## Stata 15 help for boxcox

```
[R] boxcox -- Box-Cox regression models

Syntax

boxcox depvar [indepvars] [if] [in] [weight] [, options]

options               Description
-------------------------------------------------------------------------
Model
noconstant          suppress constant term
model(lhsonly)      left-hand-side Box-Cox model; the default
model(rhsonly)      right-hand-side Box-Cox model
model(lambda)       both sides Box-Cox model with same parameter
model(theta)        both sides Box-Cox model with different parameters
notrans(varlist)    do not transform specified independent variables

Reporting
level(#)            set confidence level; default is level(95)
lrtest              perform likelihood-ratio test

Maximization
nolog               suppress full-model iteration log
nologlr             suppress restricted-model lrtest iteration log
maximize_options    control the maximization process; seldom used
-------------------------------------------------------------------------
depvar and indepvars may contain time-series operators; see tsvarlist.
bootstrap, by, jackknife, rolling, statsby, and xi are allowed; see
prefix.
Weights are not allowed with the bootstrap prefix.
fweights and iweights are allowed; see weight.
See [R] boxcox postestimation for features available after estimation.

Statistics > Linear models and related > Box-Cox regression

Description

boxcox finds the maximum likelihood estimates of the parameters of the
Box-Cox transform, the coefficients on the independent variables, and the
standard deviation of the normally distributed errors.  Any depvar or
indepvars to be transformed must be strictly positive.  Options can be
used to control which variables remain untransformed.

Options

+-------+
----+ Model +------------------------------------------------------------

noconstant; see [R] estimation options.

model(lhsonly|rhsonly|lambda|theta) specifies which of the four models to
fit.

model(lhsonly) applies the Box-Cox transform to depvar only.
model(lhsonly) is the default.

model(rhsonly) applies the transform to the indepvars only.

model(lambda) applies the transform to both depvar and indepvars, and
they are transformed by the same parameter.

model(theta) applies the transform to both depvar and indepvars, but
this time, each side is transformed by a separate parameter.

notrans(varlist) specifies that the variables in varlist not be
transformed when included in the model.  You can specify
notrans(varlist) with model(lhsonly), but the results will be the
same as specifying the variables in varlist in indepvars.

+-----------+
----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

lrtest specifies that a likelihood-ratio test of significance be
performed and reported for each independent variable.

+--------------+
----+ Maximization +-----------------------------------------------------

nolog suppresses the iteration log when fitting the full model.

nologlr suppresses the iteration log when fitting the restricted models
required by the lrtest option.

maximize_options: iterate(#) and from(init_specs); see [R] maximize.

Model       Initial value specification
---------------------------------------
lhsonly     from(#_t, copy)
rhsonly     from(#_l, copy)
lambda      from(#_l, copy)
theta       from(#_l #_t, copy)
---------------------------------------

Examples

Setup
. sysuse auto

Apply Box-Cox transform to mpg
. boxcox mpg weight price

Same as above, but include foreign as an independent variable that has
not been transformed
. boxcox mpg weight price, notrans(foreign)

Apply Box-Cox transform to weight and price
. boxcox mpg weight price, model(rhsonly)

Use the same parameter to transform mpg, weight, and price
. boxcox mpg weight price, model(lambda)

Use a different parameter to transform mpg than that used to transform
weight and price
. boxcox mpg weight price, model(theta)

Stored results

boxcox stores the following in e():

Scalars
e(N)                     number of observations
e(ll)                    log likelihood
e(chi2)                  LR statistic of full vs. comparison
e(df_m)                  full model degrees of freedom
e(ll0)                   log likelihood of the restricted model
e(df_r)                  restricted model degrees of freedom
e(ll_t1)                 log likelihood of model lambda = theta = 1
e(chi2_t1)               LR of lambda = theta = 1 vs. full model
e(p_t1)                  p-value of lambda = theta = 1 vs. full model
e(ll_tm1)                log likelihood of model lambda = theta = -1
e(chi2_tm1)              LR of lambda = theta = -1 vs. full model
e(p_tm1)                 p-value of lambda = theta = -1 vs. full model
e(ll_t0)                 log likelihood of model lambda = theta = 0
e(chi2_t0)               LR of lambda = theta = 0 vs. full model
e(p_t0)                  p-value of lambda = theta = 0 vs. full model
e(rank)                  rank of e(V)
e(ic)                    number of iterations
e(rc)                    return code

Macros
e(cmd)                   boxcox
e(cmdline)               command as typed
e(depvar)                name of dependent variable
e(model)                 lhsonly, rhsonly, lambda, or theta
e(wtype)                 weight type
e(wexp)                  weight expression
e(ntrans)                yes if untransformed indepvars
e(chi2type)              LR; type of model chi-squared test
e(lrtest)                lrtest, if requested
e(properties)            b V
e(predict)               program used to implement predict
e(marginsnotok)          predictions disallowed by margins

Matrices
e(b)                     coefficient vector
e(V)                     variance-covariance matrix of the estimators
(see note below)
e(pm)                    p-values for LR tests on indepvars
e(df)                    degrees of freedom of LR tests on indepvars
e(chi2m)                 LR statistics for tests on indepvars

Functions
e(sample)                marks estimation sample

e(V) contains all zeros, except for the elements that correspond to the
parameters of the Box-Cox transform.

```