Hi all,

I am running the following mixed model (code and results shown below). Notes: Y is continuous, dar is continuous, alp is dichotomous, mup is dichotomous, and zol is dichotomous.

Y = 70.63 + -.144 dar + .0039 dar2 + -.00003 dar3 + 7.57 alp + 18.59 mup + 11.28 zol + -6.302 mup*zol

This is how I interpret the coefficients:
  • constant = value of Y when all variables=0
  • dar, dar2 ,and dar3 => will plot the results.
  • alp (not part of interaction), I interpret as: increase in Y for alp=1 v. alp=0
  • mup (part of interaction): change in Y when move from mup=0 to mup=1 when zol=0
  • zol (part of interaction): change in Y when move from zol=0 to zol=1 when mup=0
  • mup*zol: difference in Y when move from mup=0 to mup=1 for zol=1 v. zol=0

My questions:
  • For variables NOT included in an interaction (e.g. alp), since they are not in an interaction, are they interpreted in the same way as if the interaction was not in the model? For example, I interpret alp as "increase in Y for alp=1 v. alp=0." This interpretation does not mention any other variables.
  • For the variables INCLUDED in the interaction (mup, zol, and mup*zol); are they only interpreted with respect to the other variables included in the interaction? (and not other variables in the model). For example, I interpret mup as "change in Y when move from mup=0 to mup=1 when zol=0".

Not sure if this is clear enough but would appreciate any comments. THANK YOU!!!


Code:
. mixed lex c.dar##c.dar##c.dar i.alp i.mup i.zol i.mup#i.zol || _all: R.bor || _all: R.mol || _all: R.pop, reml

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood =  -55055.98  
Iteration 1:   log restricted-likelihood =  -55055.98  

Computing standard errors:

Mixed-effects REML regression                   Number of obs     =     12,040
Group variable: _all                            Number of groups  =          1

                                                Obs per group:
                                                              min =     12,040
                                                              avg =   12,040.0
                                                              max =     12,040

                                                Wald chi2(7)      =     558.36
Log restricted-likelihood =  -55055.98          Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------
              lex |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
              dar |  -.1442413   .0679903    -2.12   0.034    -.2774999   -.0109827
                  |
      c.dar#c.dar |   .0039578   .0017025     2.32   0.020      .000621    .0072946
                  |
c.dar#c.dar#c.dar |  -.0000359   .0000113    -3.19   0.001     -.000058   -.0000138
                  |
            1.alp |    7.56537   1.792743     4.22   0.000     4.051658    11.07908
            1.mup |   18.59015   2.898774     6.41   0.000     12.90866    24.27164
            1.zol |   11.27925   .6055326    18.63   0.000     10.09243    12.46607
                  |
          mup#zol |
             1 1  |   -6.30276   .8396218    -7.51   0.000    -7.948388   -4.657131
                  |
            _cons |   70.63327    2.85485    24.74   0.000     65.03787    76.22868
-----------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
_all: Identity               |
                  var(R.bor) |   81.68924   16.43907      55.06427    121.1881
-----------------------------+------------------------------------------------
_all: Identity               |
                  var(R.mol) |   47.87758   14.45347      26.49525    86.51596
-----------------------------+------------------------------------------------
_all: Identity               |
                  var(R.pop) |   42.53744   8.664709      28.53546       63.41
-----------------------------+------------------------------------------------
               var(Residual) |    528.271    6.84953      515.0153    541.8679
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 2653.43               Prob > chi2 = 0.0000

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

.
. margins i.alp i.mup i.zol i.mup#i.zol

Predictive margins                              Number of obs     =     12,040

Expression   : Linear prediction, fixed portion, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         alp |
          0  |   81.48609   2.200303    37.03   0.000     77.17357     85.7986
          1  |   89.05146   2.200272    40.47   0.000       84.739    93.36391
             |
         mup |
          0  |   77.23285   2.501806    30.87   0.000      72.3294     82.1363
          1  |   92.66743   2.435716    38.05   0.000     87.89351    97.44134
             |
         zol |
          0  |   81.26372   2.020338    40.22   0.000     77.30393    85.22351
          1  |   89.26177   2.020341    44.18   0.000     85.30197    93.22156
             |
     mup#zol |
        0 0  |   71.58573   2.518609    28.42   0.000     66.64934    76.52211
        0 1  |   82.86498   2.521506    32.86   0.000     77.92292    87.80704
        1 0  |   90.17588    2.45509    36.73   0.000     85.36399    94.98776
        1 1  |   95.15237   2.450946    38.82   0.000      90.3486    99.95613
------------------------------------------------------------------------------