Dear Statlist,

I am estimating whether elderly age in a healthier way because of the Long-term care system they are in. I do this by grouping European countries in different LTCsystem groups. I regress health (grip strength) on factors determining health and an interaction of age with the LTC system categorical variable to see whether the age health slopes statistically differ between the LTC system groups. I estimate this using random effects. However, I also included age square, which leaves me with two interactions.

xtreg maxgrip c.age i.LTCsystem c.age#i.LTCsystem c.age#c.age c.age#c.age#i.LTCsystem bmi if female==1, re vce(cluster mergeid_n)

How can I test whether the slope of the age health slopes significantly differ for the four clusters? (I know I can do testparm i.LTCsystem#c.age or test 2.LTCsystem#c.age=2.LTCsystem#c.age but then I can only conclude something about the first polynomial of age.)

Any help would be greatly appreciated.


Ouput in case you would need it:
VARIABLES Max. of grip strength measure
Age at interview (in years) 0.380*
(0.204)
LTCsystem = 2, Cluster 2 12.961
(10.910)
LTCsystem = 3, Cluster 3 14.001
(11.303)
LTCsystem = 4, Cluster 4 34.450**
(13.460)
1b.LTCsystem#co.age
2.LTCsystem#c.age -0.295
(0.288)
3.LTCsystem#c.age -0.386
(0.298)
4.LTCsystem#c.age -0.963***
(0.357)
c.age#c.age -0.005***
(0.001)
1b.LTCsystem#co.age#co.age
2.LTCsystem#c.age#c.age 0.002
(0.002)
3.LTCsystem#c.age#c.age 0.002
(0.002)
4.LTCsystem#c.age#c.age 0.007***
(0.002)
Body mass index 0.077***