st: xtmixed- testing difference between intercepts and slopes

[Bernadette Puckett <puckett.bernadette@gmail.com>]

Dear Stata List,

I am currently conducting a multilevel longitudinal model with time
point clustered in student and student nested within high school to
examine the association between high school quality and achievement. I
have 3 categorical levels of school quality that I am interacting with
4 time points in order to test whether the slope significantly differs
across time point and quality level. I have a host of child-level and
school-level controls.

How do test whether there is a significant intercept difference
between quality levels at Time 2? Or at Time 3? Are my coefficients
displaying differences in slope or intercept? If intercept, then how
do I test for significant differences between slope of quality at
quality level 2* time 2, and quality level 3*time2.

Here is my code:

xtmixed achievement time quality##time vector.of.controls  || school:,
variance cov(un) || child_id: time, variance cov(un) mle.

And example output:
achieve       Coef.	Std. Err.	z	P>z	
						
quality
2     -1.41589	1.628779	-1.48	0.138	
3    -2.989446	1.683687	-1.18	0.237	

time
1     15.55104	24.33336	1.05	     0.294	
2     23.36034	24.53234	1.77  	0.077	
3     56.20899	24.9002	3.06	     0.002	

quality#
time
2 1     2.991244	.986465	4.05	0.000	
2 2      1.5299	        1.094144	1.76	0.078	
2 3     1.441748	1.256821	1.15	0.251	
3 1     2.798601	1.064483	3.76	0.000	
3 2     1.127278	1.162627	0.88	0.377	
3 3     1.970249	1.316493	1.42	0.155	

ex.
control-.5441684   .4442959    -1.22   0.221    -1.414972    .3266356
 _cons |  -34.72625   25.54131    -1.36   0.174    -84.78629    15.33379


Thank you,
Bernadette
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