Description Usage Arguments Details Value Author(s) References See Also

`orglm`

is used to fit generalised linear models with restrictions on the parameters, specified by giving a description of the linear predictor, a description of the error distribution, and a description of a matrix with linear constraints. The `quadprog`

package is used to apply linear constraints on the parameter vector.

1 2 3 4 5 6 7 8 | ```
orglm(formula, family = gaussian, data, weights, subset, na.action,
start = NULL, etastart, mustart, offset, control = list(...),
model = TRUE, method = "orglm.fit", x = FALSE, y = TRUE,
contrasts = NULL, constr, rhs, nec, ...)
orglm.fit(x, y, weights = rep(1, nobs), start = NULL, etastart = NULL,
mustart = NULL, offset = rep(0, nobs), family = gaussian(),
control = list(), intercept = TRUE, constr, rhs, nec)
``` |

`formula` |
an object of class |

`family` |
a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See |

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

`weights` |
an optional vector of ‘prior weights’ to be used in the fitting process. Should be |

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

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

`start` |
starting values for the parameters in the linear predictor. |

`etastart` |
starting values for the linear predictor. |

`mustart` |
starting values for the vector of means. |

`offset` |
this can be used to specify an |

`control` |
a list of parameters for controlling the fitting process. For |

`model` |
a logical value indicating whether |

`method` |
the method to be used in fitting the model. The default method |

`x` |
is a design matrix of dimension |

`y` |
is a vector of observations of length |

`contrasts` |
an optional list. See the |

`constr` |
a matrix with linear constraints. The columns of this matrix should correspond to the columns of the design matrix. |

`rhs` |
right hand side of the linear constraint formulation. A numeric vector with a length corresponding to the rows of |

`nec` |
Number of equality constrints. The first |

`...` |
For |

`intercept` |
logical. Should an intercept be included in the |

Non-`NULL`

`weights`

can be used to indicate that different observations have different dispersions (with the values in `weights`

being inversely proportional to the dispersions); or equivalently, when the elements of `weights`

are positive integers *w_i*, that each response *y_i* is the mean of *w_i* unit-weight observations. For a binomial GLM prior weights are used to give the number of trials when the response is the proportion of successes: they would rarely be used for a Poisson GLM.
If more than one of `etastart`

, `start`

and `mustart`

is specified, the first in the list will be used. It is often advisable to supply starting values for a `quasi`

family, and also for families with unusual links such as `gaussian("log")`

.
For the background to warning messages about ‘fitted probabilities numerically 0 or 1 occurred’ for binomial GLMs, see Venables & Ripley (2002, pp. 197–8).

An object of class `"orglm"`

is a list containing at least the following components:

- coefficients
a named vector of coefficients

- residuals
the

*working*residuals, that is the residuals in the final iteration of the IWLS fit. Since cases with zero weights are omitted, their working residuals are`NA`

.- fitted.values
the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function.

- rank
the numeric rank of the fitted linear model.

- family
the

`family`

object used.- linear.predictors
the linear fit on link scale.

- deviance
up to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero.

- null.deviance
The deviance for the null model, comparable with

`deviance`

. The null model will include the offset, and an intercept if there is one in the model. Note that this will be incorrect if the link function depends on the data other than through the fitted mean: specify a zero offset to force a correct calculation.- iter
the number of iterations of IWLS used.

- weights
the

*working*weights, that is the weights in the final iteration of the IWLS fit.- prior.weights
the weights initially supplied, a vector of

`1`

s if none were.- df.residual
the residual degrees of freedom of the unconstrained model.

- df.null
the residual degrees of freedom for the null model.

- y
if requested (the default) the

`y`

vector used. (It is a vector even for a binomial model.)- converged
logical. Was the IWLS algorithm judged to have converged?

- boundary
logical. Is the fitted value on the boundary of the attainable values?

Modification of the original glm.fit by Daniel Gerhard.
The original **R** implementation of `glm`

was written by Simon Davies working for Ross Ihaka at the University of Auckland, but has since been extensively re-written by members of the R Core team.
The design was inspired by the S function of the same name described in Hastie & Pregibon (1992).

Dobson, A. J. (1990)

*An Introduction to Generalized Linear Models.*London: Chapman and Hall.Hastie, T. J. and Pregibon, D. (1992)

*Generalized linear models.*Chapter 6 of*Statistical Models in S*eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks//Cole.McCullagh P. and Nelder, J. A. (1989)

*Generalized Linear Models.*London: Chapman and Hall.Venables, W. N. and Ripley, B. D. (2002)

*Modern Applied Statistics with S.*New York: Springer.

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