# Re: st: Re: interactions, slopes, and standard errors

 From [email protected] To [email protected] Subject Re: st: Re: interactions, slopes, and standard errors Date Tue, 30 Mar 2004 23:06:53 -0800 (PST)

```Dear stata users, i need some help with estimating marginal effect and the std error with more than one interaction term.

the regression, y= cons + a*x + b*x*z1 +c*x*z2 + d*x*z3 +e

so, the marginal effect of x on y : dy/dx = a+ b*z1+ c*z2+ d*z3

Is it possible to evaluate the marginal effect at different percentile of z's , say 10th of z1, 50th of z2 and 90th of z3? how should i estimate the std error? does it work with xtivreg ?

Thanks a lot.

kazi

On Tue, 30 Mar 2004, Scott Merryman wrote:

> Date: Tue, 30 Mar 2004 20:40:08 -0600
> From: Scott Merryman <[email protected]>
> To: [email protected]
> Subject: st: Re: interactions, slopes, and standard errors
>
> Chip,
>
> Below is an updated version. It can use values that are returned
> from -summarize, detail- or  specific values. It does not perform all the error
> trapping it should, but it should still be of use.
>
> Examples:
>
> . sysuse auto
> (1978 Automobile Data)
>
> . gen mpgXprice = mpg*price
>
> . qui reg weight price mpg mpgXprice
>
> . ****Evaluated at the mean
>
> . marginalx, x(price) y(mpg) xy(mpgXprice)
>
> Marginal effect of price interacted with mpg
> Evaluated at the mean (21.297297) of mpg
> --------------------------------------------------------------------------------
> ----
>       variable |   mfx       Std. Err.     z       P>|z|     [ 95% Conf.
> Interval ]
> ---------------+----------------------------------------------------------------
> ----
>         price  | .0475011     .026751     1.78     0.076     -.0049308
> .099933
> --------------------------------------------------------------------------------
> ----
>
> . *****Evaluated at the 75th percentile
>
> . marginalx, x(price) y(mpg) xy(mpgXprice) stat(p75)
>
> Marginal effect of price interacted with mpg
> Evaluated at the p75 (25) of mpg
> --------------------------------------------------------------------------------
> ----
>       variable |   mfx       Std. Err.     z       P>|z|     [ 95% Conf.
> Interval ]
> ---------------+----------------------------------------------------------------
> ----
>         price  | .0417085     .038794     1.08     0.282     -.0343262
> .1177433
> --------------------------------------------------------------------------------
> ----
>
> . ****Evaluated at a value of 30
>
> . marginalx, x(price) y(mpg) xy(mpgXprice) value(30)
>
> Marginal effect of price interacted with mpg
> Evaluated at the value (30) of mpg
> --------------------------------------------------------------------------------
> ----
>       variable |   mfx       Std. Err.     z       P>|z|     [ 95% Conf.
> Interval ]
> ---------------+----------------------------------------------------------------
> ----
>         price  | .0338864     .057716     0.59     0.557     -.0792354
> .1470082
> --------------------------------------------------------------------------------
> ----
>
> Hope this helps,
>
> Scott
>
> --------------------------------------------
>
> *! version 1.1,  Scott Merryman 3/30/2004
> * statistic can any value returned from -summarize-
> * the value option needs to be number, this error should be trapped
> * does not check if variables x and y were in model
>
> program marginalx, rclass
> version 8.2
> syntax , x(varname) y(varname) xy(varname) [stat(str) value(str) level(integer
> 95)]
>
> if e(cmd)~="regress" & e(cmd)~="areg" & e(cmd)~="xtreg" & e(cmd)~="xtgls"{
>         display in red "marginalx only works with regress, xtreg, xtgls or areg"
>         exit 301
> }
>
> if "`stat'" ~= "" & `"`value'"' != "" {
>  disp in red "Select either a value or statistic for the interaction term"
>  exit 301
> }
>
> if "`value'" == "" {
>  if "`stat'" == "" {
>   local stat mean
>  }
>
> qui sum `y' if e(sample), detail
> local stat2 r(`stat')
> local eval `stat'
> }
>
> else {
>  local stat2 = `value'
>  local eval value
> }
>
> local marginal = _b[`x'] + _b[`xy']*`stat2'
>
> matrix A = e(V)
> matrix B1 = A["`x'" , "`x'"]
> local var_b1 = B1[1,1]
>
> matrix B2 = A["`xy'" , "`xy'"]
> local var_b2 = B2[1,1]
>
> matrix B3 = A["`x'" , "`xy'"]
> local covar_b1b2 = B3[1,1]
>
> local variance = `var_b1' + (`stat2'^2)*`var_b2' + 2*`stat2'*`covar_b1b2'
>
> if (`level'<10 | `level'>99) {
>         local level 95
> }
>
> tempname Z
>
> local se = sqrt(`variance')
> scalar `Z' = invnorm(1-(1-`level'/100)/2)
> local ll = `marginal' - `Z'*`se'
> local ul = `marginal' + `Z'*`se'
> local z =  `marginal'/`se'
> local pvalue = 2*normprob(-abs(`z'))
>
> disp ""
> disp in smcl in gr "Marginal effect of `x' interacted with `y' "
> disp in smcl in gr "Evaluated at the `eval' (" in ye `stat2' in gr ") of `y'"
>
> disp in smcl in gr "{hline 15}{c TT}{hline 68}"
> disp in smcl in gr   "{ralign 14:variable}"  _col(15) " {c |} " ///
>         _col(20) "mfx"  ///
>         _col(30)  `"Std. Err."' ///
>         _col(44) "z" ///
>         _col(52) "P>|z|" ///
>         _col(62) `"[ `level'% Conf. Interval ]"' ///
>         _n  "{hline 15}{c +}{hline 68}"
>
> di in smcl in  gr "{ralign 14: `x' }" _col(15) " {c |} " ///
>  _col(18) in ye %-9.0g `marginal' ///
>  _col(30) in ye %8.0g `se' ///
>  _col(42) in ye %5.2f `z' ///
>  _col(52) in ye %5.3f  `pvalue' ///
>  _col(62) in ye %9.0g `ll' "   " in ye %9.0g `ul' ///
>  _n "{hline 15}{c BT}{hline 68}"
>
>
> return scalar mfx = `marginal'
> return scalar se_mfx = `se'
> return scalar pvalue = `pvalue'
>
> end
>
> ----- Original Message -----
> From: "Chip Hunter" <[email protected]>
> To: <[email protected]>
> Sent: Friday, March 26, 2004 12:13 PM
> Subject: st: interactions, slopes, and standard errors
>
>
> > Has anyone written a general program to calculate and display the estimated
> > slope and associated error of Y on x1 at various values of x2, where Y = b0
> > + b1x1 + b2x2 + b3x1x2
> >
> > Last fall Scott Merryman posted a nice program (which I copy in, below)
> > which takes care of this at the mean of x2. Thanks, Scott!, We could also
> > be interested in doing it for other values.
> >
> > Chip Hunter
> >
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

=========================================
University of Washington
Department of Economics
302 Savery Hall
Box 353330
Seattle, WA 98195-3330
USA

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```