bracl: Bias reduction for adjacent category logit models for ordinal responses using the Poisson trick.

Description

bracl() is a wrapper of brglmFit() that fits adjacent category logit models with or without proportional odds using implicit and explicit bias reduction methods. See Kosmidis & Firth (2011) for details.

Usage

bracl(
  formula,
  data,
  weights,
  subset,
  na.action,
  parallel = FALSE,
  contrasts = NULL,
  model = TRUE,
  x = TRUE,
  control = list(...),
  ...
)

Arguments

formula: a formula expression as for regression models, of the form response ~ predictors. The response should be a factor (preferably an ordered factor), which will be interpreted as an ordinal response, with levels ordered as in the factor. The model must have an intercept: attempts to remove one will lead to a warning and be ignored. An offset may be used. See the documentation of formula for other details.
data: an optional data frame, list or environment in which to interpret the variables occurring in formula.
weights: optional case weights in fitting. Default to 1.
subset: expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.
na.action: a function to filter missing data.
parallel: if FALSE (default), then a non-proportional odds adjacent category model is fit, assuming different effects per category; if TRUE then a proportional odds adjacent category model is fit. See Details.
contrasts: a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.
model: logical for whether the model matrix should be returned.
x: should the model matrix be included with in the result (default is TRUE).
control: a list of parameters for controlling the fitting process. See brglmControl() for details.
...: arguments to be used to form the default control argument if it is not supplied directly.

Author

Ioannis Kosmidis [aut, cre] ioannis.kosmidis@warwick.ac.uk

Details

The bracl() function fits adjacent category models, which assume multinomial observations with probabilities with proportional odds of the form

$\log \frac{π_{i j}}{π_{i j + 1}} = α_{j} + β^{T} x_{i}$

or with non-proportional odds of the form

$\log \frac{π_{i j}}{π_{i j + 1}} = α_{j} + β_{j}^{T} x_{i}$

where $x_{i}$ is a vector of covariates and $π_{i j}$ is the probability that category $j$ is observed at the covariate setting $i$ .

References

Kosmidis I, Kenne Pagui E C, Sartori N (2020). Mean and median bias reduction in generalized linear models. Statistics and Computing, 30, 43-59. tools:::Rd_expr_doi("10.1007/s11222-019-09860-6").

Agresti, A (2010). Analysis of Ordinal Categorical Data (2nd edition). Wiley Series in Probability and Statistics. Wiley.

Albert A, Anderson J A (1984). On the Existence of Maximum Likelihood Estimates in Logistic Regression Models. Biometrika, 71, 1-10. tools:::Rd_expr_doi("10.2307/2336390").

Kosmidis I, Firth D (2011). Multinomial logit bias reduction via the Poisson log-linear model. Biometrika, 98, 755-759. tools:::Rd_expr_doi("10.1093/biomet/asr026").

Palmgren J (1981). The Fisher Information Matrix for Log Linear Models Arguing Conditionally on Observed Explanatory Variables. Biometrika, 68, 563-566. tools:::Rd_expr_doi("10.1093/biomet/68.2.563").

Examples

Run this code


data("stemcell", package = "brglm2")

# Adjacent category logit (non-proportional odds)
fit_bracl <- bracl(research ~ as.numeric(religion) + gender, weights = frequency,
                   data = stemcell, type = "ML")
# Adjacent category logit (proportional odds)
fit_bracl_p <- bracl(research ~ as.numeric(religion) + gender, weights = frequency,
                    data = stemcell, type = "ML", parallel = TRUE)

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