Fractional polynomial modelling (extended)                      [STB-21: sg26]
------------------------------------------

  ^fpx^ yvar [nvar] xvar [^in^ range] [^if^ exp] [^weight^] [^,^ ^cm^d^(^regression_cmd^)^
	^cont^inuous^(^contvars^)^ ^ba^se^(^basevars^)^ ^po^wers^(^powlist^)^ ^add^powers^(^addlist^)^
	^fix^powers^(^fixlist^)^ ^df(^#^)^ ^ex^px^(^#|^sd)^ ^ori^gin^(^#^)^ ^na^me^(^newxvar^)^ ^dev^thr^(^#^)^
	^log^ ^zer^o regression_cmd_options ]


Description
-----------

^fpx^ fits fractional polynomial (FP) models in xvar to yvar.  The functionality
of ^fpx^ considerably overlaps that of ^fp^, so you should see ^help fp^ before
consulting this help file.

As ^fpx^ runs, it displays line(s) of dots to indicate progress in searching the
different FP models for the best fit.




Description, continued
----------------------

^fpx^ extends ^fp^ in two ways:

1.  With ^fpx^, you can fit an FP model with an arbitrarily large number of
degrees of freedom (^df()^), whereas ^fp^ is limited to ^df(4)^.  This permits
a much wider family of models to be explored.

2.  ^fpx^ outputs the value of the Akaike Information Criterion (AIC) for each
model it fits.  Some statisticians recommend selecting as `best' the model
which has the minimum AIC.  The AIC is defined as -2 times the log likelihood
plus 2 times the number of parameters estimated; thus, overfitting tends to be
penalized.  Each additional degree (m) of FP model fitted increases the df by 2
and therefore adds 4 to the AIC.

The main omissions from ^fpx^ concern model comparisons: ^fpx^ does not fit
quadratic, cubic or Box-Tidwell models, nor does it calculate P-values for
comparing selected models.

^fpgraph^ (see ^help fpgraph^) is available after using ^fpx^ to plot the
best-fitting model.


Options
-------

The following options of ^fp^ are unavailable in ^fpx^:

^fast^, ^gplot()^, ^saving()^, ^repeat^, ^powers(none)^.

All the other options are identical to those of ^fp^ except for ^df()^:

^df(^#^)^ specifies the degrees of freedom of the highest-degree FP model to be
fitted.  The default is # = 4, which gives all models with degree m = 2.  Odd
values of # give models in which one power is always 1.


Examples
--------

 . ^fpx mpg weight, base(length displ) df(5)^
 . ^fpx mpg weight, log fixpowers(0)^





Saved Results
-------------

^fpx^ saves in the ^$S_^# macros as follows. 

	^S_1^    number of observations
	^S_2^    deviance of base model

	^S_23^   zeta (see ^origin()^ option and Examples in ^help fp^)

^$S_3^, ^$S_4^, etc. contain the deviances of the models with df=1, 2, ... .
These are followed by the best powers for models with df=1, 2, ... .


Also see
--------

    STB:  sg26 (STB-21)
On-line:  ^help^ for ^fp^, ^fpgraph^, ^fpgen^, ^swfp^.