Cubic Hermite interpolation using both values and gradients to approximate a log likelihood function
Source:R/LikelihoodApproximation.R
hermiteInterpolation.RdCubic Hermite interpolation using both values and gradients to approximate a log likelihood function
hermiteInterpolation(x, profile)Arguments
- x
The log(hazard ratio) for which to approximate the log likelihood.
- profile
A profile as created with
approximateLikelihood()withapproximation = "grid with gradients". This is a data frame with 3 columns:point,value, andderivative, sorted bypoint.
Value
The approximate log likelihood for the given x.
Details
Performs spline interpolation using cubic Hermite polynomials (Catmull et al. 1974) between the points specified in the profile. We use linear extrapolation outside the points.
References
Catmull, Edwin; Rom, Raphael (1974), "A class of local interpolating splines", in Barnhill, R. E.; Riesenfeld, R. F. (eds.), Computer Aided Geometric Design, New York: Academic Press, pp. 317–326
Examples
profile <- data.frame(point = c(1.1, 2.1), value = c(1, 1), derivative = c(0.1, -0.1))
hermiteInterpolation(x = 0:3, profile = profile)
#> [1] 0.890 0.990 1.009 0.910