How to specify random slope in a mixed effect linear model with non-clustered random effects?

[Chuan Tang]

Hi, all,

I try to use the mixed command to run some mixed effect model. Here is an example to show what I am doing:

. sysuse auto2.dta
(1978 Automobile Data)

. mixed price mpg ||_all:rep78 || _all:foreign

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log likelihood = -639.24539  
Iteration 1:   log likelihood = -639.18966  
Iteration 2:   log likelihood = -639.17544  
Iteration 3:   log likelihood = -639.17536  
Iteration 4:   log likelihood = -639.17536  

Computing standard errors:

Mixed-effects ML regression                     Number of obs      =        69
Group variable: _all                            Number of groups   =         1

                                                Obs per group: min =        69
                                                               avg =      69.0
                                                               max =        69


                                                Wald chi2(1)       =     21.84
Log likelihood = -639.17536                     Prob > chi2        =    0.0000

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -265.2104   56.75339    -4.67   0.000     -376.445   -153.9758
       _cons |   11462.59   1185.269     9.67   0.000     9139.502    13785.67
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
_all: Identity               |
                  var(rep78) |   7.58e-09   .0000215             0           .
-----------------------------+------------------------------------------------
_all: Independent            |
                var(foreign) |    1423223    2870677      27313.56    7.42e+07
                  var(_cons) |   1.13e-08   4.73e-07      3.63e-44    3.55e+27
-----------------------------+------------------------------------------------
               var(Residual) |    6348319    1092162       4531254     8894041
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(3) =     1.17   Prob > chi2 = 0.7612

Note: LR test is conservative and provided only for reference.

In this model, rep78 and foreign are two non-clustered random intercepts. My questions is, is it possible to specify the mpg as a random slope within the foreign level? What I want is something like:

. mixed price mpg ||rep78:mpg || foreign:

I can't use the above code since stata will automatically assume foreign is clustered within rep78, but actually those two variables are not clustered. The estimation is not correct. That's why I am using _all:R.varname to claim those 2 non-clustered random intercepts. But I don't know how to add a random slope in my first model. I read through the help documents, but didn't see any information about this. Any suggestions and ideas are greatly appreciated!

BTW:

I am also a R user, if you are familiar with R and lme4 package. What I want is something like (in R):

lmer(price ~ mpg + (1|rep78) + (1+ mpg|foreign), auto2, REML = F)

Thank you in advance!

[Clyde Schechter]

Is this what you want:

mixed price mpg || _all:R.rep78 || foreign:mpg

[Chuan Tang]

Hi, Clyde:

Thank you. It works perfect!

chuan