bracl {brglm2}R Documentation

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


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.


  parallel = FALSE,
  contrasts = NULL,
  model = TRUE,
  x = TRUE,
  control = list(...),



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.


an optional data frame, list or environment in which to interpret the variables occurring in formula.


optional case weights in fitting. Default to 1.


expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.


a function to filter missing data.


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.


a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.


logical for whether the model matrix should be returned.


should the model matrix be included with in the result (default is TRUE).


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.


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

log(pi[i, j]/pi[i, j+1]) = alpha[j] + sum(beta * x[i, ])

or with non-proportional odds of the form

log(pi[i, j]/pi[i, j+1]) = alpha[j] + sum(beta[j, ] * x[i, ])

where x[i, ] is a vector of covariates and pi[i, j] is the probability that category j is observed at the covariate setting i.


Ioannis Kosmidis


Kosmidis I, Kenne Pagui E C, Sartori N (2020). Mean and median bias reduction in generalized linear models. *Statistics and Computing*, **30**, 43-59 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 doi: 10.2307/2336390

Kosmidis I, Firth D (2011). Multinomial logit bias reduction via the Poisson log-linear model. *Biometrika*, **98**, 755-759 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 doi: 10.1093/biomet/68.2.563

See Also

multinom, brmultinom


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)

[Package brglm2 version 0.7.1 Index]