# Quantile Regression for Counts

### Description

This function is used to fit a quantile regression model when the response is a count variable.

### Usage

1 2 3 4 |

### Arguments

`formula` |
an object of class |

`data` |
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which |

`tau` |
quantile to be estimated. |

`tsf` |
transformation to be used. Possible options are |

`symm` |
logical flag. If |

`dbounded` |
logical flag. If |

`lambda` |
a numerical value for the transformation parameter. This is provided by the user or set to zero if not specified. |

`subset` |
an optional vector specifying a subset of observations to be used in the fitting process. |

`weights` |
an optional vector of weights to be used in the fitting process. |

`na.action` |
a function which indicates what should happen when the data contain |

`contrasts` |
an optional list. See the |

`offset` |
an optional offset to be included in the model frame. |

`method` |
estimation method for the fitting process. See |

`M` |
number of dithered samples. |

`zeta` |
small constant (see References). |

`B` |
right boundary for uniform random noise U[0,B] to be added to the response variable (see References). |

`cn` |
small constant to be passed to |

`alpha` |
significance level. |

### Details

A linear quantile regression model is fitted to the log–transformed response. The transformation of the response can be changed with arguments `tsf`

, `symm`

, `dbounded`

, `lambda`

(see `bc`

). The notation used here follows closely that of Machado and Santos Silva (2005). This function is based on routines from package `quantreg`

(Koenker, 2013). See also `lqm.counts`

from package `lqmm`

(Geraci, 2014) for Laplace gradient estimation.

### Value

a list of class `rq.counts`

containing the following components

`call` |
the matched call. |

`method` |
the fitting algorithm for |

`x` |
the model matrix. |

`y` |
the model response. |

`tau` |
the order of the estimated quantile(s). |

`tsf` |
tranformation used (see also |

`coefficients` |
regression quantile (on the log–scale). |

`fitted.values` |
fitted values (on the response scale). |

`tTable` |
coefficients, standard errors, etc. |

`offset` |
offset. |

`M` |
specified number of dithered samples for standard error estimation. |

`Mn` |
actual number of dithered samples used for standard error estimation that gave an invertible D matrix (Machado and Santos Silva, 2005). |

`InitialPar` |
starting values for coefficients. |

`terms` |
the terms object used. |

`term.labels` |
names of coefficients. |

`rdf` |
the number of residual degrees of freedom. |

### Author(s)

Marco Geraci

### References

Geraci M and Jones MC. Improved transformation-based quantile regression. Canadian Journal of Statistics 2015;43(1):118-132.

Koenker R (2013). quantreg: Quantile Regression. R package version 5.05. URL http://CRAN.R-project.org/package=quantreg.

Machado JAF and Santos Silva JMC (2005). Quantiles for counts. Journal of the American Statistical Association, 100(472), 1226–1237.

### See Also

`residuals.rq.counts`

, `predict.rq.counts`

, `coef.rq.counts`

, `maref.rq.counts`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# Esterase data
data(esterase)
# Fit quantiles 0.25 and 0.75
fit1 <- rq.counts(Count ~ Esterase, tau = 0.25, data = esterase, M = 50)
coef(fit1)
fit2 <- rq.counts(Count ~ Esterase, tau = 0.75, data = esterase, M = 50)
coef(fit2)
# Plot
with(esterase, plot(Count ~ Esterase))
lines(esterase$Esterase, fit1$fitted.values, col = "blue")
lines(esterase$Esterase, fit2$fitted.values, col = "red")
legend(8, 1000, lty = c(1,1), col = c("blue", "red"), legend = c("tau = 0.25","tau = 0.75"))
``` |