Interpretation of interaction term with ologit regression

[Jacob Joris]

Hi all,

I have a question about the interpretation of my results, regarding a moderator in an ologit regression.

My IV is 'green attitude', my DV is 'greenbuying' and my moderator is 'ecolabel trust'. Control variables are age and gender.



anew=attitude (towards green products), and can be:
- zero
- low
- medium
- high

gnew= greenbuying (how often you buy green products), and can be:
-1 - never
-2
-3
-4
-5
-6 - every day

tnew=ecolabel trust, and can be:
- zero
- low
- medium
- high

My regression results are:

. ologit gnew tnew##anew age i.gender 

Iteration 0:   log likelihood = -28944.057  
Iteration 1:   log likelihood = -27348.317  
Iteration 2:   log likelihood = -27259.086  
Iteration 3:   log likelihood = -27251.011  
Iteration 4:   log likelihood =  -27251.01  

Ordered logistic regression                     Number of obs     =     24,623
                                                LR chi2(17)       =    3386.09
                                                Prob > chi2       =     0.0000
Log likelihood =  -27251.01                     Pseudo R2         =     0.0585

------------------------------------------------------------------------------
        gnew |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        tnew |
          2  |   1.052075   .2152138     4.89   0.000      .630264    1.473887
          3  |   1.304467    .217954     5.99   0.000     .8772846    1.731649
          4  |   .8888412   .2646973     3.36   0.001      .370044    1.407638
             |
        anew |
          2  |   1.321674   .2067314     6.39   0.000     .9164875     1.72686
          3  |   2.480465   .1951027    12.71   0.000     2.098071    2.862859
          4  |   2.955394   .1982461    14.91   0.000     2.566839    3.343949
             |
   tnew#anew |
        low low  |  -.4183916    .251595    -1.66   0.096    -.9115087    .0747256
        low med  |  -.5871072   .2375724    -2.47   0.013    -1.052741   -.1214739
        low high  |  -.4778066   .2409796    -1.98   0.047     -.950118   -.0054952
        med low  |  -.3663611   .2526495    -1.45   0.147    -.8615449    .1288228
        med med  |  -.5181469   .2386876    -2.17   0.030    -.9859659   -.0503279
        med high  |  -.2446669   .2413479    -1.01   0.311    -.7177002    .2283663
        high low  |   .0376205   .3112913     0.12   0.904    -.5724993    .6477403
        high med  |  -.0507737    .286457    -0.18   0.859     -.612219    .5106716
        high high  |   .2414048   .2865594     0.84   0.400    -.3202413    .8030509
             |
         age |   .0080733   .0007564    10.67   0.000     .0065907    .0095559
             |
      gender |
     Female  |   .0491804   .0256802     1.92   0.055    -.0011519    .0995128
-------------+----------------------------------------------------------------
       /cut1 |   .1818974   .1740457                     -.1592259    .5230208
       /cut2 |   .5712073   .1741778                      .2298251    .9125895
       /cut3 |   1.381783   .1747356                      1.039307    1.724258
       /cut4 |   1.808177    .174998                      1.465188    2.151167
       /cut5 |   4.742743   .1766713                      4.396473    5.089012
------------------------------------------------------------------------------

I have two questions about this:

My current interpretation is this:
The coefficient of low trust X med attitude is negative and significant at the 5% level. This entails that med attitude has a stronger negative effect on green buying when trust is low compared to when trust is zero.

Is this correct?

Should I form three hypotheses to test for this moderator?

1. The relationship between attitude and behaviour is mediated by trust in eco-labels for consumers rating environmental impact not very important (attitude = low)

2. The relationship between attitude and behaviour is mediated by trust in eco-labels for consumers rating environmental impact fairly important (attitude = med)

3. The relationship between attitude and behaviour is mediated by trust in eco-labels for consumers rating environmental impact very important (attitude = high)

Is it correct that I need 3 seperate hypotheses as attitude can have 4 values?

It would greatly help me if someone can tell me if I am on the right track! I am struggling a bit with moderation in combination with an ologit regression and two categorical variables as I've never done this before. Any help is greatly appreciated!

Kind regards,
Joris

[Jacob Joris]

If someone could tell me if I'm in the right direction, I will be very grateful. This is for my thesis and right now, I am unsure how to continue.

Thank you in advance.

[Joseph Coveney]

Here: first, use a likelihood-ratio test see whether you have a moderation to talk about, and if so plot the linear predictions to see what kind of interaction you have.

Below, I create a dummy dataset to illustrate the two steps; begin at the "Begin here" comment.

version 16.0

clear *

set seed `=strreverse("1522357")'
quietly set obs 250

forvalues i = 1/2 {
    generate byte pr`i' = runiformint(1, 4)
}
generate byte sex = runiformint(1, 2)
generate double age = runiform()

generate byte rsp = runiformint(1, 6)

*
* Begin here
*
ologit rsp i.pr1##i.pr2 c.age i.sex, nolog
estimates store Full

ologit rsp i.(pr? sex) c.age, nolog
lrtest Full

// If you have an overall significant interaction
quietly estimates restore Full
margins pr1#pr2, predict(xb)
marginsplot , ///
    plotopts(lcolor(black) mcolor(black) msymbol(circle) mlcolor(white) ///
        mfcolor(white) mlabel(pr2) mlabposition(0) mlabcolor(black)) ///
            ylabel(, angle(horizontal) nogrid) noci title("") legend(off)

exit