Stata 15 help for testnl

[R] testnl -- Test nonlinear hypotheses after estimation

Syntax

testnl exp = exp [= exp ...] [, options]

testnl (exp = exp [= exp...]) [(exp = exp [= exp ...]) ...] [, options]

options Description ------------------------------------------------------------------------- mtest[(opt)] test each condition separately iterate(#) use maximum # of iterations to find the optimal step size

df(#) use F distribution with # denominator degrees of freedom for the reference distribution of the test statistic nosvyadjust carry out the Wald test as W/k ~ F(k,d); for use with svy estimation commands when the df() option is also specified ------------------------------------------------------------------------- df(#) and nosvyadjust do not appear in the dialog box.

The second syntax means that if more than one expression is specified, each must be surrounded by parentheses.

exp is a possibly nonlinear expression containing _b[coef] _b[eqno:coef] [eqno]coef [eqno]_b[coef]

eqno is ## name

coef identifies a coefficient in the model. coef is typically a variable name, a level indicator, an interaction indicator, or an interaction involving continuous variables. Level indicators identify one level of a factor variable and interaction indicators identify one combination of levels of an interaction; see fvvarlist. coef may contain time-series operators; see tsvarlist.

Distinguish between [], which are to be typed, and [], which indicate optional arguments.

Menu

Statistics > Postestimation

Description

testnl tests (linear or nonlinear) hypotheses about the estimated parameters from the most recently fit model.

testnl produces Wald-type tests of smooth nonlinear (or linear) hypotheses about the estimated parameters from the most recently fit model. The p-values are based on the delta method, an approximation appropriate in large samples.

testnl can be used with svy estimation results, see [SVY] svy postestimation.

The format (exp1=exp2=exp3... ) for a simultaneous-equality hypothesis is just a convenient shorthand for a list (exp1=exp2) (exp1=exp3), etc.

testnl may also be used to test linear hypotheses. test is faster if you want to test only linear hypotheses; see [R] test. testnl is the only option for testing linear and nonlinear hypotheses simultaneously.

Options

mtest[(opt)] specifies that tests be performed for each condition separately. opt specifies the method for adjusting p-values for multiple testing. Valid values for opt are

bonferroni Bonferroni's method holm Holm's method sidak Sidak's method noadjust no adjustment is to be made Specifying mtest without an argument is equivalent to mtest(noadjust).

iterate(#) specifies the maximum number of iterations used to find the optimal step size in the calculation of numerical derivatives of the test expressions. By default, the maximum number of iterations is 100, but convergence is usually achieved after only a few iterations. You should rarely have to use this option.

The following options are available with testnl but are not shown in the dialog box:

df(#) specifies that the F distribution with # denominator degrees of freedom be used for the reference distribution of the test statistic. With survey data, # is the design degrees of freedom unless nosvyadjust is specified.

nosvyadjust is for use with svy estimation commands when the df() option is also specified; see [SVY] svy estimation. It specifies that the Wald test be carried out without the default adjustment for the design degrees of freedom. That is, the test is carried out as W/k ~ F(k,d) rather than as (d-k+1)W/(kd) ~ F(k,d-k+1), where k = the dimension of the test and d = the design degrees of freedom specified in the df() option.

Remarks

In contrast to likelihood-ratio tests, different -- mathematically equivalent -- formulations of an hypothesis may lead to different results for a nonlinear Wald test (lack of "invariance"). For instance, the two hypotheses

H0: b1 = b2

H0: exp(b1) = exp(b2)

are mathematically equivalent expressions but do not yield the same test statistic and p-value. In extreme cases, under one formulation, one would reject H0, whereas under an equivalent formulation one would not reject H0.

Likelihood-ratio testing does satisfy representation invariance.

Examples

Setup . sysuse auto . generate weightsq = weight^2 . regress price mpg trunk length weight weightsq foreign

Test one nonlinear constraint . testnl _b[mpg] = 1/_b[weight]

Test multiple nonlinear constraints . testnl (_b[mpg] = 1/_b[weight]) (_b[trunk] = 1/_b[length])

Test multiple nonlinear constraints separately, and adjust p-values using Holm's method . testnl (_b[mpg] = 1/_b[weight]) (_b[trunk] = 1/_b[length]), mtest(holm)

Stored results

testnl stores the following in r():

Scalars r(df) degrees of freedom r(df_r) residual degrees of freedom r(chi2) chi-squared r(p) p-value for Wald test r(F) F statistic

Macros r(mtmethod) method specified in mtest()

Matrices r(G) derivatives of R(b) with respect to b; see Methods and formulas in [R] testnl r(R) R(b)-q; see Methods and formulas in [R] testnl r(mtest) multiple test results


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