TaylorFit is a regression program that makes fitting Multivariate
Polynomial Regression models easy. ORDER
It is a text-based program runs under a DOS window, although the
interface has an easy to use interactive menu organization.
The program uses a stepwise algorithm to select the best terms
to include in the model, while keeping the model small by excluding
terms that do not improve the fit. Fitting is done by least squares
using the Singular Value Decomposition method (the Normal Equations
method can also be selected).
The user selects exponents that the program can use in generating
candidate polynomial terms, as well as the possible number of multiplicands
in each term. If the model to be fitted is a time series, the user
can input the lags to be used in generating terms. These parameters
can all be changed during the fitting process. This allows the user
to start with simpler models, and gradually increase model complexity
until the fit can no longer be improved.
TaylorFit allows all or part of an input data file to be used for
fitting. It also allows data files to be split into a "fit"
and "test" dataset so each portion can be used for cross-validation
and for final validation.
The user can select from among seven criteria for selecting model
terms. These include optimizing Mean Square Error (MSE), model F-statistic,
term t-statistics, Akaike Information Criterion (AIC), or Bayesian
Information Criterion (BIC). These can be combined in several ways
in cross-validation. For example, you can choose terms that have
a t-statistic probability greater than 95%, and that produce an
increase in the model F-statistic for the test dataset.
The program has an Auto mode, in which the best term is selected
automatically and the program continues without user attention to
generate a model that cannot be improved by addition or removal
of a single term.
Alternatively, the user can run in Manual mode, in which the ten
best terms are presented to the user, who then can choose among
them. There is also a batch mode that can be used to generate a
model file without the need to enter any program commands interactively.
Output files generated by TaylorFit include a model description
file and a file containing model predictions based on data file
The predictions file can also contain residuals and confidence
intervals. All input and output files are text-formatted files that
can easily be read by other programs. ORDER