walsNBfitIterate: Iteratively fitting walsNB, internal function for walsNB.formula and walsNB.matrix.

Description

Wrapper around walsNBfit that allows iteratively (re-)fitting walsNB models.

Usage

walsNBfitIterate(
  y,
  X1,
  X2,
  link = "log",
  na.action = NULL,
  weights = NULL,
  offset = NULL,
  prior = weibull(),
  controlInitNB = controlNB(),
  keepY = TRUE,
  keepX = FALSE,
  iterate = FALSE,
  tol = 1e-06,
  maxIt = 50,
  nIt = NULL,
  verbose = FALSE,
  ...
)

Value

A list containing all elements returned from walsNBfit

and additionally the following elements:

y: If keepY = TRUE, contains the response vector.
x: list. If keepX = TRUE, then it is a list with elements x1 and x2 containing the design matrices of the focus and auxiliary regressors, respectively.
initialFit: List containing information (e.g. convergence) on the estimation of the starting values for walsNBfit. See return of fitNB2 for more information.
weights: returns the argument weights.
offset: returns the argument offset.
converged: Logical. Only relevant if iterate = TRUE. Equals TRUE if iterative fitting converged, else FALSE. Is NULL if iterate = FALSE.
it: Number of iterations run in the iterative fitting algorithm. NULL if iterate = FALSE.
deviance: Deviance of the fitted (conditional) NB2 regression model.
residuals: Raw residuals, i.e. response - fitted mean.

Arguments

y: Count response as vector.
X1: Design matrix for focus regressors. Usually includes a constant (column full of 1s) and can be generated using model.matrix.
X2: Design matrix for auxiliary regressors. Usually does not include a constant column and can also be generated using model.matrix.
link: specifies the link function, currently only "log" is supported.
na.action: Not implemented yet.
weights: Not implemented yet.
offset: Not implemented yet.
prior: Object of class "familyPrior". For example weibull or laplace.
controlInitNB: Controls estimation of starting values for one-step ML, see controlNB.
keepY: If TRUE, then output keeps response.
keepX: If TRUE, then output keeps the design matrices.
iterate: if TRUE then the WALS algorithm is iterated using the previous estimates as starting values.
tol: Only used if iterate = TRUE and nIt = NULL. If the Euclidean distance between the previous and current coefficient vector divided by the square root of the length of the vector falls below tol and the absolute difference between the previous and current dispersion parameter falls below tol, then the algorithm stops. See below for more details.
maxIt: Only used if iterate = TRUE and nIt = NULL. Aborts iterative fitting when number of iterations exceed maxIt.
nIt: Only used if iterate = TRUE. If this is specified, then tol is ignored and the algorithm iterates nIt times.
verbose: If verbose = TRUE, then it prints the iteration process (only relevant if iterate = TRUE).
...: Arguments to be passed to the workhorse function walsNBfit.

Details

The parameter tol is used to control the convergence of the iterative fitting algorithm. Let $i$ be the current iteration step for the coefficient vector $\beta_{i} = (\beta_{i,1}, \ldots, \beta_{i,k})'$, $k > 0$, and dispersion parameter $\rho_{i}$. If $$\frac{||\beta_{i} - \beta_{i-1}||_{2}}{\sqrt{k}} = \sqrt{\frac{\sum_{j = 1}^{k} (\beta_{i,j} - \beta_{i-1,j})^{2}}{k}} < \texttt{tol},$$ and $$|\rho_{i} - \rho_{i-1}| < \texttt{tol},$$ then the fitting process is assumed to have converged and stops.

Examples

Run this code

data("NMES1988", package = "AER")
NMES1988 <- na.omit(NMES1988)
form <- (visits ~ health + chronic + age + insurance + adl + region + gender
         + married + income + school + employed)
X <- model.matrix(form, data = NMES1988)
focus <- c("(Intercept)", "healthpoor", "healthexcellent", "chronic", "age",
        "insuranceyes")
aux <- c("adllimited", "regionnortheast", "regionmidwest", "regionwest",
         "gendermale", "marriedyes", "income", "school", "employedyes")
X1 <- X[, focus]
X2 <- X[, aux]
y <- NMES1988$visits

str(walsNBfitIterate(y, X1, X2, prior = weibull(), link = "log",
                     method = "fullSVD", iterate = TRUE))