Maximum likelihood estimation of
 the 1-parameter extended log-F distribution.

extlogF1

An implementation of about 6 major classes of
statistical regression models. The central algorithm is
Fisher scoring and iterative reweighted least squares.
At the heart of this package are the vector generalized linear
and additive model (VGLM/VGAM) classes. VGLMs can be loosely
thought of as multivariate GLMs. VGAMs are data-driven
VGLMs that use smoothing. The book "Vector Generalized
Linear and Additive Models: With an Implementation in R"
(Yee, 2015) <DOI:10.1007/978-1-4939-2818-7> gives details of
the statistical framework and the package. Currently only
fixed-effects models are implemented. Many (100+) models and
distributions are estimated by maximum likelihood estimation
(MLE) or penalized MLE. The other classes are RR-VGLMs
(reduced-rank VGLMs), quadratic RR-VGLMs, doubly constrained
RR-VGLMs, quadratic RR-VGLMs, reduced-rank VGAMs,
RCIMs (row-column interaction models)---these classes perform
constrained and unconstrained quadratic ordination (CQO/UQO)
models in ecology, as well as constrained additive ordination
(CAO). Hauck-Donner effect detection is implemented.
Note that these functions are subject to change;
see the NEWS and ChangeLog files for latest changes.

Thomas Yee

VGAM

Vector Generalized Linear and Additive Models

Cleve Moler

extlogF1 function

Maximum likelihood estimation of
 the 1-parameter extended log-F distribution.

Extended log-F Distribution
        Family Function — extlogF1

<dl>

 <dt>tau</dt>
<dd>Numeric, the desired quantiles. A strictly increasing sequence,
 each value must be in $(0, 1)$.
 The default values are the three quartiles, matching
 <code>lms.bcn</code>.


</dd>

 <dt>parallel</dt>
<dd>Similar to <code>alaplace1</code>, applying to the
 location parameters.
 One can try fix up the quantile-crossing problem after fitting
 the model by calling <code>fix.crossing</code>.
 Use <code>is.crossing</code> to see if there is a problem.
 The default for <code>parallel</code> is totally <code>FALSE</code>, i.e.,
 <code>FALSE</code> for every variable including the intercept.
 Quantile-crossing can occur when values of <code>tau</code> are too
 close, given the data. How the quantiles are modelled with
 respect to the covariates also has a big effect, e.g.,
 if they are too flexible or too inflexible then the problem
 is likely to occur.
 For example, using <code><a href='https://rdrr.io/r/splines/bs.html'>bs</a></code> with
 <code>df = 10</code> is likely to create problems.


Setting <code>parallel = TRUE</code> results in a totally
 parallel model; all quantiles are parallel
 and this assumption can be too strong for some data sets.
 Instead, <code>fix.crossing</code> only repairs the
 quantiles that cross.
 So one must carefully choose values of <code>tau</code> for
 fitting the original fit.



 








 

</dd>

 <dt>seppar, tol0</dt>
<dd>Numeric, both of unit length and nonnegative,
 the separation and shift parameters.
 If <code>seppar</code> is positive then any crossing quantile
 is penalized by the difference cubed multiplied by <code>seppar</code>.
 The log-likelihood subtracts the penalty.
 The shift parameter ensures that the result is strictly
 noncrossing when <code>seppar</code> is large enough; otherwise
 if <code>tol0 = 0</code> and <code>seppar</code> is large
 then the crossing quantiles remain
 crossed even though the offending amount becomes small but never
 exactly 0.
 Informally, <code>tol0</code> pushes the adjustment enough
 so that <code>is.crossing</code> should return <code>FALSE</code>.


If <code>tol0</code> is positive then that is the shift in absolute
 terms. But <code>tol0</code> may be assigned a negative value, in
 which case it is interpreted multiplicatively
 relative to the midspread of the response;
 <code>tol0 &lt;- abs(tol0) * midspread</code>.
 Regardless,
 <code>fit@extra$tol0</code> is the amount in absolute terms.


If avoiding the quantile crossing problem is of concern to you,
 try increasing <code>seppar</code> to decrease the amount of crossing.
 Probably it is best to choose the smallest value of <code>seppar</code>
 so that <code>is.crossing</code> returns <code>FALSE</code>.
 Increasing <code>tol0</code> relatively or absolutely
 means the fitted quantiles are
 allowed to move apart more.
 However, <code>tau</code> must be considered when choosing <code>tol0</code>.
 

</dd>

</dl>





























 
 



<dl>

 <dt>llocation, ilocation</dt>
<dd>See <code>Links</code> for more choices and
 <code>CommonVGAMffArguments</code> for more information.
 Choosing <code>loglink</code> should usually be good
 for counts.
 And choosing <code>logitlink</code> should be a reasonable for
 proportions. However, avoid choosing <code>tau</code> values close to
 the boundary, for example, if $p_0$ is the proportion of
 0s then choose $p_0 \ll \tau$.
 For proportions grouped data is much better than ungrouped data,
 and the bigger the groups the more the
 granularity so that the empirical proportion can approximate
 <code>tau</code> more closely.



</dd>

 <dt>lambda.arg</dt>
<dd>Positive tuning parameter which controls the sharpness of the cusp.
 The limit as it approaches 0 is probably very similar to
 <code>dalap</code>.
 The default is to choose the value internally.
 If <code>scale.arg</code> increases, then probably <code>lambda.arg</code>
 needs to increase accordingly.
 If <code>lambda.arg</code> is too large then the empirical quantiles
 may not be very close to <code>tau</code>.
 If <code>lambda.arg</code> is too close to 0 then the convergence
 behaviour will not be good and local solutions found, as well
 as numerical problems in general.
 Monitoring convergence is recommended when varying
 <code>lambda.arg</code>.

 

</dd>

 <dt>scale.arg</dt>
<dd>Positive scale parameter and sometimes called <code>scale</code>.
 The transformation used is <code>(y - location) / scale</code>.
 This function should be okay for response variables
 having a moderate range (0--100, say), but if very different
 from this then experimenting with this argument will be
 a good idea. 

</dd>

 <dt>ishrinkage, idf.mu, digt</dt>
<dd>Similar to <code>alaplace1</code>.

 
</dd>

 <dt>imethod</dt>
<dd>Initialization method.
 Either the value 1, 2, or ....
 See <code>CommonVGAMffArguments</code> for more information.

</dd>

</dl>

extlogF1: Extended log-F Distribution Family Function

Description

Usage

Arguments

Value

Details

References

See Also

Examples