BIreg | R Documentation |

`BIreg`

function fits a binomial logistic regression model, i.e., it links the probability parameter of a binomial distribution with the given covariates by means of a logistic link function. There is the option to include a dispersion parameter in the binomial distribution, which will be estimated by the bias corrected method of moments.

BIreg(formula,m,data,disp=FALSE,maxiter=20)

`formula` |
an object of class |

`m` |
number of trials in each binomial observation. |

`data` |
an optional data frame, list or environment (or object coercible by |

`disp` |
if TRUE a dispersion parameter will be estimated. Default FALSE. |

`maxiter` |
the maximum number of iterations in IWLS method. Default 20. |

`BIreg`

function performs a regression model linking by a logistic function the probability paramater of a binomial distribution with a linear predictor that consists of the given covariates. Following the exponential family theory, the binomial distribution with dispersion parameter has the following log-likelihood function:

*l=[y*log(p/(1-p))+m*log(1-p)]/phi+c(y,phi)*

where *c()* is a known function. If we any dispersion parameter is not considered the usual density function of the binomial distribution will be used,

*l=y*log(p)+(m-y)*log((1-p)).*

As explained before we link the probablity parameter with the given covariates by

*logit(p)=log(p/(1-p))=x_i'*beta*

where *beta* are the regression coefficients and *x_i* is the *i*th row of a full rank design matrix *X* composed by the given covariables.

The estimation of the regression parameters *beta* is done via maximum likelihood approach, where the iterative weighted least square (IWLS) method is applied.

If `disp`

is TRUE, a dispersion parameter will be added in the binomial distribution and, consequently, the method will deal with the general definition of the log-likelihood formula, otherwise the usual and simpler one will be used. In case the dispersion parameter is included, the estimation will be done with a bias-corrected method of moments:

*phi=Var[y]/[(m-q)*p*(1-p)]*

where *q* is the number of estimated regression paramters, and *p* is the estimated probability parameter.

The deviance of the model is defined by the ratio between the log-likelihood of the estimated model and saturated or null model. If the dispersion paramter is included the scaled deviance is obtained dividing the deviance by the dispersion parameter.

`BIreg`

returns an object of class "`BIreg`

".

The function `summary`

(i.e., `summary.BIreg`

) can be used to obtain or print a summary of the results.

`coefficients` |
the estimated value of the regression coefficients. |

`vcov` |
the variance and covariance matrix of the estimated regression coefficients. |

`phi` |
if |

`fitted.values` |
the fitted mean values of the model. |

`residuals` |
working residuals, i.e. the residuals in the final iteration of the IWLS method. |

`deviance` |
deviance of the model. |

`df` |
degrees of freedom of the model. |

`null.deviance` |
null-deviance, deviance for the null model. The null model will include only an intercept. |

`df.null` |
degrees of freedom for the null model. |

`iter` |
number of iterations in the IWLS method. |

`conv` |
if the algorithm has converged it returns "yes", otherwise "no". |

`X` |
model matrix. |

`y` |
dependent variable in the model. |

`balanced` |
if the response binomial variable is balanced it returns "yes", otherwise "no". |

`m` |
number of trials in each binomial observation. |

`nObs` |
number of observations. |

`call` |
the matched call. |

`formula` |
the formula supplied. |

J. Najera-Zuloaga

D.-J. Lee

I. Arostegui

Pawitan Y. (2001): In All Likelihood: Statistical Modelling and Inference Using Likelihood, *Oxford University Press*

Williams D. A. (1982): Extra-Binomial Variation in Logistic Linear Regression, *Journal of the Royal Statistical Society. Series C*, **31**, 144-148

Iterative weighted least squares method function `BIiwls`

in R-package `HRQoL`

.

set.seed(1234) # We simulate a covariable and construct the outcome variable applying # an inverse logit link function on it. m <- 10 k <-100 covariate <- rnorm(k,2,0.5) beta <- c(-6,4) p <- 1/(1+exp(-(beta[1]+beta[2]*covariate))) # without dispersion parameter outcome <- rBI(k,m,p) model <- BIreg(outcome~covariate,m,disp=FALSE) model # with dispersion parameter phi <- 2 outcome.disp <- rBI(k,m,p,phi) model.disp <- BIreg(outcome.disp~covariate,m,disp=TRUE) model.disp

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.