fff {VGAM} | R Documentation

## F Distribution Family Function

### Description

Maximum likelihood estimation of the (2-parameter) F distribution.

### Usage

    fff(link="loge", earg=list(), idf1=NULL, idf2=NULL,
        method.init=1, zero=NULL)

### Arguments

`link` | Parameter link function for both parameters. See `Links` for more choices. The default keeps the parameters positive.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.
`idf1, idf2` | Numeric and positive. Initial value for the parameters. The default is to choose each value internally.
`method.init` | Initialization method. Either the value 1 or 2. If both fail try setting values for `idf1` and `idf2`.
`zero` | An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The value must be from the set {1,2}, corresponding respectively to df1 and df2. By default all linear/additive predictors are modelled as a linear combination of the explanatory variables.

### Details

The F distribution is named after Fisher and has a density function that has two parameters, called `df1` and `df2` here. This function treats these degrees of freedom as positive reals rather than integers. The mean of the distribution is df2/(df2-2) provided df2>2, and its variance is 2*df2^2*(df1+df2-2)/ (df1*(df2-2)^2*(df2-4)) provided df2>4. The estimated mean is returned as the fitted values. Although the F distribution can be defined to accommodate a non-centrality parameter `ncp`, it is assumed zero here.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm` and `vgam`.

### Warning

Numerical problems will occur when the estimates of the parameters are too low.

### Note

This family function uses the BFGS quasi-Newton update formula for the working weight matrices. Consequently the estimated variance-covariance matrix may be inaccurate or simply wrong! The standard errors must be therefore treated with caution; these are computed in functions such as `vcov()` and `summary()`.

### Author(s)

T. W. Yee

### References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

### See Also

`FDist`.

### Examples

    x = runif(n <- 4000)
    df1 = exp(2+0.5*x)
    df2 = exp(2-0.5*x)
    y = rf(n, df1, df2)
    fit = vglm(y  ~ x, fff, trace=TRUE)
    fit = vglm(y  ~ x, fff(link="logoff", earg=list(offset=0.5)), trace=TRUE)
    coef(fit, matrix=TRUE)
    Coef(fit)
    vcov(fit)   # caution needed!

[Package VGAM version 0.7-9 Index]