Stata 15 help for boxcox

[R] boxcox -- Box-Cox regression models


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


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.


+-------+ ----+ 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) ---------------------------------------


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.

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