R quantreg : boundary condition rq() function goes into infinite loop - r

Question

I'm facing a problem that
rq(y ~ x, tau = 0.50, method = "br")
doesn't complete calculation. There is no error and warning.
I traced code and found .Fortran() in rq.fit.br() does not finish calculation. I'm not familiar with Fortran so let me ask this question here.
I would like to know boundary condition that causes this infinite loop. I can avoid this endless calculation if I know it.
Thank you for your help in advance.
# The problematic input data :
y <- c(
0, 0, 0, 0, 0, 0, 0.234, 0.117, 0.351, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0,
0.117, 0, 0, 0, 0, 0.117, 0.117, 0, 0.117, 0.117, 0, 0, 0.117, 0, 0, 0, 0,
0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.234, 0, 0.117, 0.117, 0,
0.351, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.234, 0, 0, 0, 0.117, 0.117, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0,
0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.117, 0, 0, 0, 0, 0.117, 0.117, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.117, 0, 0, 0, 0.234, 0, 0.234, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0, 0.234,
0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.585, 0, 0, 0.117, 0.234,
0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0.234, 0.117, 0, 0, 0.117, 0.234, 0, 0.117, 0,
0, 0, 0.234, 0, 0.117, 0, 0.117, 0.117, 0, 0, 0, 0, 0.234, 0, 0, 0.234, 0.234,
0.234, 0.234, 0.117, 0, 0, 0, 0, 0, 0, 0.117, 0.117, 0, 0, 0, 0, 0, 0, 0, 0,
0.117, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0.117,
0.117, 0, 0.117, 0, 0.117, 0, 0, 0.117, 0, 0.117, 0, 0, 0.234, 0, 0, 0, 0, 0,
0, 0, 0.234, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0.234, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0.234, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0, 0.117, 0, 0.117, 0, 0, 0, 0.117,
0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0.117, 0, 0, 0.234, 0.351, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0,
0.117, 0, 0, 0, 0.117, 0.117, 0, 0.117, 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, 0.117, 0, 0, 0, 0, 0,
0.117, 0, 0, 0.117, 0.117, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117,
0.234, 0, 0, 0, 0, 0, 0.117, 0.117, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0.117, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0,
0, 0.117, 0, 0.703, 0.117, 0.117, 0.234, 0, 0.117, 0, 0.117, 0.117, 0, 0, 0,
0.117, 0, 0, 0, 0.234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.234, 0, 0.117, 0, 0, 0,
0.117, 0, 0, 0, 0, 0, 0.117, 0.234, 0.234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117,
0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0, 0, 0,
0, 0, 0, 0.117, 0.234, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0.234, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0.234, 0, 0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.234, 0, 0,
0, 0, 0.117, 0, 0, 0, 0, 0, 0, 0, 0.351, 0, 0, 0, 0, 0, 0, 0, 0.117, 0.117, 0,
0.234, 0.117, 0, 0, 0.117, 0.234, 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, 0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0.117, 0.351, 0, 0.468, 0.234, 0.234, 0, 0, 0, 0, 0.234, 0, 0.117, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117, 0, 0,
0.117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.234, 0, 0,
0, 0, 0, 0, 0, 0.117, 0, 0, 0.585, 0, 0, 0.234, 0, 0.117, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.468, 0, 0, 0, 0, 0.117, 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, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0.234, 0, 0, 0, 0, 0, 0, 0.234, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0.351, 0.234, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.117,
0.117, 0, 0, 0, 0
)
x <- c(
24.4018079, 28.8807817, 40.4440632, 22.6231939, 21.5390181, 27.6194884,
32.9537276, 23.0931019, 24.6333219, 32.2419818, 23.401991, 32.4394215,
18.980218, 36.1419718, 52.0712614, 24.5704906, 60.3779992, 31.7383285,
33.7286139, 17.3276892, 30.7991282, 50.9481105, 31.080127, 53.3908315,
17.6551953, 27.7416689, 27.2468471, 27.1576005, 23.1742951, 41.4709552,
41.967935, 27.8544524, 19.8297627, 27.620431, 15.2351169, 18.3377948,
25.0163879, 25.2405723, 33.3461355, 48.2266249, 24.3607428, 27.7216683,
26.6296912, 28.4811453, 30.1760888, 26.8148476, 25.128683, 23.8027916,
30.7355199, 30.5610606, 41.6265463, 26.175877, 27.9212294, 37.9277741,
25.1736093, 24.4808208, 28.8720055, 23.4672164, 20.0011668, 24.0894199,
28.4711092, 21.9160106, 26.516336, 16.7173241, 24.9135346, 26.2081573,
21.091112, 32.6515246, 30.2453634, 24.3514448, 27.8053967, 27.0362428,
25.8530264, 40.8166319, 21.7807126, 30.2581439, 35.0799978, 38.2687556,
46.9241502, 35.4400451, 25.0417079, 20.9683041, 18.9136417, 26.9527511,
32.5955477, 24.1518614, 33.2041696, 29.5174409, 31.9583297, 38.5216324,
46.6958841, 31.8675876, 29.4891597, 32.2909144, 27.8331436, 27.3906857,
36.2563286, 17.9700065, 26.2149315, 29.4081605, 40.4465888, 24.6274318,
32.0388361, 22.6569988, 21.6720743, 16.7256267, 16.852218, 13.8423948,
25.4936663, 26.6811577, 26.812348, 29.8681522, 27.7055245, 15.006916,
27.7348524, 26.4439379, 30.0100718, 37.0017757, 14.5881997, 31.0969282,
18.1142671, 14.4049902, 37.6274298, 44.3967524, 27.5595956, 19.4116367,
20.0019715, 16.9236606, 26.246288, 35.607556, 30.3840455, 30.3815949,
24.5976682, 37.809445, 21.577438, 21.8125242, 14.5899396, 23.6670936,
25.268452, 31.6692812, 22.690343, 24.3731279, 33.3598046, 29.6117162,
39.1297631, 15.2346245, 26.0681545, 25.4259568, 42.6836935, 23.7939986,
41.4657106, 25.8638121, 41.9544915, 26.7980014, 19.7041992, 19.8906546,
33.3622323, 28.7616006, 36.8331863, 38.3432724, 13.2298725, 18.7853833,
25.4594015, 30.0428453, 24.0999749, 28.5411825, 23.7460138, 15.7947625,
36.502406, 46.1166203, 26.2032695, 19.0759098, 25.7247696, 27.8923323,
35.3435019, 28.7847773, 28.7935475, 18.5619149, 39.1965545, 28.0817298,
26.4450131, 28.0224018, 30.3223318, 35.6540999, 28.2432116, 25.3455388,
25.9718787, 32.34494, 44.2724262, 31.45872, 29.6019651, 20.3401629,
18.4580252, 37.232467, 34.3359164, 44.1724399, 23.4782245, 27.4645108,
27.1781198, 18.6422675, 19.2272688, 30.8315997, 25.5801722, 22.4312101,
15.3473977, 27.472274, 24.4604204, 22.5680019, 14.6711321, 17.4751012,
59.8056645, 24.4605417, 22.4188914, 24.111513, 18.9521777, 29.562426,
21.1020296, 31.1739265, 24.7056341, 22.9724849, 22.0160131, 30.531877,
18.4457535, 28.0308361, 27.8577984, 23.3738145, 33.924868, 23.397325,
29.6069946, 18.181721, 31.6132161, 25.0790305, 28.2104791, 22.931505,
29.4002554, 18.5959381, 25.0670957, 18.7296132, 24.770169, 24.9230376,
29.4113636, 20.8127034, 24.3650603, 16.2016467, 24.9011517, 28.7432186,
31.7488893, 15.4118624, 32.5145935, 15.0132364, 22.2026089, 28.3184513,
30.7058983, 30.7271516, 42.0031247, 44.6998899, 36.0661786, 21.6462755,
32.1853902, 43.8380628, 27.4295037, 33.3694872, 24.8508583, 26.4525086,
27.7657697, 28.7656539, 27.8993627, 24.1259411, 31.7960144, 20.1717771,
24.6846924, 31.3695283, 16.9871094, 27.3006097, 24.353586, 24.2973128,
22.2143346, 32.5385164, 46.238405, 15.87873, 24.8137702, 31.6289988,
16.7381839, 28.4660331, 38.6910685, 34.4105544, 26.0612181, 21.1271684,
26.6423251, 24.5583478, 23.493619, 26.539979, 28.6731828, 28.239095,
18.9509248, 24.0585342, 27.0629323, 25.4465092, 26.7561273, 32.5888733,
34.5808151, 29.2271733, 39.7868991, 25.690253, 39.4753614, 15.3304099,
43.0529772, 26.977613, 12.5825155, 19.4012753, 21.718714, 26.4869929,
26.1744893, 18.1392682, 27.6152192, 21.0045136, 28.0224205, 26.5692797,
28.9952192, 35.6324021, 27.6756153, 24.1850861, 27.8542562, 30.6187182,
25.4835887, 27.6732922, 27.6414935, 19.2370806, 26.8892099, 23.5372461,
26.8561243, 31.2019592, 42.2955339, 30.0204426, 32.4021614, 20.7569456,
27.2942332, 23.9750141, 26.2850638, 16.7624382, 33.0947322, 24.0859599,
32.1946124, 29.4301999, 30.2732967, 21.4577098, 49.1818696, 51.8139063,
38.768469, 35.5710685, 26.370072, 30.6496823, 39.3829068, 15.2329246,
26.0432293, 35.6630347, 29.6303257, 41.2432668, 45.2378368, 34.3707241,
30.5024637, 19.9775718, 17.801213, 26.1688732, 28.4875885, 29.7568102,
29.1107832, 36.2328291, 31.8214314, 38.6204676, 36.8834063, 42.6788448,
28.7272819, 28.626164, 34.291455, 13.2104893, 46.3331664, 25.6895379,
15.6121566, 24.8888988, 15.5789419, 26.7369002, 46.104393, 23.2856908,
20.3333047, 30.5485, 15.6038882, 28.7037872, 32.3490014, 28.0980547,
30.1026873, 15.7965292, 23.5073005, 23.9334505, 19.6343642, 22.1035284,
24.9623722, 17.4625706, 19.5039162, 28.129359, 26.2476225, 26.7068015,
30.9865519, 26.9848648, 25.3245441, 27.8976892, 27.4579313, 41.9166111,
17.2998378, 29.7315102, 25.7406406, 22.2793813, 36.3643588, 20.9277299,
44.1597183, 27.5133605, 25.6170785, 50.9843355, 26.9664186, 49.9873232,
20.9170467, 24.1125628, 36.8751858, 34.3871658, 20.4164672, 25.8413742,
40.4310466, 21.2163069, 36.3361406, 38.0197324, 33.3294001, 21.4165966,
28.4923429, 22.1280619, 22.4756409, 30.2215385, 41.7292709, 36.8907943,
31.5413965, 26.1837229, 37.0218326, 25.6081831, 28.1776375, 29.8671555,
29.3736138, 35.4604974, 18.7050421, 22.255564, 33.6674798, 29.5201891,
24.0745051, 31.8653496, 27.0345565, 26.0525699, 23.0252921, 28.5281226,
33.71177, 29.0951349, 21.7951779, 31.0860777, 22.6393045, 19.0780616,
24.3621088, 29.5905486, 26.5586841, 42.5486628, 33.6081618, 25.1165999,
17.9542253, 24.9186609, 38.5966133, 17.0141855, 23.0060186, 30.1943135,
27.1080814, 28.6187819, 24.1290464, 41.5916513, 43.4616517, 21.3195541,
26.1493297, 20.9077832, 25.7692305, 29.4261399, 29.2463376, 28.8000356,
25.1911071, 35.8697203, 22.2615425, 31.4633835, 24.1877693, 22.8952581,
15.1601842, 32.3567013, 27.3661214, 39.0040261, 32.0344394, 18.0945006,
23.8093766, 31.8086423, 40.3121132, 30.3588501, 25.9724817, 44.6408476,
43.4099194, 30.3728664, 33.5631618, 23.0705636, 27.4936808, 36.8187291,
32.9492242, 29.5742094, 25.5605033, 23.7780532, 25.3959579, 38.1226182,
24.9726063, 46.6698573, 51.4411263, 25.9290155, 31.1392917, 52.7543492,
31.7838842, 30.0237536, 25.819024, 29.7256644, 28.6428477, 32.1406846,
42.8654594, 33.7451799, 37.9804767, 28.7298898, 26.8582201, 46.1198892,
32.7408768, 55.5203714, 31.495731, 51.0941729, 24.314699, 33.4828115,
24.4570093, 29.5138786, 21.5354954, 30.317556, 24.6148894, 17.7956648,
31.7810597, 30.4743448, 19.8238082, 32.3247417, 27.3858365, 29.8964156,
29.7147584, 25.2144471, 43.6346636, 28.5816332, 26.0747485, 39.6629311,
29.0223235, 28.5093962, 26.6550715, 30.5273411, 20.8669945, 29.1348172,
21.710507, 24.8998055, 32.975078, 39.652974, 17.3980911, 40.1282322,
35.8886658, 27.829678, 49.7612583, 31.9280938, 28.5301198, 27.4779753,
25.1837491, 32.5874968, 25.1871786, 21.9365623, 26.8613984, 24.9095698,
32.8732303, 27.1493754, 22.0098701, 34.8794858, 32.4926707, 15.6674662,
24.9172861, 27.4232858, 28.6305736, 32.8272527, 20.0910068, 40.1099478,
23.6793994, 26.1303681, 32.4211306, 36.3060647, 13.3999648, 29.8795415,
42.9840395, 24.9583988, 22.7460185, 43.3399476, 25.5209943, 18.1369994,
28.7716568, 25.3741116, 30.5742097, 32.1805709, 23.9898692, 28.0885658,
30.6875465, 22.8677012, 34.825549, 29.3668426, 34.999954, 41.5279957,
22.285163, 24.0556159, 15.200475, 21.4487252, 19.0435518, 30.7447739,
15.9420322, 16.7287114, 28.6306528, 29.554746, 16.4364149, 31.3476225,
34.9007223, 30.0167197, 27.4047092, 27.0686892, 26.8545017, 16.7846713,
23.2117939, 31.6776801, 29.9123239, 32.8621553, 21.3552832, 50.75349,
23.991315, 29.7791991, 24.7992546, 27.5752878, 17.4821681, 26.911058,
25.3942484, 31.8553779, 29.6222535, 22.8196871, 31.0947927, 41.7734339,
35.4348117, 20.5096086, 28.8058813, 38.8916449, 24.7993731, 33.1395299,
21.5910174, 27.5014509, 15.826052, 27.9783595, 40.0840328, 28.2133025,
32.194761, 54.2405209, 31.9051349, 25.4699985, 25.2212782, 22.0680464,
14.9236318, 37.6760713, 33.189865, 33.3475948, 23.3487752, 26.42338,
30.3284095, 24.8590412, 15.1272312, 24.4415683, 24.3445192, 32.8710454,
43.5016354, 38.9345868, 15.6964367, 33.7304737, 21.6569327, 26.3130489,
22.4141185, 28.3356213, 31.1180693, 26.1339403, 19.5924288, 27.3062312,
70.0232447, 31.4218925, 31.6894943, 70.6923221, 27.8249275, 45.9796955,
27.5667195, 39.3534247, 25.2532679, 26.6210675, 42.0462846, 57.8231799,
32.1834225, 35.3014761, 21.4324152, 30.7373532, 29.6940796, 51.0814799,
26.3502205, 19.3649445, 24.7811548, 21.3144558, 44.4579779, 30.3942605,
24.9829469, 30.9145726, 22.6600533, 33.542845, 25.0688544, 23.3785057,
31.7691544, 30.4176433, 37.8272268, 36.0808069, 31.3964826, 18.1158916,
22.5676528, 27.3483272, 23.0186353, 20.550375, 39.3741719, 20.2418609,
21.1396468, 66.5203361, 62.4761334, 29.6869787, 26.3493349, 37.4383524,
11.9058338, 26.0618828, 27.7359828, 16.1160718, 15.9020783, 24.2150908,
25.8994792, 27.4616096, 32.8780234, 27.1384018, 14.7083443, 36.2070307,
36.4121969, 30.5070904, 29.0891587, 20.2350553, 25.2963738, 15.7358134,
16.9517607, 34.2212512, 27.7858155, 28.1410475, 29.6620824, 26.7803718,
27.2988802, 19.9575323, 30.1752288, 27.5984041, 28.1399913, 16.9137777,
32.6449213, 23.451331, 30.4658547, 21.8190914, 22.1539569, 24.4125483,
24.8686785, 26.2065556, 16.5003938, 35.8479682, 24.0469412, 40.4014116,
33.4889847, 22.8764475, 47.3298653, 18.5901704, 30.3538952, 36.3691136,
31.4970049, 19.9467581, 29.2147637, 27.4377932, 36.0034333, 37.0777657,
29.8718446, 32.4984043, 32.6625905, 35.8877784, 32.6524614, 54.8709701,
16.2960404, 25.8058264, 23.3658142, 22.3081803, 19.9078811, 63.384812,
28.1309744, 37.47588, 30.4532575, 44.6020145, 33.2618816, 24.0572143,
13.706158, 37.4377234, 26.3083542, 21.7035413, 55.5107049, 15.4091252,
41.8114748, 32.530624, 51.0474142, 46.2803631, 23.4427667, 38.9682187,
26.6724182, 21.1864403, 40.0251724, 36.3530887, 17.4979165, 35.06262,
23.74311, 36.424138, 27.5016505, 16.5533966, 21.071959, 32.0166696,
31.6319279, 58.1904527, 29.5304514, 26.0416582, 33.6718921, 40.8230363,
38.4883028, 27.2786438, 24.1567016, 18.165015, 39.4164839, 25.5206923,
29.2113946, 54.5010605, 28.7706133, 18.5841954, 44.3722705, 20.11255,
29.4044921, 30.7372406, 14.0238355, 33.6927312, 16.1737632, 38.0253688,
26.6644105, 18.53842, 27.7307437, 51.8477646, 32.6874462, 30.5680848,
30.9982972, 27.7979667, 21.532476, 24.7052444, 39.1467731, 58.5943291,
23.1092334, 36.9199715, 29.3797749, 15.8163776, 28.6779247, 33.0831701,
22.6006952, 22.7515948, 38.4527168, 31.9983674, 40.9573834, 23.3273802,
19.8011584, 35.6943063, 35.3977388, 22.0540011, 34.1045856, 27.5684501,
25.5696024, 23.621706, 21.9372108, 30.2297453, 32.0413651, 34.8618642,
37.8348272, 25.6725508, 26.6521851, 18.6582369, 35.5246539, 25.1168522,
25.1152485, 27.4422305, 27.5549447, 40.7587422, 46.997187, 16.5311856,
28.7304576, 28.3537612, 29.3829696, 30.9081955, 33.0904867, 54.6381586,
38.9128035, 35.0343507, 23.9988363, 28.0781288, 22.4621496, 32.9971513,
25.2213571, 30.1988958, 23.9096162, 46.0506056, 32.1925042, 35.8170223,
23.8509302, 38.5036865, 38.731735, 29.397908
)

Answer 1

Pity the poor simplex algorithm! In this example there are 934 observations, 780 of which are 0. So simplex would like to choose which two of the 780 it should pick to make a solution to say that the conditional median of y|x is 0. Any two will do, but how to choose? One could dither the y's, dither(y, value = 1e-8) -- this breaks the ties, and delivers a single precision answer, but as the other responder suggests it is better to switch to method = "fn". Even better would be to avoid using QR at all for problems like this where the response variable is discrete.

Answer 2

Your response vector is a bit too sparse so I am not sure how efficiently the default algorithm can solve that, if you check the help page for rq, under method:
The default method is the modified version of the Barrodale and
Roberts algorithm for l1-regression, used by ‘l1fit’ in S, and is
described in detail in Koenker and d'Orey(1987, 1994), default =
‘"br"’. This is quite efficient for problems up to several thousand
observations, and may be used to compute the full quantile
regressionprocess. [...]For larger problems it is advantageous to use
the Frisch-Newton interior point method ‘"fn"’.
If you need something specifically from the default algorithm, you can try:
library(quantreg)
fit = rq(y ~ x, tau = 0.50, method = "fn")