Slope as a predictor?
Message/Author
 Jiangang Xia posted on Thursday, December 01, 2016 - 9:31 pm
I have been trying to model a cross-level relationship's effect on level-1 or level-2 outcomes. For example, the relationship is between school principal's influence on decision-making and teacher's influence on decision-making. Here the relationship could be estimated through a 2-level model. My question is, how to if I want to model the relationship's effect on teacher job satisfaction? The relationship is already a slope. I am considering a random slope model that the relationship varies by a higher level such as school district. Could we use this random slope to predict other outcomes such as teacher job satisfaction? If so, how? Should I save the random slopes as a level-3 variable and then run a new regression, or I could directly model this slope's effect? Would appreciate for any thoughts.

Jiangang
 Bengt O. Muthen posted on Friday, December 02, 2016 - 5:32 pm
If you have 3-level modeling a random slope defined on level 2 can be used to predict outcomes on level 3.
 Jiangang Xia posted on Friday, December 02, 2016 - 8:54 pm
If I have a 3-level modeling, could I use this random slope to predict a level-1 or level-2 outcomes?
 Bengt O. Muthen posted on Saturday, December 03, 2016 - 11:41 am
The random slope defined on level 2 varies across the units of level 3. This means that this random slope can predict level 3 variables, for instance the level-3 part of the variation in variables measured on level 1 or level 2. That's how multilevel modeling works.
 Jiangang Xia posted on Saturday, December 03, 2016 - 4:04 pm
I just want to confirm whether a random slope defined on level 2 varies across the units of level 3 could predict level-1 or level-2 variables. You know the focused outcomes are usually measured at lower levels.
 Bengt O. Muthen posted on Saturday, December 03, 2016 - 4:17 pm
 Kirill Fayn posted on Tuesday, February 20, 2018 - 4:56 am
Dear Bengt,

I am trying to use a slope as a predictor in a three-level model. My model is set up as follows:

USEVARIABLES ARE happy TIME swl level2 level3;
CLUSTER = level2 level3;
WITHIN = TIME;
BETWEEN =(level2) swl ;
MISSING ARE all (-9999);
ANALYSIS: TYPE = THREELEVEL RANDOM;
MODEL: %WITHIN%
s1 | happy ON TIME;
%BETWEEN level2%
s1 ON swl;
%BETWEEN level3%
OUTPUT: TECH1 TECH8;

I get the following error:

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILL-CONDITIONED
FISHER INFORMATION MATRIX....

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-POSITIVE
DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUES
BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION
NUMBER IS 0.650D-16.

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED.
PROBLEM INVOLVING THE FOLLOWING PARAMETER:
Parameter 10, %BETWEEN LEVEL2%: HAPPY2

I have tried to play around with some random starting values, but the error persists.

Any advice would be greatly appreciated.