S4 class for generalized linear models with quasi-likelihood methods. It inherits from GLM class.

## Details

The overall test involves a constrained optimization problem. All
the parameters except for the intercept are constrained to zero. The
`optim`

slot contains the results. When there is no intercept, all
parameters are set to zero, and the results need to be understood in terms
of EL class since no constrained optimization is involved.
Once the solution is found, the log probabilities (`logp`

) and the
(constrained) empirical likelihood values (`logl`

, `loglr`

, `statistic`

)
readily follow, along with the degrees of freedom (`df`

) and the
\(p\)-value (`pval`

). The significance tests for each parameter also
involve constrained optimization problems where only one parameter is
constrained to zero. The `sigTests`

slot contains the results.

## Slots

`family`

A

`family`

object used.`dispersion`

A single numeric for the estimated dispersion parameter.

`sigTests`

A list of the following results of significance tests:

`statistic`

A numeric vector of minus twice the (constrained) empirical log-likelihood ratios with asymptotic chi-square distributions.`iterations`

An integer vector for the number of iterations performed for each parameter.`convergence`

A logical vector for the convergence status of each parameter.`cstr`

A single logical for whether constrained EL optimization is performed or not.

`call`

A matched call.

`terms`

A

`terms`

object used.`misc`

A list of various outputs obtained from the model fitting process. They are used in other generics and methods.

`optim`

A list of the following optimization results:

`par`

A numeric vector of the solution to the (constrained) optimization problem.`lambda`

A numeric vector of the Lagrange multipliers of the dual problem corresponding to`par`

.`iterations`

A single integer for the number of iterations performed.`convergence`

A single logical for the convergence status.

`logp`

A numeric vector of the log probabilities of the (constrained) empirical likelihood.

`logl`

A single numeric of the (constrained) empirical log-likelihood.

`loglr`

A single numeric of the (constrained) empirical log-likelihood ratio.

`statistic`

A single numeric of minus twice the (constrained) empirical log-likelihood ratio with an asymptotic chi-square distribution.

`df`

A single integer for the degrees of freedom of the statistic.

`pval`

A single numeric for the \(p\)-value of the statistic.

`nobs`

A single integer for the number of observations.

`npar`

A single integer for the number of parameters.

`weights`

A numeric vector of the re-scaled weights used for the model fitting.

`coefficients`

A numeric vector of the maximum empirical likelihood estimates of the parameters.

`method`

A single character for the method dispatch in internal functions.

`data`

A numeric matrix of the data for the model fitting.

`control`

An object of class ControlEL constructed by

`el_control()`

.

## Examples

```
showClass("QGLM")
#> Class "QGLM" [package "melt"]
#>
#> Slots:
#>
#> Name: family dispersion sigTests call terms
#> Class: family numeric ANY call terms
#>
#> Name: misc optim logp logl loglr
#> Class: list list numeric numeric numeric
#>
#> Name: statistic df pval nobs npar
#> Class: numeric integer numeric integer integer
#>
#> Name: weights coefficients method data control
#> Class: numeric numeric character ANY ControlEL
#>
#> Extends:
#> Class "GLM", directly
#> Class "LM", by class "GLM", distance 2
#> Class "CEL", by class "GLM", distance 3
#> Class "EL", by class "GLM", distance 4
```