Re: st: odds ratios and confidence intervals after mlogit with a dummy X

[Maarten Buis <maartenlbuis@gmail.com>]

The fact that mathematically equivalent null hypotheses do not
necessarily lead to the same test outcome with non-linear Wald tests
is documented in -help testnl-. I would use -lincom- with the -rrr-
option. That will exactly reproduce the results as returned by
-mlogit-:

*------------------- begin example --------------------
sysuse auto, clear
recode rep78 1/2=3
replace weight = (weight -3000) / 2000
replace price = (price - 6000) / 1000

// regular interaction effect
mlogit rep78 c.price##i.foreign weight, rrr

// create the odds ratios of price for foreign cars
// using lincom
lincom _b[4:price] + _b[4:1.foreign#c.price], rrr

// check against -mlogit- without reference category
// the results are the same
mlogit rep78 c.price#ibn.foreign ibn.foreign weight, nocons rrr
*-------------------- end example ---------------------

Hope this helps,
Maarten

On Tue, Mar 5, 2013 at 7:07 PM, Jeremy Reynolds <jeremyr@uga.edu> wrote:
> Dear Statalist,
>
> I would like to calculate odds ratios and associated confidence
> intervals after a multinomial logit that involves an interaction
> between a dummy variable and a continuous variable along with other
> covariates.  The confidence intervals for the different levels of the
> continuous variable are important because the dummy variable has a
> negative sign and the interaction a positive sign.  I would like to
> determine when the dummy variable decreases and and when it increases
> the odds of one outcome in the mlogit.
>
> Drawing on posts to the statalist and Martin Buis' website
> (http://www.maartenbuis.nl/publications/interactions.html
> ), I have written code to calculate the odds ratios associated with
> the dummy variable for different levels of the continuous variable
> (please see below).
>
> However, there appear to be two potential problems with this approach.
>
> First, nlcom tests whether the odds ratios are different from zero. I
> have subtracted 1 from the odds ratio to get the equivalent of testing
> whether it is different from 1, but the help file for nlcom makes me
> wonder if this procedure is appropriate.
>
> From the help file for nlcom:
> "For instance, the two hypotheses
>         H0: coefficient = 0
>         H0: exp(coefficient) - 1 = 0
> are mathematically equivalent expressions but do not yield the same
> test statistic and p-value."
>
> Second, exchanges on the statalist have suggested that the confidence
> intervals calculated by nlcom may not be the what I want:
> http://www.stata.com/statalist/archive/2011-12/msg00389.html
>
> I would be grateful to hear recommendations regarding how to calculate
> the odds ratios I want.
>
> Is the approach in the code below okay?
>
> Should I use the margins command instead?
> When I have seen people use the margins command to get odds and then
> calculate odds ratios, they have been working with interactions
> between dummy variables and logistic regression.
> For example:  http://www.stata.com/statalist/archive/2011-05/msg00776.html
>
> I am not sure how to use margins with a dummy X continuous interaction
> and a mlogit model where I must specify which outcome I want.  The use
> of expression(exp(xb())) for getting the odds seems to preclude the
> use of the predict() option that is used to specify which outcome to
> use.
>
> Thanks,
>
> Jeremy
>
>
>
> ******************
> *mlogit with binary by continuous interaction
> *slightly modified from example posted at
> http://www.stata.com/statalist/archive/2010-10/msg00149.html
> *****************
> sysuse auto, clear
>
> // create an indicator variable that is
> // 1 when an observation has valid values
> // on mpg, price, and rep78, and 0 otherwise
> gen byte touse = !missing(mpg, price, rep78)
>
> // center mpg
> sum mpg if touse, meanonly
> gen c_mpg = mpg - r(mean)
>
> // center price and change unit to 1000s of $
> sum price if touse, meanonly
>
> *recode price so cheapest car =0
> gen c_price = (price - r(min))/1000  // I have changed this line to
> subtract the min rather than the mean
> sum c_price
>
> // see the example FAQ
> recode rep78 1/2 = 3
> gen byte baseline = 1
>
> // add value labels to rep78
> label define rep78 3 "Average" ///
>                    4 "Good"    ///
>                    5 "Excellent"
> label value rep78 rep78
>
> // the model
> mlogit rep78 foreign##c.c_price c_mpg baseline, rrr nocons  // the
> original post had an interaction between c_mpg and c_price
>
> *calculate odds ratio for foreign (outcome=Good) with 1,000-9,000
> increases in price
> sum c_price if e(sample)
> foreach x of numlist 1/9 {
>     di "Odds Ratio for foreign with a `x' thousand dollar increase in price."
>     nlcom exp(_b[Good:1.foreign])*exp(_b[Good:1.foreign#c.c_price])^`x' - 1
> }
>
>
> --
> ********************
> Dr. Jeremy Reynolds
> Associate Professor
> Undergraduate Coordinator
> Department of Sociology
> 117 Baldwin Hall
> University of Georgia
> Athens, GA 30602-1611
> Phone: (706) 583-8072
> Web: http://uga.edu/soc/people/faculty/reynolds_jeremy.php
> Fax: (706) 542-4320
> *
> *   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/



-- 
---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
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