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 0.7-7 Index]