R中沿“S”曲线的加权点

Question

I have data in an R data frame and want to weight one column ( days_since ) along an S-curve (logit curve). Particularly, a backwards S-curve such that more recent events will be weighted more. My reasoning for using this curve as a weighting function is that it will heavily weight recent events as well as lightly weight distant events. Thus, I would like to write a function that for a give number of observations I could create an S-curve that provides the weights, such that as in the image below, the weights would be on the y-axis and the days since would be on the x-axis.

[Please ignore the points and labels on this graph, I was able to use the model of a reverse s-curve/logit function from another stackoverflow question].

Answer 1

This builds upon an answer provided to a similar question here .

You can create the curve using a formula of your own or the sigmoid function from the e1071 package, and the curve() function. Then, predict the values along the curve for given days in your dataset.

Here's a simple example.

library(scales)
library(e1071)

# Data set with points of interest. Suppose these are days. 
days <- data.frame( d = seq.int( 1, 365, 1 ) )

The curve() function will create x and y coordinates for your S-curve.

p <- invisible(curve(-sigmoid(x) , -6,6))

Rescale x and y to ensure the range contains your data values of interest. You will want to be able to predict y from x later. Rescaling y to upper and lower bounds will set upper and lower thresholds for your weights.

x <- rescale(p$x, to = c(1, 365))
y <- rescale(p$y, to = c(0,1))

Next, predict the values on the curve for your data of interest. In this example, days go from 1 to 365. You'll feed the loess() function to predict() . The loess() function will fit the curve surface (setting span to 0.1 will minimize any smoothing).

days$pred <- predict( loess( y ~ x, span=.1 ), days$d ) 

plot(days$d,days$pred)

Your weights are now in days$pred.