= Stata Stepwise =

The '''`stepwise`''' command runs a model iteratively with stepwise removal (or addition) of terms.

<<TableOfContents>>

----



== Usage ==

{{{
use http://stata-press.com/data/r14/auto, clear
generate weight2 = weight * weight
stepwise, pr(.2): regress mpg weight weight2 (displ gear) turn headroom foreign price
}}}

This is equivalent to interactively running:

{{{
// Full model
regress mpg weight weight2 (displ gear) turn headroom foreign price

// Observe that the `headroom` parameter has the greatest non-significant (>=0.2) p-value, so remove it
regress mpg weight weight2 (displ gear) turn foreign price

// ... remove the `(displ gear)` parameter
regress mpg weight weight2 turn foreign price

// ... remove the `price` parameter
regress mpg weight weight2 turn foreign

// Observe that all remaining parameters are significant
}}}

Implicitly this method uses [[Econometrics/WaldTest|Wald tests]].

----



== Syntax ==

After using `stepwise`, calling the command again (or the underlying modeling command) without any arguments reproduces the stepwise estimation results.

The `stepwise` command is aliased to `sw`.



=== Terms ===

Terms on a modeling command are commonly variable names. They can also be [[Stata/Regress#Factor_Variables|factor variables]].

Terms are considered with respect to parentheses. For example, in this model:

{{{
stepwise, pr(.2): regress y x1 x2 x3 x4 i.a
}}}

...each factor variable of `a` is considered separately. Alternatively, in this model:

{{{
stepwise, pr(.2): regress y x1 x2 x3 x4 (i.a)
}}}

...the factor variables of `a` are considered altogether.



=== Options ===

The `pr()` option specifies a signficance level over which parameters are stepwise removed. This mode is called '''backward selection'''.

Compare to the '''`pe()`''' option, which specifies a significant level at which parameters are stepwise added. This mode is called '''forward selection'''.

`pr()` and `pe()` can be used simultaneously. At first the model is fit with backward selection. Then excluded terms are re-examined for re-addition. Then included terms are re-examined for re-removal. This is repeated until all included parameters are significant and all excluded parameters are non-significant. Because of how equivalence is treated by the significance tests, it can be necessary to combine these options with unusual numbers, like:

{{{
stepwise, pr(0.050001) pe(0.05): regress mpg weight weight2 (displ gear) turn headroom foreign price
}}}

The '''`forward`''' is only effective when using the `pr()` and `pe()` options simultaneously. At first the model is fit with forward selection. Then included terms are re-examined for re-removal. Then excluded terms are re-examined for re-addition.

The '''`hierarchical`''' option directs `stepwise` to consider parameters in order. Given a model fit on `x1`, `x2`, and `x3` and a backward selection mode: `x3` is the first parameter considered for removal regardless of how its p-value compares to other parameters'. (This can be called '''backward hierarchical selection'''.) Instead fiven a forward selection mode: `x1` is the first parameter considered for addition. (This can be called '''forward hierarchical selection'''.)

The '''`lockterm`''' option locks the first independent variable into the model. For example, to lock the parameter for `x1`, try:

{{{
stepwise, pr(0.2) lockterm1: logistic y x1 x2 x3
}}}

This option respects parentheses. To lock the parameters for `x1` and `x2`, try:

{{{
stepwise, pr(0.2) lockterm1: logistic y (x1 x2) x3
}}}

Note that some modeling commands do not take a dependent variable, and some take more than one dependent variable, so it is misleading to assume that `lockterm1` locks the second specified term.

The '''`lr`''' option specifies the [[Econometrics/LikelihoodRatioTest|likelihood ratio test]] instead of the [[Econometrics/WaldTest|Wald test]].

----



== See also ==

[[https://www.stata.com/manuals/rstepwise.pdf|Stata manual for stepwise]]



----
CategoryRicottone