R: Summarizing 'selm' fits

summary.selm {sn} | R Documentation

## Summarizing `selm` fits

### Description

`summary` method for class `"selm"` and `"mselm"`.

### Usage

    ## S4 method for signature 'selm'
    summary(object, param.type = "CP", cov = FALSE, cor = FALSE)

    ## S4 method for signature 'mselm'
    summary(object, param.type = "CP", cov = FALSE, cor = FALSE)

### Arguments

`object` | an object of class `"selm"` or `"mselm"` as created by a call to function `selm`.
`param.type` | a character string which indicates the required type of parameter type; possible values are `"CP"` (default), `"DP"`, `"pseudo-CP"` and their equivalent lower-case expressions.
`cov` | a logical value, to indicate if an estimate of the variance and covariance matrix of the estimates is required (default: `FALSE`).
`cor` | a logical value, to indicate if an estimate of the correlation matrix of the estimates is required (default: `FALSE`).

### Value

An S4 object of class `summary.selm` with 12 slots.

``call`:` | the calling statement.
``family`:` | the parametric family of skew-ellitically contoured distributed (SEC) type.
``logL`:` | the maximized log-likelihood or penalized log-likelihood value
``method`:` | estimation method (`"MLE"` or `"MPLE"`)
``param.type`:` | a characer string with the chosen parameter set.
``param.table`:` | table of parameters, std.errors and z-values
``fixed.param`:` | a list of fixed parameter values
``resid`:` | residual values
``control`:` | a list with control parameters
``aux`:` | a list of auxiliary quantities
``size`:` | a numeric vector with various lengths and dimensions
``boundary`:` | a logical value which indicates whether the estimates are on the boundary of the parameter space

### Note

There are two reasons why the default choice of `param.type` is `CP`. One is the the easier interpretation of cumulant-based quantities such as mean value, standard deviation, coefficient of skewness.

The other reason is more technical and applies only to cases when the estimate of the slant parameter alpha of the SN distribution is close to the origin: standard asymptotic distribution theory of maximum likelihood estimates (MLE's) does not apply in this case and the corresponding standard errors are not trustworthy. The problem is especialy severe at α=0 but to some extent propagates to its vicinity. If d=1, adoption of `CP` leads to MLE's with regular asymptotic distribution across the parameter space, including α=0. For d>1 and α=0, the problem is still unsolved at the present time, which is the reason why `selm` issues a warning message when the MLE is in the vicinity of α=0; see ‘Details’ of `selm`. For background information, see Sections 3.1.4–6 and 5.2.3 of Azzalini and Capitanio (2014) and references therein.

This problem does not occur with the the SC and the ST distribution (unless its tail-weight parameter `nu` diverges, that is, when we are effectively approaching the `SN` case).

### Author(s)

Adelchi Azzalini

### References

Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.

### See Also

`selm` function, `selm` (and `mselm`) class, `plot.selm`, `dp2cp`

### Examples

    data(wines, package="sn")
    m5 <- selm(acidity ~ phenols + wine, family="SN", data=wines)
    summary(m5)
    summary(m5, "dp")
    s5 <- summary(m5, "dp", cor=TRUE, cov=TRUE)
    dp.cor <- slot(s5, "aux")$param.cor
    cov2cor(vcov(m5, "dp")) # the same
    #
    # m6 <- selm(acidity ~ phenols + wine, family="ST", data=wines) # boundary!?
    #
    m12 <- selm(cbind(acidity, alcohol) ~ phenols + wine,  family="SN", data=wines)
    s12 <- summary(m12)
    coef(m12, 'dp')
    coef(m12, "dp", vector=FALSE)
    #
    # see other examples at function selm

[Package sn version 1.5-3 Index]