Help interpreting Proc Mixed output with three way interaction term

[stjsmith]

Hello,

I am having trouble interpreting the estimates and slopes from proc mixed output with a three way interaction term. I have a treatment variable indicator (treatment = 1, comparison = 0), Time indicator variable (0,1,2). Respondents are categorized into one of four regions (North Central, Pacific, Southern, and Southwest)

Picture of output:

Output in table format:

Solution for Fixed Effects
Effect	Campus	Treatment	Estimate	Standard	DF	t Value	Pr > |t|
Error
Intercept			3.8495	0.1521	1129	25.3	<.0001
Treatment		0	0.123	0.03584	1129	3.43	0.0006
Treatment		1	0	.	.	.	.
Time			0.04476	0.02467	1129	1.81	0.0699
Campus	North Central		-0.03694	0.051	1129	-0.72	0.469
Campus	Pacific		0.01366	0.05097	1129	0.27	0.7887
Campus	Southern		-0.01249	0.05062	1129	-0.25	0.8052
Campus	Southwest		0	.	.	.	.
Time*Treatment*Campus	North Central	0	-0.06649	0.03482	1129	-1.91	0.0564
Time*Treatment*Campus	Pacific	0	-0.08515	0.03452	1129	-2.47	0.0138
Time*Treatment*Campus	Southern	0	-0.05736	0.03452	1129	-1.66	0.0969
Time*Treatment*Campus	Southwest	0	-0.04947	0.037	1129	-1.34	0.1814
Time*Treatment*Campus	North Central	1	-0.06978	0.03345	1129	-2.09	0.0372
Time*Treatment*Campus	Pacific	1	-0.01768	0.03392	1129	-0.52	0.6023
Time*Treatment*Campus	Southern	1	-0.01683	0.03286	1129	-0.51	0.6086
Time*Treatment*Campus	Southwest	1	0	.	.	.	.

This is my interpretation, is this correct:

The estimate for the NORTH CENTRAL treatment group's intercept is 3.813 (3.8495 + (-0.03694))

The estimate for the PACIFIC treatment group's intercept is 3.863 (3.8495 + 0.01366)

The estimate for the SOUTHERN treatment group's intercept is 3.837 (3.8495 + (-0.01249))

The estimate for the SOUTHWEST treatment group's intercept is 3.850 (simply the intercept)

The estimate for the NORTH CENTRAL comparison group's intercept is 3.936 (3.8495 + (-0.03694) +0.123)

The estimate for the PACIFIC comparison group's intercept is 3.986 (3.8495 + 0.01366 + 0.123)

The estimate for the SOUTHERN comparison group's intercept is 3.960 (3.8495 + (-0.01249) + 0.123)

The estimate for the SOUTHWEST comparison group's intercept is 3.973 (3.8495 + 0.123)

The estimate for the NORTH CENTRAL treatment group's slope is -0.02502 (0.04476 + (-0.06978))

The estimate for the PACIFIC treatment group's slope is 0.02708 (0.04476 + (-0.01768))

The estimate for the SOUTHERN treatment group's slope is 0.02793 (0.04476 + (-0.01683))

The estimate for the SOUTHWEST treatment group's slope is 0.04476 (simply the time variable)

The estimate for the NORTH CENTRAL comparison group's slope is -0.02173 (0.04476 + (-0.06649))

The estimate for the PACIFIC comparison group's slope is -0.04039 (0.04476 + (-0.08515))

The estimate for the SOUTHERN comparison group's slope is -0.0126 (0.04476 + (-0.05736))

The estimate for the SOUTHWEST comparison group's slope is -0.00471 (0.04476 +-0.04947)

My interpretation was based of this SAS resource:

https://support.sas.com/documentation/cdl/en/statug/66103/HTML/default/viewer.htm#statug_mixed_examp...

Thank you!

[Ksharp]

https://support.sas.com/kb/38/384.html