R: Bias reduction for adjacent category logit models for ordinal...

bracl {brglm2} | R Documentation

## 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.
`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.

### Details

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.

### Author(s)

Ioannis Kosmidis ioannis.kosmidis@warwick.ac.uk

### 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 https://doi.org/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 https://doi.org/10.2307/2336390

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

### See Also

`multinom`, `brmultinom`

### Examples

    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 0.7.0 Index]