HLM-Random intercept or random slope?

[#1]

I am buidling a heirchical linear model for nested data: level 1 student, level 2 teacher, level 3 school. I am interested in controlling for school and student contexts and get at teacher effect. 

This is how I built the mdel:

In fit model, I used standard least squares as the personality, and assigned school (i. e. school name) and student variables (i. e. student gender, ethnicity and lunch status) fixed effect, while teacher and teacher interaction with student variables as random effect. This way I get BLUP as teacher effect. 

My question is: is the random effect random intercept or random slope? 

P. S.  I assigned random by selecting "random" in the attribute dropdown menu. 

I have been trying to find answer to this question for days. Really appreciate your help!

[#2 · Accepted solution]

The type of the factors you specified as the random effects give you the random intercepts, not the random slopes. A slope in a regression is the coefficient on a continuous variable. However, continuous random effects are only supported in JMP Pro 12 or after.

 Here is an example in JMP Pro:

http://www.jmp.com/support/help/13/Example_Using_Mixed_Model.shtml#1263694

Statistical details: 

http://www.jmp.com/support/help/13/Random_Coefficient_Model.shtml#1273501

[#3]

Hi, 

I would like to ask for help since I have difficulties in understanding three types of strategies applied to study the repeated measures. In my study, all of them give different results. These models include the following:

 1) Full factorial mixed ANOVA add-in

 2) Mixed model analysis by using the fit model and random subject in the attribute section: https://community.jmp.com/t5/JMP-Academic-Knowledge-Base/Mixed-Model-Analysis-OPG/ta-p/21747

 3) Mixed model personality with Pro

My question is if full factorial ANOVA add-in accounts for any random variation? And if I do not have Mixed model personality with JMP Pro, is it enough to use the second option? 

[#4]

Hi,

This JMP blog entry may be helpful.

https://community.jmp.com/t5/JMP-Blog/JMP-Pro-for-linear-mixed-models-Part-1/ba-p/30433

The results between the mixed model in JMP Pro and Base JMP random effects should be equivalent.