Hi All,

I have having some trouble interpreting some interaction effects of some panel data ordinal regression models I ran.

I am using STATA/SE 15.

I ran dataex for my variables of interest (shown below) as an example of my data:

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input float newid int assessmentnumber float(nature selfdiag lonely)
1  0 0 2 .
1  2 0 2 3
1  3 0 2 1
1  4 1 2 1
1  5 0 2 3
1  6 1 2 1
1  8 0 2 2
1 11 0 2 3
4  0 0 1 .
8  0 0 1 .
8  3 1 1 5
8  5 1 1 5
8  7 1 1 5
8  8 1 1 5
8  9 0 1 5
8 13 1 1 1
8 21 1 1 5
8 23 0 1 5
8 36 0 1 2
3  0 0 2 .
3  1 1 2 4
3  2 0 2 3
3  5 1 2 5
9  0 0 2 .
9  1 1 2 3
9  9 1 2 5
9 22 1 2 5
5  0 0 1 .
7  0 0 2 .
7  3 1 2 2
7  4 1 2 5
7  5 0 2 3
6  0 0 2 .
2  0 0 2 .
end
label values selfdiag noyes
label def noyes 1 "No", modify
label def noyes 2 "Yes", modify
My data is panel data, with multiple participants responding to multiple assessments.

I'm trying to explore the interaction effect between diagnosis (selfdiag: yes or no *answered once by participants*) and loneliness (lonely: ordered likert 1-5 *answered at every timepoint*) and exposure to nature (nature: yes no *answered at every timepoint*).

I ran the following xtologit command to explore my query but this is where I need a bit of help with interpretation of the odds ratios.

Code:
xtologit lonely i.selfdiag##i.nature, or

Fitting comparison model:

Iteration 0:   log likelihood = -11940.828  
Iteration 1:   log likelihood = -11853.136  
Iteration 2:   log likelihood = -11853.023  
Iteration 3:   log likelihood = -11853.023  

Refining starting values:

Grid node 0:   log likelihood = -9989.8616

Fitting full model:

Iteration 0:   log likelihood = -9989.8616  
Iteration 1:   log likelihood = -9574.7404  
Iteration 2:   log likelihood = -9532.0663  
Iteration 3:   log likelihood = -9526.9694  
Iteration 4:   log likelihood = -9526.7409  
Iteration 5:   log likelihood = -9526.7408  

Random-effects ordered logistic regression      Number of obs     =      9,575
Group variable: newid                           Number of groups  =        339

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =         21
                                                              avg =       28.2
                                                              max =         42

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(3)      =      56.33
Log likelihood  = -9526.7408                    Prob > chi2       =     0.0000

---------------------------------------------------------------------------------
         lonely | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
                |
       selfdiag |
           Yes  |   1.558753   .4191598     1.65   0.099     .9202021    2.640411
       1.nature |   .6323547   .0426758    -6.79   0.000     .5540075    .7217816
                |
selfdiag#nature |
         Yes#1  |   1.301939   .1564135     2.20   0.028     1.028794    1.647605
----------------+----------------------------------------------------------------
          /cut1 |   .0264557   .1458407                     -.2593867    .3122982
          /cut2 |   1.834789   .1471281                      1.546424    2.123155
          /cut3 |   3.232257   .1503294                      2.937617    3.526897
          /cut4 |   5.114032   .1645409                      4.791537    5.436526
----------------+----------------------------------------------------------------
      /sigma2_u |   4.156539   .3770802                      3.479454    4.965382
---------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
LR test vs. ologit model: chibar2(01) = 4652.56       Prob >= chibar2 = 0.0000
The main effect of a diagnosis here is non-significant, and the main effect of nature is significant.
I can see that there is a significant interaction effect, but what does this mean?

Having a diagnosis (yes) and exposure to nature (1) increases the odds of higher loneliness by 1.30 times? Compared to what? Compared to having no diagnosis (no) and no exposure to nature (0)?

Am I correct in thinking that compared to no diagnosis/no nature:
  • Diagnosis/no nature = 1.55 times increased odds of higher loneliness
  • Diagnosis/nature = 1.30 times increased odds of higher loneliness
  • No diagnosis/no nature = reference
  • No diagnosis/nature = 0.63 times decreased odds of higher loneliness
Would this mean that people with diagnosis are at increased odds of higher lonely scores, but these odds are reduced in contact with nature??

Thanks for any help you can provide!

Kind regards,
Ryan