R: Gradient of the log-likelihood of univariate Davidian curves

dc_grad {dcurver} | R Documentation

## Gradient of the log-likelihood of univariate Davidian curves

### Description

Provides the gradient for use in estimation.

### Usage

    dc_grad(x, phi)

### Arguments

`x` | A vector of observations.
`phi` | phi Davidian curve parameters. A maximum of 10 parameters is allowed.

### Details

Woods & Lin (2009) provide the gradient (Equations 17 and 18). Note that the gradient is not defined for phi = 0.0.

### References

Woods, C. M., & Lin, N. (2009). Item response theory with estimation of the latent density using Davidian curves. Applied Psychological Measurement, 33(2), 102-117. doi: 10.1177/0146621608319512

### Examples

    # The loglikelihood of a univariate Davidian curve is given by,
    dc_LL <- function(phi, dat) {
      sum(log(ddc(dat, phi)))
    }

    # dc_grad can be used for obtaining the gradient of this loglikelihood as follows:
    dc_LL_GR <- function(phi, dat) {
      colSums(dc_grad(dat, phi))
    }

    # This can be verified by numerical approximation.
    # For instance, using numDeriv package:
    ## Not run:
    phi <- c(-5, 2.5, 10)
    d <- runif(10, -5, 5)
    dc_LL_GR(phi, d)
    numDeriv::grad(dc_LL, x = phi, dat = d)

    phi <- c(-5, 0, 10)
    dc_LL_GR(phi, d)

    ## End(Not run)

[Package dcurver version 0.9.2 Index]