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# Re: st: margins dydx for logit model with interaction terms

 From Richard Williams To statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu Subject Re: st: margins dydx for logit model with interaction terms Date Fri, 10 Aug 2012 13:48:41 -0500

```At 09:36 AM 8/10/2012, David Quinn wrote:
```
```Thanks for that article, Richard.  Very helpful.  I now understand how
much of an improvement the factor notation is.

Quick follow-up question, related to the topic:

Is there any way that you can use the -margins- command to instruct
Stata to calculate the discrete change between two specific values of
the predictor of interest?  In other words, if I had a three-category
ordinal predictor variable, and I wanted to calculate the discrete
change in probability between the lowest (1) and highest (3) value of
this variable (rather than a one-unit change from the baseline), can I
use the -margins, dydx()- command to set the two values between which
I want to calculate the discrete change?
```
```
```
Are you treating the ordinal variable as continuous or discrete? If discrete, i.e. if you are saying something like i.ordvar in the logit command, you will get 2 marginal effects, one of which will be the difference between 2 and 1, the other of which will be the difference between 3 and 1.
```

```
```I guess I could just use -margins- to find the predicted probabilities
at each of the two above values, and then use -lincom- to assess the
size, direction, and statistical significance of the difference in
probability between those two values.  But I'm wondering if -margins,
dydx()- can do this all by itself.

On Thu, Aug 9, 2012 at 5:50 PM, Richard Williams
<richardwilliams.ndu@gmail.com> wrote:
> At 03:32 PM 8/9/2012, David Quinn wrote:
>>
>> Thanks, Richard.  I did not use factor variable notation.  Hence,
>> that's why I also set the interactions at specific values in the
>> margins command.  Is there a reason to use the factor notation
>
>
> Yes. You want to get the correct results. ;-) See
>
> http://www.nd.edu/~rwilliam/stats/Margins01.pdf
>
> There is also an article in the current Stata Journal that expands on the
> above. You can probably do it without factor variables, but the odds are
> much greater you will make a mistake.
>
>
>
>> I think that Stata is interpreting the "atmeans" part of the margins
>> command as setting all variables at their means, including the
>> variable of interest (the one placed in parentheses after dydx).
>> Perhaps what I need to do is remove the "atmeans" part, and instead
>> include the control variable (X4) in the -at- specification and set it
>> at its mean value.
>>
>> --Dave
>>
>> On Thu, Aug 9, 2012 at 4:20 PM, Richard Williams
>> <richardwilliams.ndu@gmail.com> wrote:
>> > At 11:30 AM 8/9/2012, David Quinn wrote:
>> >>
>> >> Hello,
>> >>
>> >> I am estimating a logit model as such: Y=X1 + X2 + X3 + X4 + X1*X3 +
>> >> X2*X3.
>> >
>> >
>> > What was the actual logit command? Did you use factor variable notation?
>> > If
>> > not -margins- will assume x1 and x2 are continuous rather than
>> > dichotomous.
>> > Assuming you want to treat x3 as continuous, The command should be
>> > something
>> > like
>> >
>> > logit y i.x1 i.x2 x3 x4 i.x1#c.x3 i.x2#c.x3
>> >
>> >
>> >
>> >> X1 and X2 are binary predictors.  X3 is an ordinal predictor.  X4 is a
>> >> control variable.  X1*X3 and X2*X3 are the interaction of X1 and X2,
>> >> respectively, with X3.
>> >>
>> >> I'd like to assess the discrete change in my dependent variable for X1
>> >> at different levels of X3, given that I expect there to be interaction
>> >> effects of X1 and X3.   I also need to set X2 and X2*X3 at zero while
>> >> doing this in order to calculate the proper discrete change of
>> >> interest.  As for the control variable X4, I'd like to just keep it at
>> >> its mean value.
>> >>
>> >> I used the following margins command to calculate the discrete change
>> >> in
>> >> X1:
>> >>
>> >> margins, dydx(X1) atmeans at(X3=(1 2 3) X1*X3=(1 2 3) X2=0 X2*X3=0)
>> >
>> >
>> > if you have used factor variable notation, I think all you need is
>> >
>> > margins, dydx(x1) atmeans at(x3=1 2 3) x2 = 0)
>> >
>> > I could be wrong so make sure it looks right.
>> >
>> >
>> >
>> >> "Atmeans" places X4 at its mean, while the stuff after "at" specifies
>> >> the specific values at which to hold the other variables while
>> >> calculating the change.
>> >>
>> >> But in the legend that accompanies the results, it keeps saying that
>> >> X1 is being held at its mean value when the discrete change
>> >> calculations are being made.  Why does margins set the variable of
>> >> interest--located after the dydx command--to its mean value when
>> >> calculating the discrete change, when clearly one would want the dydx
>> >> calculations to be made at specific values of the variable of
>> >> interest?  I just assumed that placing the variable of interest after
>> >> dydx would tell Stata to calculate the change in Y as that variable
>> >> moves from zero to one, holding all other variables at the values
>> >> specified after "at."
>> >>
>> >> Am I doing something incorrectly?
>> >>
>> >> Perhaps I should just use King et al.'s CLARIFY package to calculate
>> >> the predicted probabilities, or perhaps even follow Buis' (2010)
>> >> advice and calculate the odds.  From what I gather, those two are a
>> >> bit more straightforward then using the margins command.
>> >>
>> >> Thanks in advance,
>> >> --Dave
>> >> *
>> >> *   For searches and help try:
>> >> *   http://www.stata.com/help.cgi?search
>> >> *   http://www.stata.com/support/statalist/faq
>> >> *   http://www.ats.ucla.edu/stat/stata/
>> >
>> >
>> > -------------------------------------------
>> > Richard Williams, Notre Dame Dept of Sociology
>> > OFFICE: (574)631-6668, (574)631-6463
>> > HOME:   (574)289-5227
>> > EMAIL:  Richard.A.Williams.5@ND.Edu
>> > WWW:    http://www.nd.edu/~rwilliam
>> >
>> >
>> > *
>> > *   For searches and help try:
>> > *   http://www.stata.com/help.cgi?search
>> > *   http://www.stata.com/support/statalist/faq
>> > *   http://www.ats.ucla.edu/stat/stata/
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW:    http://www.nd.edu/~rwilliam
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```
```
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```