Average age of household adults and children between group X and Y.

[Miracle]

Hi there.

Can I please ask your advise on how can I find out if households in group X are made up of older/younger adults and children than households in group Y e.g. are adults in X an average of 50yrs old, whilst Y families are 40yrs old?

I would do an ANOVA between X and Y but I am stuck on how I should aggregate my data at the household level. Which approach is appropriate? Or are they both incorrect?

Your insight is very much appreciated.

					Approach A	Approach B
Household	MemberID	Membership	Age	Group	Average Household Adult Age	Average Household Children Age	Total adult's age	Total children's age
1	1	Adult	56	X	42.8	10	214	10
1	2	Adult	21	X
1	3	Adult	70	X
1	4	Adult	23	X
1	5	Child	10	X
1	6	Adult	44	X
.	.	.	.	.
.	.	.	.	.
.	.	.	.	.
256	1	Adult	88	X	88	11	88	22
256	2	Child	7	X
256	3	Child	15	X
100	1	Adult	53	Y	37	0	112	0
100	2	Adult	34	Y
100	3	Adult	25	Y
.	.	.	.	.
.	.	.	.	.
.	.	.	.	.
300	1	Adult	34	Y	32	4	64	4
300	2	Adult	30	Y
300	3	Child	4	Y
Approach A:
The total number of household in group X is 256.
Hence, the average for household in group X is thus
Adult: (42.8+…+88)/256
Children: (10+…+11)/256
Approach B:
Hence, the average for household in group X is thus
Adult: (214+…+88)/256
Children: (10+…+22)/256

[Kurt_Bremser]

proc sql;
create table want as select group, mean(age) from have group by group;
quit;

[Reeza]

Is you metric of interest average adults household age? Or average age of adults in all households? 

Thats the difference in your metrics. 

One is correct for your purposes - but it depends on your purpose. 

Also, maybe you should use a different type,of analysis that can handle the variable number of adults per household. 

[Miracle]

Sorry @Reeza. I am not too sure. 

However, my interest is to find out whether

1) households in group X are made up of younger or older adults than households in group Y.

2) households in group X are made up of younger or older children than households in group Y.

I need to produce an average and std error for both group X and Y and p-value for test of difference for (1) and (2) if that sounds correct? 

Also is model-based analysis using the individual-level data more appropriate?

- proc mixed/genmod with random effect or repeated subject statement being household and covariate being the interaction term of membership and group in the model?

- proc surveyreg with cluster being household, domain being the membership and group as the covariate?

Thank you.

[Ksharp]

Since it is Lift Time(age) data ,which does not conform to Normal distribution,

and you can not apply it into ANOVA. So I use Gamma distribution + LOG link function,

since age is not censored . 

Check the example of GENMOD:

Example 44.3: Gamma Distribution Applied to Life Data

data have;
call streaminit(12345678);
 do household=1 to 200;
  do id=1 to 200;
   age=ceil(80*rand('uniform'));
   member=ifc(age lt 18,'Child','Adult');
   group=ifc(rand('bern',0.5)=0,'X','Y');
   output;
  end;
 end;
run;
  
  
proc genmod data=have;
class member group;
model age=member group household member*group
          /dist=gamma link=log type3 ;
lsmeans member*group/ ilink exp diff cl;
effectplot interaction(x=group sliceby=member);
run;

OUTPUT:

Differences of member*group Least Squares Means
member	group	_member	_group	Estimate	Standard Error	z Value	Pr > |z|	Alpha	Lower	Upper	Exponentiated	Exponentiated Lower	Exponentiated Upper
Adult	X	Adult	Y	0.003689	0.005204	0.71	0.4784	0.05	-0.00651	0.01389	1.0037	0.9935	1.0140
Adult	X	Child	X	1.6941	0.008011	211.47	<.0001	0.05	1.6784	1.7098	5.4419	5.3571	5.5280
Adult	X	Child	Y	1.6987	0.008052	210.97	<.0001	0.05	1.6830	1.7145	5.4670	5.3814	5.5540
Adult	Y	Child	X	1.6904	0.008010	211.05	<.0001	0.05	1.6747	1.7061	5.4218	5.3374	5.5076
Adult	Y	Child	Y	1.6950	0.008050	210.56	<.0001	0.05	1.6793	1.7108	5.4469	5.3616	5.5335
Child	X	Child	Y	0.004613	0.01009	0.46	0.6477	0.05	-0.01517	0.02440	1.0046	0.9849	1.0247

[Miracle]

Hi @Ksharp.

Thank you for yor reply.

I am not familiar with modelling by gamma with log-link.

However, I would have thought stating household in the repeated subject statement instead to account for the clustering.

And are the p-value test for difference also correct on the original scale of the response variable? Since as far as I understand it is testing the response variable on the log scale. 

Thank you again.

[Ksharp]

If it was repeated measure ,then you should use NLMIXED , I will leave it to @Steave .

" are the p-value test for difference also correct on the original scale of the response variable?"

Yes. I used ilink option, if you want see real mean value ,add option mean in it .

lsmeans member*group/ ilink exp diff cl mean ;