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I have been asked to forward this to the list.
Please respond to Marco Riani at the address given and NOT TO ME.
Merry Christmas!
Jeremy
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A new version of the forward library (see Atkinson and Riani, 2000;
Robust Diagnostic Regression Analysis, Springer Verlag, New York) for
Splus running under windows versions 6.x has been placed on (section
software and datasets)
http://stat.econ.unipr.it/riani/ar
or
http://www.riani.it/ar
The forward library can be used from the command prompt or from the
supplied GUI. This software implements the forward search for linear
regression models, transformations in regression and generalized linear
models. For GLMs, it extends the traditional links supported by Splus.
For example, the Box Cox transformation is available as a link in Gamma
regression and in binary regression it provides the user with the
arcsine link.
In order to assess the link, the so-called "goodness of link test" has
been implemented in the context of the forward search (Atkinson and
Riani, 2000; Springer Verlag, p. 200). Finally, to check the stability
of parameter estimates, an extension of Cook's distance for GLMs has
been implemented together with a series of forward plots which are easy
to interpret and powerful in revealing the structure of the data.
Clicking on a simple check box, the Data Set combo box of the supplied
GUI, lists all the data sets used in Atkinson and Riani (2000).
Additionally, when the same check box is selected, the formula, family
and link will be filled in automatically.
I look forward to receiving your feedback -- feel free to email me
([log in to unmask]) or contact Kjell Konis ([log in to unmask])
Below, you can find the help file containing a brief description of the
forward search
Merry Christmas and a Happy New Year
Marco Riani
The Forward Search
DESCRIPTION:
The forward search is a powerful general method for detecting
unidentified subsets of the data and for determining their effect on
fitted models. These subsets may be clusters of distinct observations or
there may be one or several outliers. Alternatively, all the data may
agree with the fitted model. The plots produced by the forward search
make it possible to distinguish these situations and to identify any
influential observations. The method has been implemented for
regression, Box and Cox power transformations and for generalized linear
models.
The search starts by fitting a small robustly chosen set of
observations, intended to exclude outliers. The subset is then increased
in size, one observation at a time and the behaviour of parameter
estimates, residuals and diagnostic measures monitored by plotting
against subset size. Such plots are called forward plots.
REGRESSION:
The number of observations is n and the number of parameters to be
estimated is p. The search starts by fitting the regression model to
subsets of p observations. The default is to take all of the subsets if
there are less than 3000, and to find 3000 non-singular random samples
otherwise. For each subset the median of the squared residuals is
calculated. The subset of p observations yielding the minimum median of
squared residuals provides the initial subset for the forward search.
During the search the parameters are estimated by least squares applied
to subsets of m observations as m goes from p to n. When m observations
are used in fitting, the subset yields parameter estimates from which we
calculate residuals for all observations. We square these n residuals
and order them, taking the observations corresponding to the m+1
smallest as the new subset for the next step in the forward search.
Usually this process augments the subset by one observation, but
sometimes two or more observations enter as one or more leave, an
indication of the presence of a cluster of outliers. Due to the form of
the search, outliers, if any, tend to enter as m approaches n. Forward
plots of parameter estimates and residuals are typically stable until
the outliers enter the subset.
TRANSFORMATIONS:
Regression models are often improved by a power transformation of the
response. In the Box and Cox parametric family, a value of one
corresponds to no transformation, zero to the log transformation and
minus one to the reciprocal. The value of the transformation parameter
is tested using an approximately normal score test, which is related to
the likelihood ratio test of Box and Cox.
The fan plot provides a forward plot of the score statistic for five
values of the transformation parameter between one and minus one.
However, transformation of the data alters the order in which
observations enter the forward search. The plot therefore presents the
results of five separate searches, one for each value of the
transformation parameter.
GENERALIZED LINEAR MODELS:
The forward search for generalized linear models is similar to that for
regression, except that the squared least squares residuals used in the
search are replaced by squared deviance residuals, that is individual
components of the deviance. Forward plots of deviance residuals and of
parameter estimates are again helpful in determining agreement between
the fitted model and the data.
The link function in these models is tested by a goodness of link test
using a constructed variable. There are two stages in the calculation.
In the first, the generalized linear model is fitted and the linear
predictor estimated for each observation. The constructed variable is
the square of the linear predictor. The approximately normal score
statistic is the test for the inclusion of this constructed variable in
the model. Significance indicates that the link function is
unsatisfactory.
REFERENCES:
Atkinson, A. C. and Riani, M. "Robust Diagnostic Regression Analysis",
Springer Verlag, New York (2000).
SEE ALSO:
fwdglm , fwdlm , fwdsco .
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Marco Riani, PhD
Dipartimento di Economia
Sezione di Statistica
Via J. Kennedy 6
43100 PARMA
ITALY
PHONE: +39 0521 902478
FAX: +39 0521 902375
e-mail: [log in to unmask]
http://stat.econ.unipr.it/riani
http://www.riani.it
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