PROC MIXED: Coefficients vs LS Means

[mragaa]

Hello everyone,

 I'm modeling revenues of different stores with/without marketing in a linear mixed model. The stores vary in size and location. The data is for 5 years in a strongly balanced panel structure. Could you please help me interpret these results? 

In the Solution for fixed effects, I get:

Effect	Geo	Marketing	Estimate	Standard Error	DF	t Value	Pr > |t|
Marketing		0	2510887	117028	4354	21.46	<.0001
Marketing		1	2739612	106464	4354	25.73	<.0001

In the LS-Means table I get:

Effect	Geo	Marketing	Estimate	Standard Error	DF	t Value	Pr > |t|
Marketing		0	1083537	24129	4354	44.91	<.0001
Marketing		1	1252747	21511	4354	58.24	<.0001

So, in the former, there's a 9% increase in revenues with marketing, while in the latter it's a 15 % increase. 

To add to my confusion, when I plot the simple arithmetic mean for every year, the difference between the marketing and no-marketing groups is way higher than the 9% or 15% figures.

My question is:

1- Why are the coefficients and the ls-means different?

2- Why are both of them very different than the impression from graphing the annual simple arithmetic means?

3- Finally, Which of these results I should include in my conclusion?

Thank you in advance.

[sld]

You haven't provided enough information. Refer to 

https://communities.sas.com/t5/Getting-Started/How-to-get-fast-helpful-answers/ta-p/226133/jump-to/f...

At a minimum, please show your MIXED code and an example of your data set.

[PaigeMiller]

And we also need to see all of the parameter estimates from MIXED (including the intercept).

[mragaa]

Greetings,

 I'm writing to thank you all for paying attention to my inquiry and to apologize for I couldn't share the data as requested for its confidentiality. It took a while to get back to you because I have been unsuccessfully trying to take the permission for sharing a de-identified sample. 

Thank you for your understanding.

Respectfully.

[Rick_SAS]

No one asked to see your real data. The request was to see your PROC MIXED statement and, to help understand the code, an EXAMPLE of the structure of your data. Feel free to make up the data so that no sensitive information is revealed. For example, the revenue for the stores can be 1, 2, 3, ... Often we can infer the structure of the data, so the most important information is the PROC MIXED code.

Basically, the answer to your question is that the statistics mean different things. The parameter estimates are the coefficients of the fixed effects. LSMEANS are more complicated, but you can Google the SAS documentation or conference papers to find many examples that interpret LSMEANS. Two papers I like are 

Dickey (2010: https://www.lexjansen.com/mwsug/2010/stats/MWSUG-2010-108.pdf

and

Kiernan et al (2011): https://support.sas.com/resources/papers/proceedings11/351-2011.pdf

[sld]

Even just the code would be helpful. What kept me (and possibly @PaigeMiller) from being able to provide an answer to the initial post is that the "Solution for fixed effects" table does not show one of the Marketing level estimates being set to zero. Possibly this is a no-intercept model, but then I would expect the values in the two tables to match. So I was puzzled then, and still am.