chlm_fit: Low-level fitting functions for the censored HLM model.
In mlysy/hlm: Inference for a Heteroscedastic Linear Model

Description Usage Arguments Details Value References

View source: R/chlm_fit.R

Low-level fitting functions for the censored HLM model.

chlm_fit(y, delta, X, Z, beta0, gamma0, maxit = 100, epsilon = 1e-08,
  splitE = FALSE, nIRLS = 5)

chlm_control(epsilon = 1e-05, maxit = 100, nIRLS = 5,
  splitE = TRUE)

`y`	Vector of observations of length `n`.
`delta`	Optional logical vector of length `n` indicating the censorring status (`TRUE`: uncensored, `FALSE`: uncensored).
`X`	Mean covariate matrix of size `n x p`.
`Z`	Variance covariate matrix of size `n x q`.
`beta0`	Optional initial mean parameter vector of length `p`.
`gamma0`	Optional initial variance parameter vector of length `q`.
`maxit`	Maximum number of iteration of the fitting algorithm (see Details).
`epsilon`	Tolerance threshold for termination of the algorithm (see Details).
`splitE`	If `TRUE`, perform the E-step after each conditional M-step (see Details).
`nIRLS`	Number of IRLS steps to take before switching to Fisher scoring. Can be 0 or greater than `maxit` to do only one or the other.

The heteroscedastic linear model (HLM) is defined as

y_i | x_i, z_i ~ind N(x_i'β, exp(z_i'γ)),

where for each subject i, y_i is the response, and x_i \in R^p and z_i \in R^q are mean and variance covariate vectors, respectively.

The fitting algorithm is an Expectation-Conditional-Maximization (ECM) algorithm extending the alternating weighted-LM/GLM updates of beta and gamma, proposed by Smyth (1989) for the uncensored setting. The ECM algorithm terminates when either maxit iterations have been reached, or when

1	\|ll_curr - ll_prev\| / (0.1 + \|ll_curr\|) < epsilon,

where ll_curr and ll_prev are the loglikelihood values at the current and previous iterations.

TODO:

Input checking.
print, summary, vcov methods.
residual method. Perhaps use expected lifetime for the censored observations?
Separate into chlm and hlm classes?

A list with the following elements:

beta: The MLE of the mean parameter vector.
gamma: The MLE of the variance parameter vector.
loglik: The value of the loglikelihood at the fitted parameter values.
iter: The number of steps taken by the algorithm.
error: The value of the loglikelihood relative error at the end of the algorithm.

Smyth, G.K. "Generalized Linear Models with Varying Dispersion." Journal of the Royal Statistical Society Series B 51:1 (1989): 47-60. https://www.jstor.org/stable/2345840.

mlysy/hlm documentation built on Nov. 4, 2019, 7:26 p.m.