Hypothesis testing - combined coefficients

[Rochelle Zhang]

Dear statalisters,

I have the following regression model with two dummy variables and their interactions.
Dummy 1: female
Dummy 2: overweight

Y = female_dum + overweight_dum+ female_dum* overweight_dum

I will label regression coefficients for the above three regressors as alpha, beta, and gamma. What command should I use to check if the (alpha + gamma) is significantly different from zero?

Thanks in advance,
Rochelle

[Joseph Coveney]

You can use lincom to find the linear combination of the main effects for sex and the sex × overweight interaction term. See below; start at the "Begin here" comment.

.ÿ
.ÿversionÿ14.1

.ÿ
.ÿclearÿ*

.ÿsetÿmoreÿoff

.ÿsetÿseedÿ`=date("2016-01-20",ÿ"YMD")'

.ÿquietlyÿsetÿobsÿ24

.ÿ
.ÿgenerateÿdoubleÿyÿ=ÿrnormal()

.ÿgenerateÿbyteÿfemaleÿ=ÿmod(_n,ÿ2)

.ÿgenerateÿbyteÿoverweightÿ=ÿ_nÿ>ÿ_Nÿ/ÿ2

.ÿ
.ÿregressÿyÿi.female##i.overweight

ÿÿÿÿÿÿSourceÿ|ÿÿÿÿÿÿÿSSÿÿÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿMSÿÿÿÿÿÿNumberÿofÿobsÿÿÿ=ÿÿÿÿÿÿÿÿ24
-------------+----------------------------------ÿÿÿF(3,ÿ20)ÿÿÿÿÿÿÿÿ=ÿÿÿÿÿÿ1.05
ÿÿÿÿÿÿÿModelÿ|ÿÿ1.54846392ÿÿÿÿÿÿÿÿÿ3ÿÿ.516154639ÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿ=ÿÿÿÿ0.3921
ÿÿÿÿResidualÿ|ÿÿ9.82861008ÿÿÿÿÿÿÿÿ20ÿÿ.491430504ÿÿÿR-squaredÿÿÿÿÿÿÿ=ÿÿÿÿ0.1361
-------------+----------------------------------ÿÿÿAdjÿR-squaredÿÿÿ=ÿÿÿÿ0.0065
ÿÿÿÿÿÿÿTotalÿ|ÿÿÿ11.377074ÿÿÿÿÿÿÿÿ23ÿÿ.494655391ÿÿÿRootÿMSEÿÿÿÿÿÿÿÿ=ÿÿÿÿ.70102

-----------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿyÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿ1.femaleÿ|ÿÿÿ.4878984ÿÿÿ.4047347ÿÿÿÿÿ1.21ÿÿÿ0.242ÿÿÿÿ-.3563633ÿÿÿÿÿ1.33216
ÿÿÿÿÿ1.overweightÿ|ÿÿÿ.7004801ÿÿÿ.4047347ÿÿÿÿÿ1.73ÿÿÿ0.099ÿÿÿÿ-.1437817ÿÿÿÿ1.544742
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
female#overweightÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿ1ÿ1ÿÿ|ÿÿ-.8042479ÿÿÿ.5723813ÿÿÿÿ-1.41ÿÿÿ0.175ÿÿÿÿ-1.998214ÿÿÿÿ.3897185
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.4269302ÿÿÿ.2861906ÿÿÿÿ-1.49ÿÿÿ0.151ÿÿÿÿ-1.023913ÿÿÿÿ.1700531
-----------------------------------------------------------------------------------

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿlincomÿ1.femaleÿ+ÿ1.female#1.overweight

ÿ(ÿ1)ÿÿ1.femaleÿ+ÿ1.female#1.overweightÿ=ÿ0

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿyÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿ(1)ÿ|ÿÿ-.3163495ÿÿÿ.4047347ÿÿÿÿ-0.78ÿÿÿ0.444ÿÿÿÿ-1.160611ÿÿÿÿ.5279123
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Clyde Schechter]

A likely reason you are interested in this particular sum of coefficients is that it represents the marginal effect of female conditional on overweight. If so, another way to get this is

margins, dydx(female) at (overweight = 1)

The -lincom- approach is more direct, but the -margins- approach is more directly related to how you are thinking about this sum and is easy to generalize to other similar situations.

[Rochelle Zhang]

@Joseph, Thank you for your detailed example !!!! this is the first time I saw the use of lincom. Your solution works great !

@ Clyde: Thank you for helping out again !!! I read up on margins command. Your solution is what I am looking for.


Sincerely,
Rochelle

[Rochelle Zhang]

@Joseph, sorry to trouble you again:

regress y i.female##i.overweight

I got the same output as yours

then,

lincom l.female+l.female#l.overweight

i have an error

regressor � not found

[Joseph Coveney]

Change

lincom l.female+l.female#l.overweight

to

lincom 1.female+1.female#l.overweight

That is, use ones and not ells.

[Clyde Schechter]

And you also need a one, not an ell, for the interaction term.

[Rochelle Zhang]

Thank you Joseph and Clyde for pointing out my error !

I very much appreciated it.

Rochelle