I'm currently working with a panel dataset containing information on 7903 cities from 2012 to 2022. My focus is on studying the digitalization of city administrations using survival models. Specifically, I've defined t0 to mark the beginning of the period, and t2 for the end of the period corresponding to either the year of digitalization (if the event occurred) or the end of the panel. The binary variable treat_v indicates whether the event was realized. Additionally, the variable PRO_COM serves as a unique identifier for cities. My independent variables include total population, average income, and administration software expenditure.
My dataset looks like:
PRO_COM year treat_v t0 t2 total_ln Avg_income_ln software_ln
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1001 2012 0 0 1 7.88 9.95 13.6
2 1001 2013 0 1 2 7.91 9.96 0
3 1001 2014 0 2 3 7.92 9.98 14.6
4 1001 2015 0 3 4 7.90 10.0 14.0
5 1001 2016 0 4 5 7.88 10.0 12.0
6 1001 2017 0 5 6 7.89 10.0 0
7 1001 2018 0 6 7 7.89 10.0 0
8 1001 2019 0 7 8 7.88 10.0 0
9 1001 2020 1 8 9 7.87 10.0 0
10 1002 2012 0 0 1 8.26 9.87 14.0
11 1002 2013 0 1 2 8.26 9.88 13.4
12 1002 2014 0 2 3 8.24 9.88 12.8
I need to use an accelerated failure time model and a spatial accelerated failure time model. I'm employing the survregbayes function from the spBayesSurv package. Is there a way to implement robust standard errors clustered by city in this model with this function? Here's the code I've used:
install.packages('spBayesSurv')
library(spBayesSurv)
mcmc <- list(nburn = 5000, nsave = 10000, nskip = 5, ndisplay= 2000)
prior <- list(maxL = 15)
res_prova <- survregbayes(Surv(t0, t2, treat_v) ~ total_ln + Avg_income_ln + software_ln
, data=df_prova,
survmodel="AFT", dist="lognormal",InitParamMCMC=T, mcmc=mcmc,prior=prior)
summary.survregbayes(res_prova)
Any guidance on implementing robust standard errors clustered by city in this model would be greatly appreciated. Thank you!
Here there is a reproducible example of my dataset:
df_prova <- structure(list(PRO_COM = c(1001, 1001, 1001, 1001, 1001, 1001,
1001, 1001, 1001, 1002, 1002, 1002, 1002, 1002, 1002, 1002, 1002,
1002, 1004, 1004, 1004, 1004, 1004, 1004, 1004, 1004, 1004, 1006,
1006, 1006, 1006, 1006, 1006, 1006, 1006, 1006, 1011, 1011, 1011,
1011, 1011, 1011, 1011, 1011, 1020, 1020, 1020, 1020, 1020, 1020,
1020, 1020, 1020, 1022, 1022, 1022, 1022, 1022, 1022, 1022, 1022,
1024, 1024, 1024, 1024, 1024, 1024, 1024, 1028, 1028, 1028, 1028,
1028, 1028, 1029, 1029, 1029, 1029, 1029, 1029, 1029, 1029, 1029,
1029, 1030, 1030, 1030, 1030, 1030, 1030, 1030, 1030, 1030, 1030,
1031, 1031, 1031, 1031, 1031, 1031, 1031, 1031, 1031, 1034, 1034,
1034, 1034, 1034, 1034, 1034, 1038, 1038, 1038, 1038, 1038, 1038,
1038, 1038, 1040, 1040, 1040, 1040, 1040, 1040, 1040, 1040, 1054,
1054, 1054, 1054, 1054, 1054, 1054, 1054, 1054, 2049, 2049, 2049,
2049, 2049, 2049, 2049, 2049, 2049, 1285, 1285, 1285, 1285, 1285,
1285, 1285, 1285, 1285, 1285, 4056, 4056, 4056, 4056, 4056, 4056,
4056, 4056, 4056, 4056, 6124, 6124, 6124, 6124, 6124, 6124, 6124,
6124, 6124, 6124), year = c(2012, 2013, 2014, 2015, 2016, 2017,
2018, 2019, 2020, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
2020, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2012,
2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2012, 2013, 2014,
2015, 2016, 2017, 2018, 2019, 2012, 2013, 2014, 2015, 2016, 2017,
2018, 2019, 2020, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
2012, 2013, 2014, 2015, 2016, 2017, 2018, 2012, 2013, 2014, 2015,
2016, 2017, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020,
2021, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021,
2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2012, 2013,
2014, 2015, 2016, 2017, 2018, 2012, 2013, 2014, 2015, 2016, 2017,
2018, 2019, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2012,
2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2012, 2013, 2014,
2015, 2016, 2017, 2018, 2019, 2020, 2012, 2013, 2014, 2015, 2016,
2017, 2018, 2019, 2020, 2021, 2012, 2013, 2014, 2015, 2016, 2017,
2018, 2019, 2020, 2021, 2012, 2013, 2014, 2015, 2016, 2017, 2018,
2019, 2020, 2021), treat_v = c(0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), t0 = c(0,
1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3,
4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6,
7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2,
3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2,
3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0,
1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4,
5, 6, 7, 8, 9), t2 = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4,
5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7,
8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2,
3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 1, 2,
3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2,
3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7,
8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3,
4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), total_ln = c(7.88495294575981,
7.90912218321141, 7.91862865334224, 7.90137735379262, 7.88004820097158,
7.88645727097769, 7.88532923927319, 7.87625888230323, 7.87131120332341,
8.25790419346567, 8.25660734462616, 8.24038511551633, 8.24222989137223,
8.23244015847034, 8.22309055116153, 8.20821938349683, 8.19229373114764,
8.18813341451048, 7.49942329059223, 7.49831587076698, 7.49164547360513,
7.46965417293213, 7.454719949364, 7.43897159239586, 7.42714413340862,
7.40367029001237, 7.40488757561612, 8.75557997214314, 8.76092337633884,
8.76295892076673, 8.76201995356159, 8.76201995356159, 8.76514642163902,
8.76592651372944, 8.7649903301691, 8.7681075396758, 6.7719355558396,
6.76734312526539, 6.78784498230958, 6.79234442747081, 6.78784498230958,
6.78671695060508, 6.76272950693188, 6.75925527066369, 8.10167774745457,
8.0925452638913, 8.09833884618906, 8.08548677210285, 8.0702808933939,
8.07464907506665, 8.07837810362652, 8.07246736935477, 8.06808962627824,
8.08733292647335, 8.07868822922987, 8.0805469658245, 8.07496035911586,
8.07090608878782, 8.05737748855799, 8.0507033814703, 8.0519780789023,
9.80604009037016, 9.80697665215529, 9.81022028456569, 9.80989090379854,
9.80592984894132, 9.80388818731337, 9.79701530802561, 9.51811914612709,
9.51826615090501, 9.50509735809993, 9.50479942870699, 9.50248746138712,
9.35625724687634, 6.31716468674728, 6.33859407820318, 6.32256523992728,
6.33327962813969, 6.3261494731551, 6.36647044773144, 6.37331978957701,
6.36818718635049, 6.37672694789863, 6.38350663488401, 8.21878715560148,
8.21256839823415, 8.21148291644507, 8.20985248130127, 8.21121136179302,
8.21229713822977, 8.19918935907807, 8.19726337141434, 8.18757739559151,
8.18590748148232, 6.73340189183736, 6.73221070646721, 6.71659477352098,
6.69332366826995, 6.68710860786651, 6.66949808985788, 6.68710860786651,
6.66185474054531, 6.67203294546107, 9.04168500594604, 9.05028898382796,
9.05415428878685, 9.06056344665796, 9.05777177333158, 9.05800471067248,
9.05963375455148, 9.05380351415596, 9.05450494041805, 9.05310159554969,
9.05122740031911, 9.05648964715792, 9.05555615817532, 9.05286751315162,
9.06508335931904, 7.35436233042148, 7.37086016653672, 7.35564110297425,
7.34987370473834, 7.33236920592906, 7.33367639565768, 7.3356339819272,
7.3304052118444, 6.33150184989369, 6.33505425149806, 6.34738920965601,
6.32793678372919, 6.34035930372775, 6.35088571671474, 6.3456363608286,
6.37331978957701, 6.38687931936265, 8.99044155082686, 8.98582087448204,
8.97233695775495, 8.97233695775495, 8.962391701743, 8.96200720958831,
8.95789673495042, 8.95260537589235, 8.95480275285097, 6.86797440897029,
6.8596149036542, 6.87005341179813, 6.83947643822884, 6.80682936039218,
6.8001700683022, 6.82762923450285, 6.81673588059497, 6.81892406527552,
6.85329909318608, 6.77878489768518, 6.8001700683022, 6.79570577517351,
6.8001700683022, 6.80461452006262, 6.78445706263764, 6.75460409948796,
6.71417052990947, 6.7286286130847, 6.72383244082121, 5.4553211153577,
5.45958551414416, 5.45958551414416, 5.48893772615669, 5.45958551414416,
5.4380793089232, 5.37063802812766, 5.28826703069454, 5.29831736654804,
5.31811999384422), Avg_income_ln = c(9.95100918119281, 9.95823055302686,
9.98051362913682, 10.0147662587243, 10.0278481007699, 10.0207687542477,
10.0270911612452, 10.0330884347624, 10.0182449760809, 9.87347148493794,
9.87561183232373, 9.88441973683242, 9.92989801004952, 9.93404314940026,
9.91981091852989, 9.95102684439529, 9.94812688711294, 9.93168066211429,
9.86416456839784, 9.86945437321638, 9.8786032427481, 9.90554554577413,
9.90538663594792, 9.92630779643173, 9.98743798079886, 9.95116613437205,
9.92429761999365, 10.0791467276647, 10.0785916165192, 10.0979747153919,
10.1093433768296, 10.1243592564318, 10.1313177524273, 10.1421991535854,
10.1472236062147, 10.1449984323863, 9.69115927507824, 9.71567911722924,
9.69160543576198, 9.71492718807839, 9.71905607124579, 9.71676743188018,
9.73680470874232, 9.76639980510036, 9.92603914306631, 9.94982592757546,
9.93604995592034, 9.94077330019114, 9.92289898150387, 9.9297250950782,
9.95786635866039, 9.94516720091473, 9.94471127303208, 9.98806441661829,
10.0060145152037, 10.0188792059974, 10.0196752619576, 10.0391642554939,
10.0549671389672, 10.0628991405105, 10.0664813284644, 9.91360955401906,
9.91351724905354, 9.92354149929004, 9.93975675111295, 9.94835886993867,
9.94777943409724, 9.9610919946104, 9.94103238656982, 9.95398197956198,
9.96272563160125, 9.99133830689192, 9.99197673221995, 9.98239900872108,
9.79889084129117, 9.82357613323638, 9.81960720165952, 9.84084181716343,
9.83157910177803, 9.81202650121668, 9.82928231359217, 9.86134156493655,
9.88703823704679, 9.94910113054451, 9.87753724879351, 9.89724249523534,
9.90607947398146, 9.90519143546865, 9.9142315765518, 9.91808978798171,
9.9138858431683, 9.96099551419382, 9.92927613508482, 9.97428918701486,
9.89007659776826, 9.86333699424153, 9.9545987455228, 9.9208273973496,
9.90358301867181, 9.91834450300624, 9.94004379148733, 9.97890193608502,
9.91343037983815, 9.87106393853391, 9.89693775599761, 9.90776930489766,
9.92985290969328, 9.92667574440502, 9.94548806196369, 9.9558504170754,
10.0045461815298, 10.0040571381268, 10.0066109610899, 10.0315316097753,
10.0508425375385, 10.0548054946526, 10.0803418749731, 10.0722735726998,
9.86344913382924, 9.8822058423329, 9.89932760886725, 9.9186194411311,
9.92663355064925, 9.92785383788164, 9.93416174109291, 9.93626525965158,
9.72949831819389, 9.74745110136822, 9.76147071758372, 9.78655316657569,
9.78027885232349, 9.77175673570384, 9.80192727580378, 9.80966626378322,
9.80361746543969, 9.78123384047072, 9.80427963489623, 9.81036162920114,
9.83390170021683, 9.84115273424143, 9.83480731766295, 9.8625013159703,
9.86389768912967, 9.85485403369568, 9.90384314301659, 9.87493826296659,
9.93999420618657, 9.9363366111413, 9.88791732224616, 9.91241093108613,
9.93564514067879, 9.95273053800706, 9.93609430730758, 9.98596216242694,
9.38374741621789, 9.45184851358746, 9.41579133089942, 9.4335946863867,
9.43041070002655, 9.47186127965726, 9.50965151262306, 9.52028053328393,
9.61666016444978, 9.601794269207, 9.92272263716164, 9.92155595175208,
9.97346959372429, 9.97717523796906, 9.98008692406993, 9.97383699840932,
10.0434836632773, 10.0580276164739, 10.0472839821578, 10.1340064364994
), software_ln = c(13.6312715640622, 0, 14.5906381061831, 13.9808631189336,
11.9511868474935, 0, 0, 0, 0, 13.9512740825277, 13.4135617603837,
12.7855862943222, 14.0587139583923, 13.4916332709192, 11.5230440984914,
0, 0, 8.86460536807578, 14.3240020597858, 14.2704684404963, 14.3539406483169,
14.3590347100635, 14.4039570051622, 0, 0, 0, 0, 14.6899153962449,
14.743230526571, 14.8680220129697, 14.867534606448, 14.7851149219686,
0, 12.0118869877927, 13.0448320136652, 13.6447471477057, 12.041203898549,
11.5870212941931, 11.8499047158951, 11.6818408931813, 11.8541506740155,
0, 0, 0, 14.6084447007496, 14.8797266899012, 14.5808281562597,
14.4534119062982, 14.5328790205436, 0, 0, 0, 12.4344862854999,
15.5784594599531, 15.616244799835, 15.601877681259, 16.0261207030794,
15.8415794079656, 13.2077554440183, 12.4772479782762, 14.1436712059748,
16.0849414751002, 16.3584853095525, 16.3906017740141, 16.4729037534324,
16.4527397890538, 0, 0, 15.7158535433994, 15.5645488345031, 15.7467622230442,
16.181562254047, 15.8068244635054, 0, 13.5352952067061, 13.3630670434619,
13.5382275605494, 13.2382690964485, 13.4455013928394, 0, 0, 0,
0, 0, 14.4477457004077, 14.4011337731848, 14.6907330149937, 14.4478886375212,
14.379121212925, 0, 0, 0, 0, 0, 13.3087765521015, 13.1040384977011,
14.059750800873, 13.7113393348177, 13.8261547074755, 0, 0, 0,
0, 13.3480828082904, 15.2490379191216, 14.9543888466163, 15.0572692003486,
14.2424951194326, 11.8263995454557, 12.9520233545, 14.1082376329627,
14.2414734765094, 14.2756488089983, 14.306957012763, 14.4418494433975,
0, 0, 0, 14.5645043756946, 13.8370029333024, 13.9564031652447,
14.1991805350585, 14.0526209177311, 0, 0, 13.7015599192844, 12.9618729772842,
13.0202265489677, 12.9846242876825, 13.0867589974288, 13.6406868221277,
0, 11.5492670373727, 11.6915819803642, 0, 14.9882920311983, 14.8396647106143,
15.0073122944249, 15.1917174613295, 15.4025151137662, 0, 0, 0,
0, 0, 11.2758477829995, 0, 11.2451244481116, 0, 0, 13.2746483178217,
11.5374326945246, 0, 0, 13.2678687944066, 13.7453552253669, 12.2126807637444,
13.5598386496419, 13.8382813249919, 0, 0, 0, 11.2009643610583,
11.759621466942, 12.1209449478476, 13.3736869167548, 12.3430524605059,
12.7509953018642, 13.2911690041448, 0, 0, 0, 0, 0)), row.names = c(NA,
-174L), groups = structure(list(.rows = structure(list(1L, 2L,
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