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 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.

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.

Details

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

$$\log\frac{\pi_{ij}}{\pi_{ij + 1}} = \alpha_j + \beta^T x_i$$

or with non-proportional odds of the form

$$\log\frac{\pi_{ij}}{\pi_{ij + 1}} = \alpha_j + \beta_j^T x_i$$

where $x_i$ is a vector of covariates and $\pi_{ij}$ is the probability that category $j$ is observed at the covariate setting $i$.

References

Kosmidis I, Kenne Pagui EC, Sartori N (2019). Mean and median bias reduction in generalized linear models. *arXiv e-prints*, arXiv:1804.04085. To appear in Statistics and Computing, <URL: https://arxiv.org/abs/1804.04085>.

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

Albert A. and Anderson J. A. (1984). On the Existence of Maximum Likelihood Estimates in Logistic Regression Models. *Biometrika*, **71** 1--10.

Kosmidis I. and Firth D. (2011). Multinomial logit bias reduction via the Poisson log-linear model. *Biometrika*, **98**, 755-759.

Palmgren, J. (1981). The Fisher Information Matrix for Log Linear Models Arguing Conditionally on Observed Explanatory Variables. *Biometrika*, **68**, 563-566.

Examples

Run this code

# NOT RUN {
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)


# }