brglm2: detect_separation – R documentation

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detect_separation

Method for glm that tests for data separation and finds which parameters have infinite maximum likelihood estimates in generalized linear models with binomial responses

Description

detect_separation is a method for glm that tests for the occurrence of complete or quasi-complete separation in datasets for binomial response generalized linear models, and finds which of the parameters will have infinite maximum likelihood estimates. detect_separation relies on the linear programming methods developed in Konis (2007).

Usage

detect_separation(
  x,
  y,
  weights = rep(1, nobs),
  start = NULL,
  etastart = NULL,
  mustart = NULL,
  offset = rep(0, nobs),
  family = gaussian(),
  control = list(),
  intercept = TRUE,
  singular.ok = TRUE
)

detectSeparation(
  x,
  y,
  weights = rep(1, nobs),
  start = NULL,
  etastart = NULL,
  mustart = NULL,
  offset = rep(0, nobs),
  family = gaussian(),
  control = list(),
  intercept = TRUE,
  singular.ok = TRUE
)

Arguments

`x`	`x` is a design matrix of dimension `n * p`.
`y`	`y` is a vector of observations of length `n`.
`weights`	an optional vector of ‘prior weights’ to be used in the fitting process. Should be `NULL` or a numeric vector.
`start`	currently not used.
`etastart`	currently not used.
`mustart`	currently not used.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be `NULL` or a numeric vector of length equal to the number of cases. One or more `offset` terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See `model.offset`.
`family`	a description of the error distribution and link function to be used in the model. For `glm` this can be a character string naming a family function, a family function or the result of a call to a family function. For `glm.fit` only the third option is supported. (See `family` for details of family functions.)
`control`	a list of parameters controlling separation detection. See `detect_separation_control` for details.
`intercept`	logical. Should an intercept be included in the null model?
`singular.ok`	logical. If `FALSE`, a singular model is an error.

Details

For the definition of complete and quasi-complete separation, see Albert and Anderson (1984).

detect_separation is a wrapper to the separator function from the **safeBinaryRegression** R package, that can be passed directly as a method to the glm function. See, examples.

The interface to separator was designed by Ioannis Kosmidis after correspondence with Kjell Konis, and a port of separator has been included in **brglm2** under the permission of Kjell Konis.

detectSeparation is an alias for detect_separation.

Note

detect_separation will be removed from brglm2 at version 0.8. A new version of detect_separation is now maintained in the detectseparation R package at https://cran.r-project.org/package=detectseparation. In order to use the version in detect_separation load first brglm2 and then detectseparation, i.e. library(brglm2); library(detectseparation).

Author(s)

Ioannis Kosmidis [aut, cre] ioannis.kosmidis@warwick.ac.uk, Kjell Konis [ctb] kjell.konis@me.com

References

Konis K (2007). *Linear Programming Algorithms for Detecting Separated Data in Binary Logistic Regression Models*. DPhil. University of Oxford. https://ora.ox.ac.uk/objects/uuid:8f9ee0d0-d78e-4101-9ab4-f9cbceed2a2a

Konis K (2013). safeBinaryRegression: Safe Binary Regression. R package version 0.1-3. https://CRAN.R-project.org/package=safeBinaryRegression

Kosmidis I, Firth D (2020). Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models. *Biometrika* doi: 10.1093/biomet/asaa052

Examples

## endometrial data from Heinze \& Schemper (2002) (see ?endometrial)
data("endometrial", package = "brglm2")
endometrial_sep <- glm(HG ~ NV + PI + EH, data = endometrial,
                       family = binomial("logit"),
                       method = "detect_separation")
endometrial_sep
## The maximum likelihood estimate for NV is infinite
summary(update(endometrial_sep, method = "glm.fit"))

## Not run: 
## Example inspired by unpublished microeconometrics lecture notes by
## Achim Zeileis https://eeecon.uibk.ac.at/~zeileis/
## The maximum likelihood estimate of sourhernyes is infinite
data("MurderRates", package = "AER")
murder_sep <- glm(I(executions > 0) ~ time + income +
                  noncauc + lfp + southern, data = MurderRates,
                  family = binomial(), method = "detect_separation")
murder_sep
## which is also evident by the large estimated standard error for NV
murder_glm <- update(murder_sep, method = "glm.fit")
summary(murder_glm)
## and is also reveal by the divergence of the NV column of the
## result from the more computationally intensive check
check_infinite_estimates(murder_glm)
## Mean bias reduction via adjusted scores results in finite estimates
update(murder_glm, method = "brglm_fit")

## End(Not run)

brglm2

Bias Reduction in Generalized Linear Models

v0.7.1

GPL-3

Authors

Ioannis Kosmidis [aut, cre] (<https://orcid.org/0000-0003-1556-0302>), Kjell Konis [ctb], Euloge Clovis Kenne Pagui [ctb], Nicola Sartori [ctb]

Initial release