Within-level estimates with random sl...
Message/Author
 George Pearson posted on Thursday, August 16, 2018 - 8:43 am
Hopefully not a stupid question...

However. If I conduct a model with a random intercept I am given the regression estimates with the within-level estimates as well as the between.

However, if I use a random slopes model, the within regression equation is used to define the slope.

In other words what was:

y ON x1 x2 x3

Become

s | y ON x1 x2 x3

Consequently the regression coefficients from Y on X1, X2 and X3 disappear from the output and I am left only with the estimate of S.

Is there a way to include the coefficients of Y on X1, X2 and X3 in the output while still allowing the slope of Y to vary randomly?
 Bengt O. Muthen posted on Thursday, August 16, 2018 - 4:28 pm
This statement is not Mplus syntax:

s | y ON x1 x2 x3

A random slope s refers to a single coefficient so you should have just one x on the right-hand side. If you want 3 of them, you should specify one at a time: s1, s2, s3.
 Ahmad Siddiquei posted on Friday, August 24, 2018 - 3:23 am
Hi Dr Muthen,

I am Ahmad. Firstly, I would like to say Thank you to you as your software, user guide and online interaction/discussions helped me a lot throughout my degree.

I read a lot of literature talking about 2-1-1 model or 1-2-1 model. However,my model is 1-1-2 (leader behaviours measured at individual level, team processes measured at individual level, and team performance measured at team level). I am new to using Mplus and unable to identify the right syntax to test the direct and mediating effects in my model. May I please ask for your help?

Thank you so much once again.
 Ahmad Siddiquei posted on Friday, August 24, 2018 - 3:57 am
BETWEEN= Performance;
Cluster is TeamID;
Analysis: Type= Twolevel random;

Model:
%Within%

%BETWEEN%

Performance on Slope;

This is what I understood uptil now to estimate cross level effect in my context of 1-1-2 model.
 Bengt O. Muthen posted on Friday, August 24, 2018 - 6:04 pm
You don't need a random slope. You can try this input using abbreviations of your variable names:

Between = perf;

%Within%
beh with proc;
%Between%
perf on proc (b)
beh (c);
proc on beh (a);

And then use Model Constraint with

New(ind);
ind = a*b;
 Ahmad Siddiquei posted on Friday, August 24, 2018 - 7:14 pm
Thank you, Sir. I ran the model with this syntax and it worked. Few follow up questions please,

Question 1: Is this the way to estimate 1-1-2 model (just to be absolutely sure)?
Question 2: How can I infer that its a partial or full mediation?
Question 3: How can I get the standardized estimates?
Question 4: Is there any specific estimator that you would recommend me to use? MLR, MLF, or Bayes?
Questions 5: The intercept value of outcome variable is negative and significant (not the process to performance relationship), does it matter?
 Bengt O. Muthen posted on Saturday, August 25, 2018 - 2:39 pm
Q1: Yes. It is the between-level part of beh and proc that play a role on the between level.

Q2: Significance of "c".

Q3: Ask for it in the Output command. For "a*b" you have to standardize yourself by dividing by the perf SD and multiplying by the beh between-level SD.

Q4: Bayes would be good. ML with bootstrap is in principle as good but Mplus doesn't have bootstrap for twolevel.

Q5: The intercept is not the mean so I don't see how that matters.
 Ahmad Siddiquei posted on Saturday, August 25, 2018 - 4:22 pm
That's very helpful. Thankyou so much.
If I have to test the individual level effect of behav (independent) on individual level proc (mediator) and team level perfor (outcome); meaning the cross level effect from individual level proc to team level perf. Would I be using the same analysis type and code?

Thanks so much once again,Sir.
 Bengt O. Muthen posted on Monday, August 27, 2018 - 2:09 pm
That sounds like

Between = perfor;

%Within%
proc on behav;
%Between%
perfor on proc;

or with a random slope:

%Within%
s |proc on behav;
%Between%
perfor on proc s;
 Ahmad Siddiquei posted on Monday, August 27, 2018 - 2:22 pm
Thanks. I was after the second method which you showed. Also, in the second method, how will the indirect effect be calculated?
 Bengt O. Muthen posted on Monday, August 27, 2018 - 4:57 pm
The way I wrote it, there is no indirect effect but perhaps what you have in mind is adding one more line on Between defining a:

%Within%
s |proc on behav;
%Between%
perfor on proc (b)
beh (c);
proc on beh (a);

I just want to make sure that this is really what you have in mind.

To handle the latent variable decomposition of behav in this random slope situation, you would then have to use Estimator=Bayes. See our new paper on our website:

Asparouhov, T. & Muthén, B. (2018). Latent variable centering of predictors and mediators in multilevel and time-series models. Technical Report, Version 2. August 5, 2018. Accepted for publication in Structural Equation Modeling. (Download scripts).
 Ahmad Siddiquei posted on Monday, August 27, 2018 - 5:05 pm
Yes, Sir. This is exactly what I was asking. The mediating role in cross level effect using product of coefficient of both paths, behav (level 1) to process (level 1) to peformance (level 2).
 Bengt O. Muthen posted on Tuesday, August 28, 2018 - 12:07 pm
In this case the indirect effect is simply a*b. The mean of the slope s does not play a role in this case because your Y ("perfor") is on only the between level.
 Ahmad Siddiquei posted on Tuesday, August 28, 2018 - 1:08 pm
Thank you. I have sent my license number, data and output file at support for your perusal. Just to completly sure about the syntax.