Reduced-rank vector generalized linear models.

Objects can be created by calls to `rrvglm`

.

`extra`

:Object of class

`"list"`

; the`extra`

argument on entry to`vglm`

. This contains any extra information that might be needed by the family function.`family`

:Object of class

`"vglmff"`

. The family function.`iter`

:Object of class

`"numeric"`

. The number of IRLS iterations used.`predictors`

:Object of class

`"matrix"`

with \(M\) columns which holds the \(M\) linear predictors.`assign`

:Object of class

`"list"`

, from class`"vlm"`

. This named list gives information matching the columns and the (LM) model matrix terms.`call`

:Object of class

`"call"`

, from class`"vlm"`

. The matched call.`coefficients`

:Object of class

`"numeric"`

, from class`"vlm"`

. A named vector of coefficients.`constraints`

:Object of class

`"list"`

, from class`"vlm"`

. A named list of constraint matrices used in the fitting.`contrasts`

:Object of class

`"list"`

, from class`"vlm"`

. The contrasts used (if any).`control`

:Object of class

`"list"`

, from class`"vlm"`

. A list of parameters for controlling the fitting process. See`vglm.control`

for details.`criterion`

:Object of class

`"list"`

, from class`"vlm"`

. List of convergence criterion evaluated at the final IRLS iteration.`df.residual`

:Object of class

`"numeric"`

, from class`"vlm"`

. The residual degrees of freedom.`df.total`

:Object of class

`"numeric"`

, from class`"vlm"`

. The total degrees of freedom.`dispersion`

:Object of class

`"numeric"`

, from class`"vlm"`

. The scaling parameter.`effects`

:Object of class

`"numeric"`

, from class`"vlm"`

. The effects.`fitted.values`

:Object of class

`"matrix"`

, from class`"vlm"`

. The fitted values. This is usually the mean but may be quantiles, or the location parameter, e.g., in the Cauchy model.`misc`

:Object of class

`"list"`

, from class`"vlm"`

. A named list to hold miscellaneous parameters.`model`

:Object of class

`"data.frame"`

, from class`"vlm"`

. The model frame.`na.action`

:Object of class

`"list"`

, from class`"vlm"`

. A list holding information about missing values.`offset`

:Object of class

`"matrix"`

, from class`"vlm"`

. If non-zero, a \(M\)-column matrix of offsets.`post`

:Object of class

`"list"`

, from class`"vlm"`

where post-analysis results may be put.`preplot`

:Object of class

`"list"`

, from class`"vlm"`

used by`plotvgam`

; the plotting parameters may be put here.`prior.weights`

:Object of class

`"matrix"`

, from class`"vlm"`

holding the initially supplied weights.`qr`

:Object of class

`"list"`

, from class`"vlm"`

. QR decomposition at the final iteration.`R`

:Object of class

`"matrix"`

, from class`"vlm"`

. The**R**matrix in the QR decomposition used in the fitting.`rank`

:Object of class

`"integer"`

, from class`"vlm"`

. Numerical rank of the fitted model.`residuals`

:Object of class

`"matrix"`

, from class`"vlm"`

. The*working*residuals at the final IRLS iteration.`ResSS`

:Object of class

`"numeric"`

, from class`"vlm"`

. Residual sum of squares at the final IRLS iteration with the adjusted dependent vectors and weight matrices.`smart.prediction`

:Object of class

`"list"`

, from class`"vlm"`

. A list of data-dependent parameters (if any) that are used by smart prediction.`terms`

:Object of class

`"list"`

, from class`"vlm"`

. The`terms`

object used.`weights`

:Object of class

`"matrix"`

, from class`"vlm"`

. The weight matrices at the final IRLS iteration. This is in matrix-band form.`x`

:Object of class

`"matrix"`

, from class`"vlm"`

. The model matrix (LM, not VGLM).`xlevels`

:Object of class

`"list"`

, from class`"vlm"`

. The levels of the factors, if any, used in fitting.`y`

:Object of class

`"matrix"`

, from class`"vlm"`

. The response, in matrix form.`Xm2`

:Object of class

`"matrix"`

, from class`"vlm"`

. See`vglm-class`

).`Ym2`

:Object of class

`"matrix"`

, from class`"vlm"`

. See`vglm-class`

).`callXm2`

:Object of class

`"call"`

, from class`"vlm"`

. The matched call for argument`form2`

.

Class `"vglm"`

, directly.
Class `"vlm"`

, by class "vglm".

- biplot
`signature(x = "rrvglm")`

: biplot.- Coef
`signature(object = "rrvglm")`

: more detailed coefficients giving**A**, \(\bold{B}_1\),**C**, etc.- biplot
`signature(object = "rrvglm")`

: biplot.`signature(x = "rrvglm")`

: short summary of the object.- summary
`signature(object = "rrvglm")`

: a more detailed summary of the object.

Yee, T. W. and Hastie, T. J. (2003)
Reduced-rank vector generalized linear models.
*Statistical Modelling*,
**3**, 15--41.

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 {
# Rank-1 stereotype model of Anderson (1984)
pneumo <- transform(pneumo, let = log(exposure.time),
x3 = runif(nrow(pneumo))) # x3 is unrelated
fit <- rrvglm(cbind(normal, mild, severe) ~ let + x3,
multinomial, data = pneumo, Rank = 1)
Coef(fit)
# }
```

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