How to compare two coefficients in two forthlogit regressions?

[Tong Wu]

Hello,

As my dependent variable is a rare event, I am running forthlogit regressions. In my sample, I have three groups, g1, g2, g3, and I classify g1 and g2 as GROUP A and classify g2 and g3 as GROUP B. My regressions are as follows:
firthlogit y x if GROUP A==1;
firthlogit y x if GROUP B==1.
I need to compare the coefficients on x in the two regressions. Suest doesn't work. Also I cannot use the full interaction like firthlogit y x GROUPB xGROUPB, because there is overlap between GROUP A and GROUP B. Any suggestion on how to compare the two coefficients on x in the two firthlogit regressions would be great helpful to me.

Many Thanks in Advance!

[Joseph Coveney]

I can show you the mechanics of the test below (begin at the "Begin here" comment), but you've got a conceptual issue that you'll need to work out on your own.

.ÿ
.ÿversionÿ15.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1493411")'

.ÿquietlyÿsetÿobsÿ270

.ÿ
.ÿgenerateÿbyteÿyÿ=ÿruniform()ÿ>ÿ0.5

.ÿgenerateÿbyteÿgÿ=ÿmod(_n,ÿ3)ÿ+ÿ1

.ÿgenerateÿdoubleÿxÿ=ÿruniform()ÿ-ÿ0.5

.ÿ
.ÿgenerateÿbyteÿGROUP_Aÿ=ÿinlist(g,ÿ1,ÿ2)

.ÿgenerateÿbyteÿGROUP_Bÿ=ÿinlist(g,ÿ2,ÿ3)

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿ//ÿIMPORTANT!ÿBeÿespeciallyÿsureÿtoÿdoÿtheÿnextÿtwoÿlinesÿofÿcode!
.ÿdropÿGROUP_A

.ÿdropÿGROUP_B

.ÿ
.ÿ//ÿNow,ÿtoÿtestÿwhetherÿx(gÿ=ÿ1ÿ|ÿ2)ÿisÿdifferentÿfromÿx(gÿ=ÿ2ÿ|ÿ3)
.ÿlogitÿyÿi.g##c.x,ÿnolog

LogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ270
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿLRÿchi2(5)ÿÿÿÿÿÿÿÿ=ÿÿÿÿÿÿÿ3.45
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.6316
Logÿlikelihoodÿ=ÿ-184.35869ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿPseudoÿR2ÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0093

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿyÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿgÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿ-.0478481ÿÿÿ.3018073ÿÿÿÿ-0.16ÿÿÿ0.874ÿÿÿÿ-.6393795ÿÿÿÿ.5436834
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿ-.2285962ÿÿÿÿ.302644ÿÿÿÿ-0.76ÿÿÿ0.450ÿÿÿÿ-.8217676ÿÿÿÿ.3645752
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿxÿ|ÿÿÿ1.196473ÿÿÿ.7228338ÿÿÿÿÿ1.66ÿÿÿ0.098ÿÿÿÿ-.2202549ÿÿÿÿ2.613202
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿg#c.xÿ|
ÿÿÿÿÿÿÿÿÿÿ2ÿÿ|ÿÿ-1.209489ÿÿÿ1.032927ÿÿÿÿ-1.17ÿÿÿ0.242ÿÿÿÿ-3.233988ÿÿÿÿ.8150105
ÿÿÿÿÿÿÿÿÿÿ3ÿÿ|ÿÿ-1.178161ÿÿÿ1.031192ÿÿÿÿ-1.14ÿÿÿ0.253ÿÿÿÿÿ-3.19926ÿÿÿÿ.8429382
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0852937ÿÿÿ.2143778ÿÿÿÿ-0.40ÿÿÿ0.691ÿÿÿÿ-.5054664ÿÿÿÿÿ.334879
------------------------------------------------------------------------------

.ÿtestÿ3.g#x

ÿ(ÿ1)ÿÿ[y]3.g#c.xÿ=ÿ0

ÿÿÿÿÿÿÿÿÿÿÿchi2(ÿÿ1)ÿ=ÿÿÿÿ1.31
ÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿÿÿÿ0.2532

.ÿ
.ÿ//ÿor
.ÿquietlyÿmarginsÿg,ÿdydx(x)ÿpredict(xb)ÿpost

.ÿlocalÿGROUP_Aÿ_b[1.g]ÿ+ÿ_b[2.g]

.ÿlocalÿGROUP_Bÿ_b[2.g]ÿ+ÿ_b[3.g]

.ÿtestÿ`GROUP_A'ÿ=ÿ`GROUP_B'

ÿ(ÿ1)ÿÿ[x]1bn.gÿ-ÿ[x]3.gÿ=ÿ0

ÿÿÿÿÿÿÿÿÿÿÿchi2(ÿÿ1)ÿ=ÿÿÿÿ1.31
ÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿÿÿÿ0.2532

.ÿ
.ÿ//ÿToÿdoÿtheÿsameÿwithÿtheÿ(user-written—seeÿFAQ)ÿFirth-of-Forthÿlogitÿcommand:
.ÿquietlyÿfirthlogitÿyÿi.g##c.x,ÿnolog

.ÿestimatesÿstoreÿFull

.ÿ
.ÿconstraintÿdefineÿ1ÿ_b[3.g#x]ÿ=ÿ0

.ÿquietlyÿfirthlogitÿyÿi.g##c.x,ÿconstraints(1)ÿnolog

.ÿlrtestÿFull

Likelihood-ratioÿtestÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿLRÿchi2(1)ÿÿ=ÿÿÿÿÿÿ1.28
(Assumption:ÿ.ÿnestedÿinÿFull)ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿÿÿÿ0.2586

.ÿ
.ÿexit

endÿofÿdo-file


.

[Tong Wu]

Hi Joseph Coveney,

Many Thanks for your suggestions! I got your point, but I forgot to clarify that the variable of interest x in my regression is g, that means my models are as follows:

firthlogit y g x_control if g==1|2;
firthlogit y g x_control if g==2|3,

I need to compare the coefficients on g in the two regressions.

Sorry again.

[Joseph Coveney]

Is the variable g ordered categorical?

[Rich Goldstein]

re: #3 - there is a typo in your "if" clauses: #|# will not do what you expect; Joseph showed a legitimate way to get what you want in #2; otherwise, you can use

if g==1 | g==2

[Tong Wu]

Hi Joseph, in my sample I have three types of contract designs (g1, g2, and g3). The variable g is categorical but not ordinal. Thank you!

[Tong Wu]

Thank you Rich for pointing out the typo!