Scatterplot (nonlinear relationship)

[Hugo Rocha]

Hi!

I got the following scatterplot (below) that clearly illustrates a nonlinear relationship between the coefficient and GDP per capita. I want to build a curve that best fits this relationship (as per the other picture). However, I am not finding the right way to do it. I know the plot is not a twoway line but also I think I am not properly using curvefit. Is there a way I can use my data to get something on the lines of the figure? Many Thanks!

 * Example generated by -dataex-. To install: ssc install dataex
clear
input int(country year) double(GdpCod GdpCud MvaCod MvaCud Pop) float(Mva_output GDPpercapita MVA_capita region coeff_diversi) byte _merge float predict
 4 1990           .  3559511736 1839648920  683514541 12412310   .1920248         . 148.21165 6         0 3         .
 4 1991  7907838197  3402654940 1748969501  680342026 13299020  .19994447  594.6181 131.51115 6         0 3 .51096517
 4 1998  5930467283  2935139404  665837681  298073135 19737770  .10155331  300.4629 33.734188 6         0 3 .51036495
 4 1999  5646938964  2157197316  797533419  287999806 20170850  .13350648  279.9554  39.53891 6         0 3  .5103231
 4 2001  5043434615  3598470576 1044943336  675408326 21606990  .18769316  233.4168  48.36135 6         0 3  .5102281
 4 2002  7492885091  4141523943 1432080334  720338527 22600770   .1739308  331.5323  63.36423 6 .28729656 3  .5104283
 4 2003  8677278663  4729042179 1451437991  691580599 23680870  .14624116  366.4257  61.29158 6  .6395056 3 .51049954
 4 2004  8925480897  5388482107 1385657920  746469467 24726690  .13853057 360.96545  56.03896 6  .6514391 3  .5104884
 4 2005  9595643585  6220574147 1315397188  772808251 25654270  .12423423  374.0369  51.27401 6   .625147 3  .5105151
 4 2006 10417346606  7104711445 1245626269  790852547 26433060  .11131382  394.1029   47.1238 6   .623127 3 .51055604
 4 2007 12776134707  9412161765 1191360243 1036748730 27100540   .1101499  471.4347  43.96076 6  .6246927 3  .5107138
 4 2008 12634956169 10236901594 1123828277 1075453417 27722280  .10505654   455.769  40.53881 6  .6405458 3 .51068187
 4 2009 14008170592 11595133469 1079062230  902301144 28394810  .07781723  493.3356 38.002094 6  .6217199 3  .5107585
 4 2010 14743563274 14698889678 1031099173  957689032 29185510  .06515384  505.1672 35.329147 6   .645614 3 .51078266
 4 2011 15740595785 17350694945  976531082 1097137284 30117410  .06323305  522.6411 32.424137 6  .6468787 3  .5108183
 4 2012 17267933277 19136499341  953218483 1060751259 31161380  .05543079  554.1453  30.58974 6  .6410681 3  .5108826
 4 2013 18416377364 19621802455  896922510  916920660 32269590  .04672968  570.7038 27.794666 6  .6464872 3  .5109164
 4 2014 18982386671 19550702567  809259473  837661844 33370800  .04284561  568.8322 24.250526 6  .4097601 3  .5109126
 4 2015 18713048410 18713048410  744252334  744252334 34413600  .03977184   543.769  21.62669 6 .54373574 3 .51086146
 4 2016 19021914408 18037637165  689672188  657075292 35383030 .036428012  537.5999  19.49161 6         0 3  .5108488
 4 2017 19526929963 18623026651  666428610  578753034 36296110  .03107728  537.9896 18.360882 6         0 3 .51084965
 4 2018 19835598333 17986967500 1122829139  931880027 37171920  .05180862  533.6178  30.20638 6  .5270137 3  .5108407
 4 2019 20634468349 17876546427 1015595580  851545152 38041760  .04763477 542.41626  26.69686 6   .524656 3 .51085865
 8 1990  5274245821  2145774521  560114888  428496505  3286070  .19969316 1605.0315  170.4513 4         0 3  .5130271
 8 1993  3861338953  1700439874  154157764  125767201  3195200  .07396157 1208.4812  48.24667 4  .6040229 3  .5122178
 8 1994  4181940822  1880950821  145443045  125719469  3146520  .06683826 1329.0686  46.22346 4  .6583417 3  .5124639
 8 1995  4739072837  2392764887  160719942  155988530  3112920  .06519175 1522.3883  51.62996 4  .5497537 3  .5128584
 8 1996  5170410969  3199642024  188124618  155433263  3098700  .04857833 1668.5742  60.71082 4  .5354103 3  .5131567
 8 1997  4610049287  2224654241  146057340  101965734  3099750  .04583442 1487.2327  47.11907 4  .4544601 3  .5127867
 8 1998  5017086636  2554868837  206519276  120689616  3110700  .04723907  1612.848  66.38997 4  .7088562 3   .513043
 8 1999  5663824817  3221670165  233283743  146019874  3122700  .04532428  1813.759  74.70578 4  .7213641 3   .513453
 8 2000  6057247912  3487586302  249474241  150589639  3129250  .04317876 1935.6868  79.72334 4  .7377325 3  .5137018
 8 2001  6559593147  3926887597  263837307  160961687  3129700  .04098963 2095.9175  84.30115 4  .7439562 3  .5140287
 8 2002  6857173576  4355865889  274862476  177133979  3126180  .04066562 2193.4673  87.92279 4  .7135162 3  .5142278
 8 2003  7236281323  5561459461  327911172  229365194  3118020  .04124191 2320.7937 105.16647 4  .6891021 3  .5144876
 8 2004  7635347831  7177030365  347648294  299825869  3104890  .04177576  2459.136 111.96799 4  .6965503 3  .5147699
 8 2005  8057313206  8052079314  395915701  356374257  3086810  .04425866 2610.2395 128.26047 4  .6537802 3  .5150783
 8 2006  8532902873  8896076004  447491283  436350501  3063020  .04904977  2785.781  146.0948 4  .6482455 3  .5154365
 8 2007  9043447373 10677322220  504112398  565560820  3033990  .05296841  2980.711 166.15494 4  .6657663 3  .5158343
 8 2008  9721714044 12881352058  478755671  643779238  3002680  .04997762  3237.679  159.4428 4  .6531296 3  .5163586
 8 2009 10047807410 12044210390  492614700  626006894  2973040  .05197575  3379.641 165.69394 4  .6646512 3 .51664835
 8 2010 10420269257 11926948284  549640334  650271788  2948030  .05452122  3534.655 186.44327 4   .667496 3  .5169647
 8 2011 10685510487 12890873323  607197439  729866711  2928600  .05661887  3648.675  207.3337 4   .674406 3  .5171973
 8 2012 10836949164 12319779604  512126076  568487378  2914090  .04614428  3718.811 175.74133 4  .6607661 3  .5173404
 8 2013 10945534087 12776280738  562552082  646455586  2903790   .0505981  3769.396  193.7303 4  .6591358 3 .51744366
 8 2014 11139761173 13228240079  615282097  704512442  2896310  .05325821  3846.191 212.43655 4   .664556 3 .51760036
 8 2015 11386924853 11386924853  645808390  645808390  2890520  .05671491 3939.4036  223.4229 4  .7497118 3 .51779056
 8 2016 11764400523 11861356451  675135674  674249719  2886430  .05684423 4075.7615  233.8999 4  .7355759 3 .51806885
 8 2017 12211706325 13019729856  759064475  801776692  2884170  .06158167 4234.0454 263.18298 4  .7344699 3 .51839185
 8 2018 12708881696 15147025232  806677570  931221479  2882740  .06147883  4408.612 279.83014 4  .7342588 3 .51874804
 8 2019 12990264363 15278072762  849713046  959848383  2880910 .062825225 4509.0835 294.94604 4  .7342588 3  .5189531
12 1990 80470577790 61751375957 4832504583 7065837057 25758870  .11442396  3123.995 187.60545 5 .56680983 3 .51612663
12 1991 79504930386 46565003199 4798677031 5095171687 26400470  .10942062  3011.497 181.76483 5 .55460024 3  .5158971
12 1992 80936020962 49105553595 4529951212 5388304531 27028330  .10972902 2994.4885  167.6001 5  .5333213 3  .5158624
12 1993 79236363907 50846930343 4471061816 5187863527 27635520  .10202904  2867.193 161.78677 5 .52828693 3 .51560265
12 1994 78523239367 42330711146 4274335141 4270757455 28213780  .10089029  2783.152 151.49814 5 .51635313 3  .5154311
12 1995 81507118372 41971488420 4214494569 3697157510 28757790  .08808736  2834.262  146.5514 5  .4850963 3  .5155354
12 1996 84848908978 46836290499 3847833435 3460092904 29266420  .07387632   2899.19 131.47606 5   .477547 3  .5156679
12 1997 85782246924 48068457028 3701615771 3368896781 29742980  .07008539 2884.1174 124.45342 5         0 3 .51563716
12 1998 90157144614 48079007974 4012551551 3798146618 30192750  .07899802  2986.053 132.89784 5         0 3  .5158452
12 1999 93042174640 48531031757 4076752399 3505527079 30623410  .07223269 3038.2695 133.12535 5         0 3 .51595175
12 2000 96577777276 54666896857 4139114423 3276999541 31042240  .05994486  3111.173 133.33813 5         0 3 .51610047
12 2001 99475110594 55056733057 4313240349 3432252902 31451510  .06234029  3162.809 137.13937 5         0 3 .51620585
12 2002   1.050e+11 56819210891 4542512513 3452766594 31855110  .06076759 3296.1746 142.59918 5         0 3   .516478
12 2003   1.130e+11 67863851626 4617642220 3720883688 32264160  .05482865  3502.338 143.11986 5         0 3  .5168987
12 2004   1.170e+11 85332517817 4728606728 4368154143 32692150   .0511898  3578.841 144.64043 5         0 3  .5170548
12 2005   1.240e+11   1.030e+11 4816015354 4601340228 33149720   .0446732  3740.605 145.28073 5         0 3  .5173849
12 2006   1.260e+11   1.170e+11 4955137069 4932646838 33641010  .04215937 3745.4285 147.29454 5         0 3  .5173948
12 2007   1.310e+11   1.350e+11 5088703238 5505289469 34166980  .04077992  3834.111  148.9363 5   .609933 3 .51757574
12 2008   1.340e+11   1.710e+11 5392578565 6330887377 34730600 .037022732  3858.269  155.2688 5  .6108037 3 .51762503
12 2009   1.360e+11   1.370e+11 5895044737 6420143156 35333880  .04686236  3848.997  166.8383 5  .3561771 3  .5176061
12 2010   1.410e+11   1.610e+11 6052354606 6729456789 35977450  .04179787 3919.1216 168.22633 5 .46071514 3  .5177492
12 2011   1.450e+11   2.000e+11 6288483502 7321936163 36661440  .03660968  3955.109 171.52855 5   .273728 3  .5178226
12 2012   1.500e+11   2.090e+11 6550986139 7534709160 37383900  .03605124  4012.422  175.2355 5 .28442323 3 .51793957
12 2013   1.540e+11   2.100e+11 6802273837 7776085063 38140140 .037028976  4037.741 178.34947 5   .300954 3 .51799124
12 2014   1.600e+11   2.140e+11 7016456728 8340052419 38923690  .03897221 4110.6074 180.26186 5 .31376415 3 .51813996
12 2015   1.660e+11   1.660e+11 7336274552 7336274552 39728020  .04419443  4178.411 184.66248 5  .3705145 3  .5182783
12 2016   1.710e+11   1.600e+11 7600979295 7056637058 40551400  .04410398 4216.8706  187.4406 5  .3705145 3  .5183568
12 2017   1.740e+11   1.700e+11 7934997210 7346831009 41389170  .04321665 4203.9985 191.71675 5  .3705145 3  .5183305
12 2018   1.760e+11   1.750e+11 8216694964 7436073462 42228420  .04249185  4167.809  194.5774 5         0 3 .51825666
12 2019   1.770e+11   1.710e+11 8519570680 7575810999 43053050  .04430299  4111.207  197.8854 5         0 3 .51814115
24 1991 35792474873 16189237424 1981457609 1016364681 12248900  .06278027  2922.097 161.76617 3         0 3 .51571465
24 1992 33702809709 18586675505 1539592564  735830295 12657360  .03958913 2662.7046 121.63615 3         0 3 .51518536
24 1993 25619724169 13467953136 1450296191  761606416 13075040  .05654953 1959.4375 110.92097 3         0 3 .51375026
24 1995 29857295202  6642229111 1414743628  265031328 13945210  .03990096  2141.043 101.45015 3         0 3  .5141208
24 1996 33901277662  8725773846 1451526961  300668715 14400720 .034457542 2354.1377 100.79544 3         0 3  .5145557
24 1997 36367350628 10226790656 1586518972  449465122 14871570  .04394977  2445.428 106.68134 3         0 3 .51474196
24 1998 38073396300  8617787793 1664258399  539454645 15359600  .06259781  2478.801 108.35298 3         0 3  .5148101
24 1999 38903963532  8227190091 1782420748  264960469 15866870 .032205462  2451.899   112.336 3         0 3  .5147552
24 2000 40092333430 12207354573 1941056194  352772925 16395480  .02889839 2445.3284 118.38972 3         0 3  .5147418
24 2001 41351232699 11948601236 2090682673  462762726 16945750  .03872945 2440.2126 123.37505 3         0 3 .51473135
24 2002 47359566810 15285592487 2272463879  559731748 17519420 .036618255  2703.261 129.71114 3         0 3  .5152681
24 2003 48775545863 17812704626 2352193499  712475148 18121480  .03999814 2691.5874  129.8014 3         0 3  .5152443
24 2004 54117975511 23552045850 2751454295 1102692818 18758140  .04681941 2885.0396 146.68056 3         0 3 .51563907
24 2005 62251473449 36970878079 2984452262 1446628304 19433600  .03912886  3203.291 153.57176 3         0 3 .51628846
24 2006 69502497165 52381025105 4364285817 2209968430 20149910  .04219025  3449.271 216.59084 3         0 3  .5167904
24 2007 79239331721 65266415707 4640343290 3466475980 20905360  .05311271 3790.3835 221.96907 3         0 3  .5174865
24 2008 88085965989 88538664888 4762614267 3382548902 21695640   .0382042  4060.077 219.51942 3         0 3 .51803684
24 2009 88842229341 70307193221 4946579182 4109629970 22514280  .05845248  3946.039 219.70853 3         0 3 .51780415
24 2010 93159263074 83799478930 5444855344 4194167642 23356250  .05005004 3988.6226   233.122 3         0 3 .51789105
end
label values _merge _merge
label def _merge 3 "matched (3)", modify

[Tiago Pereira]

You may want to fit a restricted cubic splines model. Check -rcsgen-

[Hugo Rocha]

Is there a particular package required to use rcsgen?, I am taking a look now. Thanks!

[Tiago Pereira]

rcsgen is a package created by Paul Lambert (University of Leicester).

Check one of the examples below:

    sysuse auto, clear  
    rcsgen weight,    gen(rcs) df(3)
    regress mpg rcs1-rcs3
    predictnl pred = xb(), ci(lci uci)
    twoway (rarea lci uci weight, sort)  (scatter mpg  weight, sort) (line pred weight, sort lcolor(black)), legend(off)

[Nick Cox]

I've rarely seen data on GDP pc without thinking that it would be better logged.

An even more fundamental problem is that you have panel data here, so expecting a simple curve across not just many countries but also several years is ambitious.

[Hugo Rocha]

I've rarely seen data on GDP pc without thinking that it would be better logged.

An even more fundamental problem is that you have panel data here, so expecting a simple curve across not just many countries but also several years is ambitious.

I can isolate for one country and do it separately for a set of countries as well.

[Hugo Rocha]

rcsgen is a package created by Paul Lambert (University of Leicester).

Check one of the examples below:

 sysuse auto, clear
rcsgen weight, gen(rcs) df(3)
regress mpg rcs1-rcs3
predictnl pred = xb(), ci(lci uci)
twoway (rarea lci uci weight, sort) (scatter mpg weight, sort) (line pred weight, sort lcolor(black)), legend(off)

Thank you! let me try it with my data