Concentration index decomposition

[Mukesh Punia]

Dear users I want to estimate the concentration index using equation 1 with wagstaff 2005 bounds. Then, with probit regression specification, I want to decompose the contribution of each predictor xrank and others. example data is given below.

\[ C = \frac{2}{n \cdot \bar{y}} \sum_{i=1}^{n} y_i R_i - 1 \] (eq-1)

Part -1 is done and result is given below.

My query is how to implement Part-2?

\[ CI_n = \left( \frac{\beta_{\text{rank}} X_{\text{rank}}}{\bar{Y}} \right) CI_r + \sum_k \left( \frac{\beta_k X_k}{\bar{Y}} \right) CI_k + \frac{GC \epsilon}{\bar{Y}} \] (eq-2)

I am using conindex (version *! conindex 1.5 18 July 2018) syntax and Stata version 15.1

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte y float xrank byte(xk1 xk2 xk3) float xk5
1  677.8285 0 0 0 146.51355
1 175.72597 1 1 0  578.2192
0 245.46584 1 0 0  586.5716
1  908.6988 1 0 1  673.6869
0  645.7861 1 1 1  753.4822
1 108.27734 1 0 0  978.2668
0  191.3244 1 1 1  564.6703
1  697.1516 1 1 1  390.6608
0 104.55543 1 1 1  815.6676
1 244.72725 0 0 1   343.749
0  593.8604 1 0 1  495.0743
0  722.7057 0 0 0 170.61075
1  686.7651 1 0 1 122.81567
0 301.84238 1 0 0  966.3835
1  740.9613 0 0 0  852.3821
0  313.5242 1 0 1  726.3768
1  392.8597 0 1 0 468.05765
1  771.8423 1 0 0  255.9649
1  684.6696 1 1 0 240.79333
0  864.3011 0 0 1  325.2186
1  691.8516 1 0 1   594.304
0  611.4777 0 0 0  743.1364
1  184.3073 1 1 1  694.1776
1  430.9442 0 1 1  351.9405
1  338.6821 0 1 1  959.3787
1  319.5907 1 1 1  764.1072
1  975.7095 1 0 0 598.91864
1   453.788 0 1 0  650.5486
1  902.8419 1 0 1    477.64
1  668.0248 1 0 1  322.9579
0  815.3302 1 1 0  420.3754
0  552.3734 0 1 0  782.0615
1  619.2135 0 1 1 112.95414
1  543.2659 0 1 0  204.4654
1  275.7187 0 1 1 141.40237
0  750.2069 0 1 1 136.65593
1  352.6951 0 1 0  869.9146
0 121.88437 0 1 0  733.2921
0   680.925 0 0 1  526.7565
1  259.3996 0 1 1 188.05075
0  946.4127 1 1 0  542.4543
0  958.5357 0 0 1  526.1246
1  923.3779 1 1 0  255.8817
1  433.1428 1 0 1  490.4665
1 113.91096 1 0 0  458.6543
1  935.4867 0 1 0  654.2651
1  485.3657 0 0 0  671.5843
0  969.9893 0 0 1  140.7736
1   967.258 0 0 1  437.1514
1  867.7085 1 0 0  663.2739
0   365.004 0 1 1 552.82263
1 446.58795 0 0 0  870.8409
0   866.023 0 1 0  692.8243
1  385.2298 0 0 1   246.641
0 252.54347 0 0 1 163.51187
1 601.12115 1 0 0  678.1774
1  942.5393 0 0 1 123.86018
0  726.4268 1 1 1   627.198
0  613.0551 0 1 0  946.2072
1 187.45885 1 0 0  617.9268
0  653.5065 0 0 1  449.3529
0  991.0485 0 1 0  678.9594
1  226.0756 1 0 0  512.4276
0  566.4967 1 0 1  591.0551
0  889.6357 1 0 0  947.3183
1  766.6918 0 1 0  447.4924
1  727.3141 1 1 1  965.0715
0  732.2357 0 1 1  914.8156
1   423.542 0 0 0 276.21204
1  364.2327 1 0 0 162.42517
1   828.425 1 1 1  190.7002
1  829.1021 0 1 1 116.39964
0  880.3651 0 1 1 184.99866
1  921.9165 1 1 1  714.7061
0  560.2081 1 0 0  164.0698
1  551.3647 1 1 1  387.0781
1  818.4656 0 0 1  860.3878
1  684.9675 0 1 0 120.94474
0  731.7702 0 0 1  833.0216
1  816.2134 0 1 0  353.6693
0  901.0048 0 1 1 206.34834
1 404.19565 0 1 1  727.0635
0  438.0247 1 1 1  666.0486
1 184.58374 0 0 0  889.7248
0  620.4521 0 1 0   761.564
0 132.34805 0 0 1  823.1328
1  519.0382 1 0 0  353.8311
0  588.3802 0 0 0  259.6956
1  357.8871 0 0 0  775.5533
1  631.7499 1 1 0  826.1512
1 127.45023 0 0 0  991.4547
1 133.61337 0 0 0  471.3559
1  840.3405 0 0 1  434.8163
1  424.1716 0 1 1  798.7717
1 214.35446 0 1 0  406.7232
1  570.0189 1 1 1  937.6816
1  792.9942 1 1 1  872.5715
1 294.23892 1 0 1  486.0946
1  660.6014 0 0 1  775.7839
0  176.8127 0 1 0  779.0886
end
label var y "outcome dummy"
label var xrank "rank continuous"
label var xk1 "xk1 dummy"
label var xk2 "xk2 dummy"
label var xk3 "xk3 dummy"
label var xk5 "xk5 continuous"

 . conindex y , rankvar( xrank ) limits(0 1) bounded wagstaff


------------------------------------------------------------------------------+
Index:             | No. of obs. | Index value | Std. error        | p-value  |
-------------------+-------------+-------------+-------------------+----------|
Wagstaff norm. CI  | 100         | -.0999571   |.12036793          |  0.4083  |
------------------------------------------------------------------------------+

[Mukesh Punia]

Respected Stephen Jenkins can you please have a look at it.

[Mukesh Punia]

Respected George Ford can you please have a look at it?

[George Ford]

Outside of my area, but maybe some help here.

https://www.statalist.org/forums/forum/general-stata-discussion/general/1373417-decomposing-erreygers-concentration-index-stata