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{* 25jun2009}{...}
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help for {hi:inteff3} {right: (Version 1.2.0) }
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{title:Compute partial effects in a probit or logit model with a triple dummy variable interaction term}

{p 8 20}{cmd:inteff3}
[if] [in], [{cmdab:average} {cmdab:at}(numlist) {cmdab:me}(newlist) {cmdab:se}(newlist) {cmdab:post} {break}
{cmdab:varx1}() {cmdab:varx2}() {cmdab:varx3}() {cmdab:varx1x2}() {cmdab:varx1x3}() {cmdab:varx2x3}() {cmdab:varx1x2x3}()  {break}
{cmdab:pex1}() {cmdab:pex2}() {cmdab:pex3}() {cmdab:pex1x2}() {cmdab:pex1x3}() {cmdab:pex2x3}() {cmdab:pex1x2x3}()  {break}
{cmdab:sx1}() {cmdab:sx2}() {cmdab:sx3}() {cmdab:sx1x2}() {cmdab:sx1x3}() {cmdab:sx2x3}() {cmdab:sx1x2x3}()]{p_end}

{p 8 16}{cmd:inteff3} is for use after a probit or logit model has been estimated. The model must include the three single dummies, 
all double interactions and the triple interaction term.{p_end}

{title:Description}

{p} Norton et al. (2004) have derived the formulae for partial effects of interaction terms of 
two variables in logit and probit models, implemented in the module {help inteff}.

{p}In the same logic, {cmd:inteff3} computes partial effects in a probit or logit model with a triple dummy variable interaction term. 
The default is to compute the partial effects at means.

{p} The model may be applied when the effect of a binary regressor on a binary dependent variable is allowed to vary over combinations of two sub-groups. 
For example, one may be interested in the way a university degree and the presence of children affect the gender difference in labour market participation. To this effect, one may run a probit model of labour market participation including
dummies for female, university degree and presence of children, as well as their pairwise and triple interaction terms.

{p} A difference-in-difference-in-differences estimator with a binary dependent variable (see for example Gruber and
Poterba 1994) may also seem to be a suitable application. However, Puhani (2008) argues that the treatment effect in 
non-linear difference-in-differences models is not given by the interaction effect à la Ai and Norton (2003). In fact, 
computing the interaction effect à la Ai and Norton (2003) would not ensure that the difference-in-differences treatment 
effect is bounded between 0 and 1.

{p} See Cornelissen and Sonderhof (2009) for the formulae of the partial effects of the interaction terms in the 
probit model with triple dummy variable interactions. {cmd:inteff3} uses the delta method to compute the standard errors
of the partial effects and partly relies on the built-in Stata functions {help nlcom} and {help predictnl} for this purpose.

{title:Options} 
{p2colset 0 23 23 0}

{p2col:{hi:varx1}() - {hi:varx1x2x3}()}can be used to specify the variable names of the the three single dummies (x1, x2, x3), all 
double interactions (x1*x2, x1*x3, x2*x3) and the triple interaction term (x1*x2*x3). By default, inteff3 
assumes (and checks) that they are given by the first seven regressors in the following order: x1 x2 x3 x1*x2 x1*x3 x2*x3 x1*x2*x3.{p_end}
  
{p2col:{hi:average}}rather than computing the partial effect at certain values (e.g. means), 
the effect is computed for each observation and then averaged over all observations. The default is to 
compute the partial effects at means.{p_end}

{p2col:{hi:at}(numlist)}specifies that partial effects are to be computed at the values passed in this option.
The first three values are those for the three dummy variables followed by the values for the control variables
(excluding the double and triple dummy interactions). The default is to compute the partial effects at means. {p_end}

{p2col:{hi:pex1}() - {hi:pex1x2x3}()}specifiy names of new variables, in which the respective partial effects are to be stored. These
 options {hi:pex1}() - {hi:pex1x2x3}() have to be combined with the option average. {p_end}

{p2col:{hi:sx1}() - {hi:sx1x2x3}()}specifiy names of new variables, in which the standard errors of the partial effects are to be stored. These
 options {hi:sx1}() - {hi:sx1x2x3}() have to be combined with the option average. {p_end}

{p2col:{hi:post}}When post is specified, {cmd:inteff3} will post the vector of partial effects and the diagonal elements of the variance-covariance matrix to e().
Important: {cmd:inteff3} only computes the variances of the partial effects needed for simple tests on the partial effects.
{cmd:inteff3} does not compute the the covariances. The covariances are posted in e(V) as {cmd:zero}, which are not 
the true covariances! {break}
The option {hi:post} overwrites the saved estimates of the preceding probit model, and inteff3 cannot be recalled 
unless another probit model is estimated.{p_end}


{title:Examples}

{p 4 8}{inp:. probit y x1 x2 x3 x1x2 x1x3 x2x3 x1x2x3 z1 z2 z3 z4}{p_end}
{p 4 8}{inp:. inteff3 }{p_end}

{p 4 8}{p_end}

{p 4 8}{inp:. probit y x1 x2 x3 x1x2 x1x3 x2x3 x1x2x3 z1 z2 z3 z4}{p_end}
{p 4 8}{inp:. inteff3, average pex1x2x3(pe) sx1x2x3(se) }{p_end}

{p 4 8}{p_end}

{p 4 8}{inp:. probit y x1 x2 x3 x1x2 x1x3 x2x3 x1x2x3 z1 z2 z3 z4}{p_end}
{p 4 8}{inp:. inteff3, at(0.5 0 1 1.2 -0.3 1 0.7 1)}{p_end}


{title:Authors}

        Thomas Cornelissen, CReAM, Department of Economics, University College London, UK.
        t.cornelissen@ucl.ac.uk

        Katja Sonderhof, Leibniz Universität Hannover, Germany
        sonderhof@aoek.uni-hannover.de


{title:References}

{p} Gruber, J. and J. Poterba (1994): Tax Incentives and the Decision to Purchase Health Insurance: 
Evidence from the Self-Employed, {it:The Quarterly Journal of Economics}, Vol. 109, No. 3, pp. 701-733.

{p} Norton, E. C., H. Wang and C. Ai (2004): Computing interaction effects and standard errors in logit and probit 
models, {it:The Stata Joumal}, 4(2), 154-167.

{p}Cornelissen and Sonderhof (2009): Partial effects in probit and logit models with a triple dummy variable interaction 
term,  
{browse "http://www.wiwi.uni-hannover.de/Forschung/Diskussionspapiere/dp-386.pdf":Leibniz Universität Hannover Discussion Paper No. 386 (revised version).}

{p}Puhani, P. (2008): The Treatment Effect, the Cross Difference, and the Interaction Term in Nonlinear “Difference-in-Differences” Models, IZA Discussion Paper No. 3478.

{title:Also see}

{p 0 9}On line: help for 
{help probit}, {help logit}, {help inteff} (if installed).