this allows for $p(t)$ outside the [0,1] interval.

Note that $p(t)$ seem to have some periodicity so a logistic model would not be suitable. The periodicity is not regular though, so I don't think incorporating some sort of Fourier analysis would work.

kjetil b halvorsen
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  • Why logistic regression does not catch the variability? – Tim Dec 06 '17 at 18:21
  • You might want to try gam from the R package mgcv; it allows you to use splines on the parameters of a logistic regression (among other things), in this case your model would look like y~s(t), family="binomial", for example, and you'd recover an appropriate estimate of $p(t)$ from the procedure. – jbowman Dec 06 '17 at 18:23
  • @Tim, there is some periodicity in the data. However it's not regular so I don't think incorporating Fourier analysis would be suitable. Updated the question now. – esten Dec 06 '17 at 18:33
  • You could use periodic splines, see also this. There is even an R package pbs. – kjetil b halvorsen Dec 29 '18 at 15:32

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