R: Methods for walsGLM, walsGLMmatrix, walsNB and walsNBmatrix...

predict.walsGLM {WALS}

R Documentation

Methods for walsGLM, walsGLMmatrix, walsNB and walsNBmatrix Objects

Description

Methods for extracting information from fitted model-averaging objects of classes "walsGLM", "walsGLMmatrix", "walsNB" and "walsNBmatrix".

Usage

## S3 method for class 'walsGLM'
predict(
  object,
  newdata,
  type = c("response", "link", "variance", "prob", "density", "logDens"),
  at = NULL,
  na.action = na.pass,
  log = FALSE,
  ...
)

## S3 method for class 'walsGLMmatrix'
predict(
  object,
  newX1,
  newX2,
  newY = NULL,
  type = c("response", "link", "variance", "prob", "density", "logDens"),
  at = NULL,
  log = FALSE,
  ...
)

## S3 method for class 'walsGLM'
residuals(object, type = c("deviance", "pearson", "response"), ...)

## S3 method for class 'walsGLM'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'walsGLM'
summary(object, ...)

## S3 method for class 'summary.walsGLM'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'walsGLM'
logLik(object, ...)

## S3 method for class 'walsNB'
summary(object, ...)

## S3 method for class 'summary.walsNB'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

`object`, `x`	An object of class `"walsGLM"`, `"walsGLMmatrix"`, `"walsNB"`, `"walsNBmatrix"`, `"summary.walsGLM"` or `"summary.walsNB"`.
`newdata`	Optionally, a data frame in which to look for variables with which to predict. If omitted, the original observations are used.
`type`	Character specifying the type of prediction, residual or model part to be returned. For details see below.
`at`	Optional. Only available if a family of class `"familyWALScount"` was used for fitting. If `type = "prob"`, a numeric vector at which the probabilities are evaluated. By default `0:max(y)` is used where `y` is the original observed response.
`na.action`	Function determining what should be done with missing values in `newdata`. The default is to predict `NA`.
`log`	Logical. If `TRUE`, then returns the log-density. If `FALSE` (default), then returns density. Only relevant if `type = "density"`.
`...`	Further arguments passed to methods.
`newX1`	Focus regressors matrix to be used for the prediction.
`newX2`	Auxiliary regressors matrix to be used for the prediction.
`newY`	Response vector to be used in predictions. Only relevant when `type = "prob"`, `type = "density"` or `type = "logDens"`.
`digits`	The number of significant digits to display.

Details

As the "-matrix" classes "walsGLMmatrix" and "walsNBmatrix" inherit from the "non-matrix" classes, i.e. "walsGLM" and "walsNB", respectively, the following text will treat them as equivalent because they inherit all methods but predict from their "non-matrix" versions. Thus, when "walsGLM" or "walsNB" are mentioned, we also refer to their "-matrix" versions, except when explicitly stated. Moreover, note that "walsNB" and "walsNBmatrix" inherit most methods from "walsGLM" and "walsGLMmatrix".

A set of standard extractor functions for fitted model objects is available for objects of class "walsGLM" and "walsNB", including methods to the generic functions print and summary which print the model-averaged estimation of the coefficients along with some further information.

The summary methods returns an object of class "summary.walsGLM" for objects of class "walsGLM" and an object of class "summary.walsNB" for objects of class "walsNB". They contain the relevant summary statistics which can then be printed using the associated print() methods. Inspired by De Luca and Magnus (2011), the summary statistics also show Kappa which is an indicator for the numerical stability of the method, i.e. it shows the square root of the condition number of the matrix \bar{\Xi} = \bar{\Delta}_{2} \bar{X}_{2}^{\top} \bar{M}_{1} \bar{X}_{2} \bar{\Delta}_{2}. The summary further shows the deviance and provides information on the prior and family used.

A logLik method is provided that returns the log-likelihood given the family used and the model-averaged estimates of the coefficients.

"walsGLM" inherits from "wals", while "walsNB" inherits from both, "walsGLM" and "wals". Thus, see predict.wals for more methods.

The predict and residuals methods, especially the different types of predictions/residuals controlled by type, are inspired by the corresponding methods in countreg version 0.2-1 (2023-06-13) (Zeileis and Kleiber 2023; Zeileis et al. 2008), see e.g. predict.hurdle() from countreg, and stats version 4.3.1 (2023-06-16) (R Core Team 2023), see e.g. residuals.glm. The summary(), print.summary(), print() and logLik() methods are also inspired by the corresponding methods for objects of class "glm" in stats, see e.g. print.summary.glm.

coef and vcov are inherited from "wals" (see predict.wals for more), except for objects of class "walsNB" (see vcov.walsNB). The type argument specifies which part of the coefficient vector/covariance matrix of the estimates should be returned. For type = "all", they return the complete vector/matrix. For type = "focus" and type = "aux" they return only the part corresponding to the focus and auxiliary regressors, respectively. Additionally, the user can choose whether to return the estimated coefficients/covariance matrix for the original regressors X (\beta coefficients) or of the transformed regressors Z (\gamma coefficients).

The extractors terms and model.matrix are also inherited from "wals". They only allow type = "focus" and type = "aux" and extract the corresponding component of the model.

Value

predict.walsGLM() and predict.walsGLMmatrix() return different types of predictions depending on the argument type:

type = "response": vector. Predicted mean
type = "link": vector. Predicted linear link
type = "variance": vector. Predicted variance
type = "prob": matrix. Only available if a family of class "familyWALScount" was used for fitting or for objects of class "walsNB" or "walsNBmatrix". Returns the probability at counts specified by at.
type = "density": vector. Predicted density
type = "logDens": vector. For convenience, returns predicted log-density. Equivalent to setting type = "density" and log = TRUE.

If type = "prob", type = "density" or type = "logDens", then newdata must contain the response or newY must be specified depending on the class of the object.

residuals.walsGLM() returns different types of residuals depending on the argument type:

type = "deviance": deviance residuals
type = "pearson": Pearson residuals (raw residuals scaled by square root of variance function)
type = "response": raw residuals (observed - fitted)

print.walsGLM() invisibly returns its input argument x, i.e. an object of object of class "walsGLM".

summary.walsGLM() returns an object of class "summary.walsGLM" which contains the necessary fields for printing the summary in print.summary.walsGLM().

print.summary.walsGLM() invisibly returns its input argument x, i.e. an object of object of class "summary.walsGLM".

logLik.walsGLM() returns the log-likelihood of the fitted model.

summary.walsNB() returns an object of class "summary.walsNB" which contains the necessary fields for printing the summary in print.summary.walsNB().

print.summary.walsNB() invisibly returns its input argument x, i.e. an object of object of class "summary.walsNB".

References

De Luca G, Magnus JR (2011). “Bayesian model averaging and weighted-average least squares: Equivariance, stability, and numerical issues.” The Stata Journal, 11(4), 518–544. doi:10.1177/1536867X1201100402.

R Core Team (2023). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

Zeileis A, Kleiber C (2023). countreg: Count Data Regression. R package version 0.2-1, https://r-forge.r-project.org/projects/countreg/.

Zeileis A, Kleiber C, Jackman S (2008). “Regression Models for Count Data in R.” Journal of Statistical Software, 27(8), 1–25. doi:10.18637/jss.v027.i08.

Examples

## Example for walsGLM objects
data("HMDA", package = "AER")
fitBinomial <- walsGLM(deny ~ pirat + hirat + lvrat + chist + mhist + phist |
                        selfemp + afam, family = binomialWALS(), data = HMDA,
                       prior = weibull())
summary(fitBinomial)
vcov(fitBinomial, type = "focus")
logLik(fitBinomial)
predict(fitBinomial, newdata = HMDA[1:10,], type = "response")
familyWALS(fitBinomial)

## Example for walsNB objects
data("NMES1988", package = "AER")

fWals <- (visits ~ chronic + age + I((age^2)/10) + insurance + medicaid |
           adl + gender + married + income + school + afam + employed)
fitNB <- walsNB(fWals, data = NMES1988, link = "log", prior = weibull(),
                method = "fullSVD")
summary(fitNB)
coef(fitNB, type = "aux")
residuals(fitNB, type = "pearson")
predict(fitNB, newdata = NMES1988[1:10,], type = "prob")
terms(fitNB, type = "aux")

[Package WALS version 0.2.5 Index]