PROC GENMOD LS-Means differences.. what are they saying of the mean dollars?

[mragaa]

Hi everyone,

Challenge:  I wanna get the differences in revenues between different management types, in different regions and time periods. 

Problem: These are the LS-Means tables and the code I used to get them. I'm interested in the estimate in Table 1 (red), but I'm not sure what it means in terms of dollar revenues (blue) in Table 2? I understand it's the difference in the estimate but, admittedly, I don't get what the estimate refers to, as I look to the mean in dollars.

SAS version: 9.4

Thanks a lot.

Table 1: Differences of Period*Management*Region Least Squares Means
Period	Management	Region	_Period	_Management	_Region	Estimate	Standard Error	z Value	Pr > |z|	Alpha	Lower	Upper
3	1	3	3	1	2	-0.6019	0.02224	-27.07	<.0001	0.05	-0.6455	-0.5583

Table 2: Period*Management*Region Least Squares Means
Period	Management	Region	Estimate	Standard Error	z Value	Pr > |z|	Alpha	Lower	Upper	Mean	Standard Error	Lower Mean	Upper Mean
3	1	3	5.7928	0.01699	340.89	<.0001	0.05	5.7595	5.8262	327.94	5.5729	317.2	339.05
3	1	2	6.3948	0.0144	444.09	<.0001	0.05	6.3665	6.423	598.7	8.6211	582.04	615.84

Code:

proc genmod data=test order=formatted;

class  Store Period Management Region / desc param=glm;

model Revenue = Management Period Region Management*Period*Region  /link=log dist=gamma;

   repeated subject=Store/type=ind;

lsmeans Management Region Period Management*Period*Region /ilink lines means diff cl;

slice Management*Period*Region /nof ilink sliceby=Management diff exp cl;

run;

[PaigeMiller · Accepted solution]

The values you see under "Estimate" in both tables are transformed to different units by the log transformation. To understand the values in real units, you have to reverse the transformation.

[mragaa]

Thank you, Paige. This is a helpful one step closer. I reversed the natural log and it works for the means but, unfortunately, not for the difference.

	Natural log (the estimates from the model)	Exp (reversing the natural log from the left column)	Means (How it should be, per the means column)
Region 2	6.394760638	598.7	598.7
Region 3	5.792830665	327.94	327.94
Difference	0.601929973	1.825639	270.76
	-0.60192997	0.547753

As you can see, the difference is not reverting back to how it should be. I tried both the negative and the absolute values and it still misses the mark. So I have two follow up questions if you don't mind:

- Should I be reversing the difference in a different way?

- Is there a way for SAS to just give me the numbers I'm looking for (in dollars here) instead of their natural logarithm?

Thank you.

[mragaa]

Follow-up: I got the first question. The difference here is the natural log of the percentage of (Region 3 mean) to (Region 2 mean).

(54.77% , -0.60193).

This leaves the second question open: Is there a more straightforward way? Am I doing something wrong?

Thank you.

[PaigeMiller]

I think your final answer is correct. Is there a different way? Not off the top of my head, because the log of a difference is not equal to the difference of the logs.

[mragaa]

Thank you, Paige. You've been most helpful as always.

To All: I'll leave my earlier wrong post up there so the evolution of thought is complete for others in the community. If it's preferable to just keep the right answer, please feel comfortable to let me know.