The use of -KHB- command in mediation analysis of linear regressions

[Giorgio Piccitto]

Dear all, I am struggling with the following issue: as far as I know, the KHB decomposition can be used both for binary and continuous dependent variables. The latter is my case, and my goal is to decompose the 'effect' of

 classify

and

 edu_3

on

 isei

.

Those on the rigth side of the command are instead the other control variables, whose I am not interested in estimating their mediation 'effect' (the way I wrote down the command should be fine, correct?)

However, I did not find any clear way how to interpret the results: in general, what does the value mean in 'Reduced', 'Full' and 'Diff' for each variable? See below my example, with data and output:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(isei migration_status_decima) byte age float(edu_3 male) int refyear byte num_pers_less15
23.46 2 27 2 0 2008 2
 56.5 0 27 2 1 2008 0
44.87 0 22 2 0 2008 0
    . 0 22 2 0 2008 0
43.06 0 17 1 0 2008 0
31.15 0 17 1 1 2008 0
    . 0 17 1 1 2008 0
19.78 0 27 2 1 2008 0
25.91 0 22 2 1 2008 0
    . 0 17 1 0 2008 0
end
label values migration_status_decima migration_status_decima
label def migration_status_decima 0 "Nat", modify
label def migration_status_decima 2 "HEC", modify
label values age age_VL
label def age_VL 17 "15-19 years of age", modify
label def age_VL 22 "20-24 years of age", modify
label def age_VL 27 "25-29 years of age", modify
label values num_pers_less15 hhnb0014_VL

. khb reg isei classify edu_3 || age   num_pers_less15 male  refyear , level(90)  

Decomposition using Linear Probability Models

Model-Type:  regress                               Number of obs     =   14305
Variables of Interest: classify edu_3              R-squared         =    0.30
Z-variable(s): age num_pers_less15 male refyear
------------------------------------------------------------------------------
        isei | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
classify     |
     Reduced |  -1.406022   .1180286   -11.91   0.000    -1.637354    -1.17469
        Full |  -1.139395   .1195589    -9.53   0.000    -1.373726   -.9050637
        Diff |  -.2666269    .046166    -5.78   0.000    -.3571106   -.1761432
-------------+----------------------------------------------------------------
edu_3        |
     Reduced |   13.74171   .1913254    71.82   0.000     13.36672     14.1167
        Full |   13.00491   .2040177    63.74   0.000     12.60504    13.40478
        Diff |   .7367982   .0823742     8.94   0.000     .5753478    .8982487
------------------------------------------------------------------------------

Any help would be super appreciated (and sorry for the apparently silly question).

Best, GP

[Felix Bittmann]

What you test here is whether the effect of classify and edu_3 on the outcome (ISEI) is mediated through your z-variables. If the p-value of "diff" is significant you can assume that there is a mediation present. What we see on your example is that there is a partial mediation.

[Giorgio Piccitto]

Dear Felix, thanks for your answer.

My goal actually is to test if the effect of classify on the outcome Isei is mediated through edu_3, while I want only to control for the other Z (without testing their mediation role).

I tried the following specification with the following results:

 

. khb reg isei classify  || edu_3, c(age   num_pers_less15 male  refyear ) level(90)  

Decomposition using Linear Probability Models

Model-Type:  regress                               Number of obs     =   14305
Variables of Interest: classify                    R-squared         =    0.30
Z-variable(s): edu_3
Concomitant: age num_pers_less15 male refyear
------------------------------------------------------------------------------
        isei | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
classify     |
     Reduced |  -2.060831   .1186818   -17.36   0.000    -2.293443   -1.828219
        Full |  -1.139395   .1195589    -9.53   0.000    -1.373726   -.9050637
        Diff |  -.9214361   .0648835   -14.20   0.000    -1.048605   -.7942667
------------------------------------------------------------------------------

How should I interpret here the values of 'Reduced' and 'Full'? Does it represent a problem the fact that the variable classify is a categorical one, without an ineherent hierarchical order of their categories of response (which then cannot be ordered in terms of 'lower' or 'higher')?

Thanks again for your kindness.

Best, Giorgio

[Felix Bittmann]

You wanna do it like this:

khb reg isei i.classify  || edu_3, c(age   num_pers_less15 male  refyear ) level(90)

[Giorgio Piccitto]

Dear Felix, thanks a lot.

If I got well, with your model I am able to say to what extent, for each category of classify, edu_3 mediates the association between classify and isei, is that correct?

May you suggest me how to interpet the 'Reduced' and 'Full' coefficients?

Since now I do not get how to read the results, which are the following

. khb reg isei i.classify  || edu_3, c(age   num_pers_less15 male  refyear ) level(90)  

Decomposition using Linear Probability Models

Model-Type:  regress                               Number of obs     =   14305
Variables of Interest: i.classify                  R-squared         =    0.31
Z-variable(s): edu_3
Concomitant: age num_pers_less15 male refyear
------------------------------------------------------------------------------
        isei | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
0.classify   |  (base outcome)
-------------+----------------------------------------------------------------
1.classify   |
     Reduced |  -4.343864   3.906887    -1.11   0.266    -12.00122    3.313495
        Full |  -8.589865   3.907493    -2.20   0.028    -16.24841    -.931319
        Diff |   4.246001   2.190089     1.94   0.053    -.0464948    8.538497
-------------+----------------------------------------------------------------
2.classify   |
     Reduced |  -12.65744   .4542886   -27.86   0.000    -13.54783   -11.76705
        Full |  -7.667254   .4614286   -16.62   0.000    -8.571638   -6.762871
        Diff |  -4.990184   2.190501    -2.28   0.023    -9.283487   -.6968808
-------------+----------------------------------------------------------------
3.classify   |
     Reduced |  -.2680611    .663135    -0.40   0.686    -1.567782     1.03166
        Full |  -.2758087    .663135    -0.42   0.677     -1.57553    1.023912
        Diff |   .0077476   2.189008     0.00   0.997     -4.28263    4.298125
-------------+----------------------------------------------------------------
4.classify   |
     Reduced |  -5.096857   .8708048    -5.85   0.000    -6.803603   -3.390111
        Full |  -1.552739   .8726964    -1.78   0.075    -3.263192    .1577148
        Diff |  -3.544118   2.189761    -1.62   0.106    -7.835971    .7477354
-------------+----------------------------------------------------------------
5.classify   |
     Reduced |  -4.581202   1.152924    -3.97   0.000    -6.840892   -2.321512
        Full |  -2.898599   1.153246    -2.51   0.012     -5.15892   -.6382771
        Diff |  -1.682603   2.189178    -0.77   0.442    -5.973313    2.608107

Thanks a lot, Giorgio

[Felix Bittmann]

We see that there are some hints for mediation going on, like for classify 2. The coefficient without the mediator is -12 but with the mediator its -7, so the effect is reduced due to the mediator, hence, a mediation is going on. However, for classify 1, the effect is actually getting larger. This makes it not so easy to interpret what is going on exactly in your model without knowing more about the details of your research. Overall I would say there is enough evidence in your results so far to tell that edu3 mediates some of the effects of classify.

[Giorgio Piccitto]

Dear Felix, thanks a lot.

Probably the strange effect for classify 1 is due to the fact that this group is very small in size (N=29) and so estimations are likely totally unreliable.

The other groups are much more sized (the one with the lowest number of observations being the 5, with nearly 500 observations), and so I believe we can 'trust' those results.

Hence, in your opinion do you think that these findings may indicate a mediation role of edu_3, and they can represent a relevant piece of information for my study?

Thanks again, Giorgio

[Felix Bittmann]

I would say that there is a mediating effect present, especially for class2, here it is a strong effect, as about 40% is mediated 1-(7.66/12.65). For class 4 there are also some effects.