Family functions for the VGAM package

Objects can be created by calls of the form `new("vglmff", ...)`

.

In the following, \(M\) is the number of linear/additive predictors.

`blurb`

:Object of class

`"character"`

giving a small description of the model. Important arguments such as parameter link functions can be expressed here.`constraints`

:Object of class

`"expression"`

which sets up any constraint matrices defined by arguments in the family function. A`zero`

argument is always fed into`cm.zero.vgam`

, whereas other constraints are fed into`cm.vgam`

.`deviance`

:Object of class

`"function"`

returning the deviance of the model. This slot is optional. If present, the function must have arguments`function(mu, y, w, residuals = FALSE, eta, extra = NULL)`

. Deviance residuals are returned if`residuals = TRUE`

.`fini`

:Object of class

`"expression"`

to insert code at a special position in`vglm.fit`

or`vgam.fit`

. This code is evaluated immediately after the fitting.`first`

:Object of class

`"expression"`

to insert code at a special position in`vglm`

or`vgam`

.`infos`

:Object of class

`"function"`

which returns a list with components such as`M1`

. At present only a very few VGAM family functions have this feature implemented. Those that do do not require specifying the`M1`

argument when used with`rcim`

.`initialize`

:Object of class

`"expression"`

used to perform error checking (especially for the variable`y`

) and obtain starting values for the model. In general,`etastart`

or`mustart`

are assigned values based on the variables`y`

,`x`

and`w`

.`linkinv`

:Object of class

`"function"`

which returns the fitted values, given the linear/additive predictors. The function must have arguments`function(eta, extra = NULL)`

.`last`

:Object of class

`"expression"`

to insert code at a special position (at the very end) of`vglm.fit()`

or`vgam.fit()`

. This code is evaluated after the fitting. The list`misc`

is often assigned components in this slot, which becomes the`misc`

slot on the fitted object.`linkfun`

:Object of class

`"function"`

which, given the fitted values, returns the linear/additive predictors. If present, the function must have arguments`function(mu, extra = NULL)`

. Most VGAM family functions do not have a`linkfun`

function. They largely are for classical exponential families, i.e., GLMs.`loglikelihood`

:Object of class

`"function"`

returning the log-likelihood of the model. This slot is optional. If present, the function must have arguments`function(mu, y, w, residuals = FALSE, eta, extra = NULL)`

. The argument`residuals`

can be ignored because log-likelihood residuals aren't defined.`middle`

:Object of class

`"expression"`

to insert code at a special position in`vglm.fit`

or`vgam.fit`

.`middle2`

:Object of class

`"expression"`

to insert code at a special position in`vglm.fit`

or`vgam.fit`

.`simslot`

:Object of class

`"function"`

to allow`simulate`

to work.`hadof`

:Object of class

`"function"`

; experimental.`summary.dispersion`

:Object of class

`"logical"`

indicating whether the general VGLM formula (based on a residual sum of squares) can be used for computing the scaling/dispersion parameter. It is`TRUE`

for most models except for nonlinear regression models.`vfamily`

:Object of class

`"character"`

giving class information about the family function. Although not developed at this stage, more flexible classes are planned in the future. For example, family functions`sratio`

,`cratio`

,`cumulative`

, and`acat`

all operate on categorical data, therefore will have a special class called`"VGAMcat"`

, say. Then if`fit`

was a`vglm`

object, then`coef(fit)`

would print out the`vglm`

coefficients plus`"VGAMcat"`

information as well.`deriv`

:Object of class

`"expression"`

which returns a \(M\)-column matrix of first derivatives of the log-likelihood function with respect to the linear/additive predictors, i.e., the score vector. In Yee and Wild (1996) this is the \(\bold{d}_i\) vector. Thus each row of the matrix returned by this slot is such a vector.`weight`

:Object of class

`"expression"`

which returns the second derivatives of the log-likelihood function with respect to the linear/additive predictors. This can be either the observed or expected information matrix, i.e., Newton-Raphson or Fisher-scoring respectively. In Yee and Wild (1996) this is the \(\bold{W}_i\) matrix. Thus each row of the matrix returned by this slot is such a matrix. Like the`weights`

slot of`vglm`

/`vgam`

, it is stored in*matrix-band*form, whereby the first \(M\) columns of the matrix are the diagonals, followed by the upper-diagonal band, followed by the band above that, etc. In this case, there can be up to \(M(M+1)\) columns, with the last column corresponding to the (1,\(M\)) elements of the weight matrices.`validfitted, validparams`

:Functions that test that the fitted values and all parameters are within range. These functions can issue a warning if violations are detected.

`signature(x = "vglmff")`

: short summary of the family function.

VGAM family functions are not compatible with
`glm`

, nor `gam`

(from either
gam or mgcv packages).

Yee, T. W. and Wild, C. J. (1996)
Vector generalized additive models.
*Journal of the Royal Statistical Society, Series B, Methodological*,
**58**, 481--493.

# NOT RUN { cratio() cratio(link = "cloglog") cratio(link = "cloglog", reverse = TRUE) # }

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