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From |
David Quinn <dxquinnx@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: marginal effects for simultaneous changes in interacted variables |

Date |
Wed, 31 Oct 2012 19:49:47 -0400 |

Thanks so much for the response, Jeff. Unfortunately, I am using Stata 11, so the -contrast- option is not available. It sure would be nice to have that. I sort of figured I would need to generate the predictive margins and then use -post- to calculate the discrete change, but I was wondering if there was an easier way to do this with -margins, dydx-. I understand that there is not. I have a quick follow-up question. Does -lincom- in Stata 11 always calculate the discrete change and associated reliability estimates (z-scores, p-values, and confidence intervals) the same way as -contrast- would in Stata 12? I notice that in the example that you use, the predictive margin of x1=0, x2=0 is statistically significant at the 95% level but x1=1, x2=1 is not, yet the discrete change between the two is statistically significant. In my data, I am encountering a similar case where one value is significant at the 95% level (p=.001) and the other is not (p=.125), and -lincom- is telling me that the .46 discrete change between the two values is only approaching significance (p=.08). This may be a function of my data, but I'm kind of surprised by the result because when I use King et al.'s Clarify program to calculate the same exact discrete change, it is also .46 but highly significant at the 95% level. On Wed, Oct 31, 2012 at 7:03 PM, Jeff Pitblado, StataCorp LP <jpitblado@stata.com> wrote: > David Quinn <dxquinnx@gmail.com> is using -margins- with -logit- results, > trying to get the change in the predictive margin when x1 and x2 are > both equal 0 to x1 and x2 both equal 1: > >> I am estimating a logit model as such: Y=X1 + X2 + X1*X2 + X3. >> >> X1 and X2 are binary predictors, and I have interacted them using >> factor notation. X3 is a >> control variable. >> >> I'd like to assess the discrete change/marginal effects in my >> dependent variable when X1 and X2 simultaneously move from 0 to 1, >> setting x3 asobserved. >> >> I used the following margins command to calculate this change: >> >> margins, dydx(X1) at(X2=(0 1)) >> >> But this is not giving me the change that I desire. It's giving me >> the following two changes: 1.) From X1=0, X2=0 to X1=1, X2=0; and 2.) >> >From X1=0, X2=1 to X1=1, X2=1. >> >> But what I want is the change from X1=0, X2=0 to X1=1, X2=1. >> >> When you use King et al's Clarify program, you can select specific >> values for which the change is to be calculated for multiple variables >> of interest simultaneously, but I cannot seem to get margins to do >> this. >> >> How do I use margins to calculate the change that I desire? > > I'll use the auto data with some generated variables, so I can show the steps > to get what David wants: > > . sysuse auto > . gen x1 = mpg > 20 > . gen x2 = head > 3 > . logit for x1##x2 turn > > In the above I generated binary predictors x1 and x2, used -foreign- for the > binary response, and -turn- as a control variable. > > Here are the results from logit: > > ***** BEGIN: > Logistic regression Number of obs = 74 > LR chi2(4) = 44.34 > Prob > chi2 = 0.0000 > Log likelihood = -22.86412 Pseudo R2 = 0.4923 > > ------------------------------------------------------------------------------ > foreign | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > 1.x1 | -1.807144 1.223086 -1.48 0.140 -4.204349 .5900617 > 1.x2 | -.9829927 1.491344 -0.66 0.510 -3.905974 1.939989 > | > x1#x2 | > 1 1 | -2.262084 2.344498 -0.96 0.335 -6.857215 2.333047 > | > turn | -.7399175 .2046417 -3.62 0.000 -1.141008 -.3388272 > _cons | 28.62676 8.020097 3.57 0.000 12.90766 44.34586 > ------------------------------------------------------------------------------ > ***** END: > > Now David wants to compare the predictive margin where x1 and x2 are both 0 to > the predictive margin when they are both 1. > > Here we use the interaction between x1 and x2 as the margining term to yield > the predictive margins that David wants: > > ***** BEGIN: > . margins x1#x2 > > Predictive margins Number of obs = 74 > Model VCE : OIM > > Expression : Pr(foreign), predict() > > ------------------------------------------------------------------------------ > | Delta-method > | Margin Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > x1#x2 | > 0 0 | .4344516 .0756514 5.74 0.000 .2861776 .5827255 > 0 1 | .3543279 .1092121 3.24 0.001 .140276 .5683798 > 1 0 | .2823868 .0419118 6.74 0.000 .2002411 .3645325 > 1 1 | .0519108 .0556121 0.93 0.351 -.0570869 .1609085 > ------------------------------------------------------------------------------ > ***** END: > > Now that we have (more than) the predictive margins of interest, we can use > contrast operators or the -contrast- option to get -margins- to compute the > discrete differences between them. > > The problem with this approach is that we only care about the '0 0' and '1 1' > margins, so instead we'll use two separate -at()- options. The first -at()- > option will identify the '0 0' predictive margin, then second will identify > the '1 1' predictive margin. > > ***** BEGIN: > . margins, at(x1=0 x2=0) at(x1=1 x2=1) > > Predictive margins Number of obs = 74 > Model VCE : OIM > > Expression : Pr(foreign), predict() > > 1._at : x1 = 0 > x2 = 0 > > 2._at : x1 = 1 > x2 = 1 > > ------------------------------------------------------------------------------ > | Delta-method > | Margin Std. Err. z P>|z| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > _at | > 1 | .4344516 .0756514 5.74 0.000 .2861776 .5827255 > 2 | .0519108 .0556121 0.93 0.351 -.0570869 .1609085 > ------------------------------------------------------------------------------ > ***** END: > > If David is using Stata 11, he'll have to use the -post- option get get > -margins- to post its results to -e()- and then use -lincom- to compute the > discrete change. > > In Stata 12, David can use the -contrast()- option and specify how he wants > margins to contrast the levels of -_at-. Here we use the reference category > operator, which will always use the first level as the base in the comparison: > > ***** BEGIN: > . margins, at(x1=0 x2=0) at(x1=1 x2=1) contrast(at(r)) > > Contrasts of predictive margins > Model VCE : OIM > > Expression : Pr(foreign), predict() > > 1._at : x1 = 0 > x2 = 0 > > 2._at : x1 = 1 > x2 = 1 > > ------------------------------------------------ > | df chi2 P>chi2 > -------------+---------------------------------- > _at | 1 16.49 0.0000 > ------------------------------------------------ > > -------------------------------------------------------------- > | Delta-method > | Contrast Std. Err. [95% Conf. Interval] > -------------+------------------------------------------------ > _at | > (2 vs 1) | -.3825407 .0942169 -.5672024 -.1978791 > -------------------------------------------------------------- > ***** END: > > --Jeff > jpitblado@stata.com > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/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/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: marginal effects for simultaneous changes in interacted variables***From:*jpitblado@stata.com (Jeff Pitblado, StataCorp LP)

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