fff {VGAM} | R Documentation |
Maximum likelihood estimation of the (2-parameter) F distribution.
fff(link="loge", earg=list(), idf1=NULL, idf2=NULL, method.init=1, zero=NULL)
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.
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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.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
Numerical problems will occur when the estimates of the parameters are too low.
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()
.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
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!