View source: R/flexreg_binom.R

flexreg_binom | R Documentation |

The function fits some flexible regression models for bounded discrete responses via a Bayesian approach to inference based on Hamiltonian Monte Carlo algorithm.
Available regression models are the flexible beta-binomial (`type = "FBB"`

, default), the beta-binomial (`type = "BetaBin"`

), and the binomial one (`type = "Bin"`

).

```
flexreg_binom(
formula,
data,
type = "FBB",
n,
link.mu = "logit",
prior.beta = "normal",
hyperparam.beta = 100,
hyper.theta.a = NULL,
hyper.theta.b = NULL,
link.theta = NULL,
prior.psi = NULL,
hyperparam.psi = NULL,
n.chain = 1,
n.iter = 5000,
warmup.perc = 0.5,
thin = 1,
verbose = TRUE,
...
)
```

`formula` |
an object of class " |

`data` |
an optional |

`type` |
a character specifying the type of regression model. Current options are |

`n` |
a character specifying the name of the variable containing the total number of trials. |

`link.mu` |
a character specifying the link function for the mean model. Currently, |

`prior.beta` |
a character specifying the prior distribution for the regression coefficients of the mean model, |

`hyperparam.beta` |
a positive numeric (vector of length 1) specifying the hyperprior scale parameter for the prior distribution of |

`hyper.theta.a` |
a numeric (vector of length 1) specifying the first shape parameter for the beta prior distribution of |

`hyper.theta.b` |
a numeric (vector of length 1) specifying the second shape parameter for the beta prior distribution of |

`link.theta` |
a character specifying the link function for the overdispersion model. Currently, |

`prior.psi` |
a character specifying the prior distribution for the regression coefficients of the overdispersion model, |

`hyperparam.psi` |
a positive numeric (vector of length 1) specifying the hyperprior scale parameter for the prior distribution of |

`n.chain` |
a positive integer specifying the number of Markov chains. The default is 1. |

`n.iter` |
a positive integer specifying the number of iterations for each chain (including warm-up). The default is 5000. |

`warmup.perc` |
the percentage of iterations per chain to discard. |

`thin` |
a positive integer specifying the period for saving samples. The default is 1. |

`verbose` |
a logical (with default |

`...` |
additional arguments from |

Let Y be a random variable whose distribution can be specified in the `type`

argument and `\mu`

be the mean of Y/n.
The `flexreg_binom`

function links the parameter `\mu`

to a linear predictor through a function `g_1(\cdot)`

specified in `link.mu`

:

`g_1(\mu) = x^t \bold{\beta},`

where `\bold{\beta}`

is the vector of regression coefficients for the mean model.
The prior distribution and the related hyperparameter of `\bold{\beta}`

can be specified in `prior.beta`

and `hyperparam.beta`

.
By default, `link.theta="identity"`

, meaning that the overdispersion parameter `\theta`

is assumed to be constant.
In that case, the prior distribution for `\theta`

is a beta with shape hyperparameters `a`

and `b`

that can be specified in `hyper.theta.a`

and `hyper.theta.b`

.
If not specified, `a=b=1`

, otherwise if only one hyperparameter is specified, the other is set equal.
It is possible to extend the model by linking `\theta`

to an additional (possibly overlapping) set of covariates through a proper link
function `g_2(\cdot)`

specified in the `link.theta`

argument:

`g_2(\theta) = z^t \bold{\psi},`

where `\bold{\psi}`

is the vector of regression coefficients for the overdispersion model.
The prior distribution and the related hyperparameter of `\bold{\psi}`

can be specified in `prior.psi`

and `hyperparam.psi`

.
In `flexreg_binom`

, the regression model for the mean and, where appropriate, for the overdispersion parameter can be specified in the
`formula`

argument with a formula of type `y ~ x1 + x2 | z1 + z2`

where covariates on the left of "|" are included in the regression model
for the mean, whereas covariates on the right of "|" are included in the regression model for the overdispersion.

If the second part is omitted, i.e., `y ~ x1 + x2`

, the overdispersion is assumed constant for each observation.

The `flexreg_binom`

function returns an object of class ``flexreg``

, i.e. a list with the following elements:

`call` |
the function call. |

`type` |
the type of regression model. |

`formula` |
the original formula. |

`link.mu` |
a character specifing the link function in the mean model. |

`link.theta` |
a character specifing the link function in the overdispersion model. |

`model` |
an object of class |

`response` |
the response variable, assuming values in (0, 1). |

`design.X` |
the design matrix for the mean model. |

`design.Z` |
the design matrix for the overdispersion model (if defined). |

Ascari, R., Migliorati, S. (2021). A new regression model for overdispersed binomial data accounting for outliers and an excess of zeros. Statistics in Medicine, **40**(17), 3895–3914. doi:10.1002/sim.9005

```
## Not run:
data(Bacteria)
fbb <- flexreg_binom(y ~ females, n = "n", data = Bacteria, type = "FBB")
## End(Not run)
```

FlexReg documentation built on Sept. 29, 2023, 9:06 a.m.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.