sim

x <- structure(list(id = 1:240, trt = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 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, 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, 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, 0, 0, 0, 0, 0, 0
), villages = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 
8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 
10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 
13L, 13L, 13L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 
15L, 15L, 15L, 15L, 15L, 15L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
16L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L, 
18L, 18L, 18L, 18L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 20L, 
20L, 20L, 20L, 20L, 20L, 20L, 20L, 21L, 21L, 21L, 21L, 21L, 21L, 
21L, 21L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 23L, 23L, 23L, 
23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 
25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 26L, 26L, 26L, 26L, 26L, 
26L, 26L, 26L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 28L, 28L, 
28L, 28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 29L, 29L, 29L, 
29L, 30L, 30L, 30L, 30L, 30L, 30L, 30L, 30L), coaches = c(1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 
9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 121L, 122L, 123L, 124L, 
125L, 126L, 127L, 128L, 129L, 130L, 131L, 132L, 133L, 134L, 135L, 
136L, 137L, 138L, 139L, 140L, 141L, 142L, 143L, 144L, 145L, 146L, 
147L, 148L, 149L, 150L, 151L, 152L, 153L, 154L, 155L, 156L, 157L, 
158L, 159L, 160L, 161L, 162L, 163L, 164L, 165L, 166L, 167L, 168L, 
169L, 170L, 171L, 172L, 173L, 174L, 175L, 176L, 177L, 178L, 179L, 
180L, 181L, 182L, 183L, 184L, 185L, 186L, 187L, 188L, 189L, 190L, 
191L, 192L, 193L, 194L, 195L, 196L, 197L, 198L, 199L, 200L, 201L, 
202L, 203L, 204L, 205L, 206L, 207L, 208L, 209L, 210L, 211L, 212L, 
213L, 214L, 215L, 216L, 217L, 218L, 219L, 220L, 221L, 222L, 223L, 
224L, 225L, 226L, 227L, 228L, 229L, 230L, 231L, 232L, 233L, 234L, 
235L, 236L, 237L, 238L, 239L, 240L), y = c(-0.331778030972082, 
0.988029496304653, 0.897183250008912, 1.47574845054647, 1.01772518896591, 
-0.596618806607905, -0.944361477475182, 0.41654320026775, -1.49024837322775, 
-1.37372937079329, 0.043872287368947, -0.308817440852125, 1.63731119839405, 
-0.46864194455032, 0.500770774456783, -1.51472501538605, -0.594620492501754, 
-0.497443041072083, 0.53597960384821, -0.231568640202276, -0.579729186616214, 
1.64985786398586, -1.9254056603094, -0.20993268064264, 0.528146219460542, 
1.4367450436326, -0.549323711529148, 1.03907555564133, 1.36166597331846, 
1.98156126266626, -0.220725846845717, -0.0712155326311143, -0.981597297600363, 
-1.04859295745199, 1.05926131771299, -0.723737295692727, 0.0154711148836809, 
-0.173141137611413, -1.02027694803558, -0.886461473361087, -1.37351772097637, 
-1.07571624287723, -1.54889364616601, 0.109473281677072, -1.90965047783226, 
-1.56809576587754, -2.10176387636473, 0.575521381987893, -0.181135195080813, 
0.952400874782299, -0.86397014699757, 1.38443589560352, 0.100006440673673, 
-0.942099894492393, 0.115832728326525, -0.737667582488404, -0.289603761556286, 
0.133325108836074, 1.87000682078485, -0.609728205647648, 1.46707007661613, 
1.82673959958592, 0.753762305168784, 0.297428412842748, 1.79038991827837, 
2.45617605361972, 0.971278544667826, -0.921370616372653, 0.338134026994478, 
1.17477818269765, 0.19312944335442, 1.43158911043361, 0.0320528000355197, 
0.141939620443437, -1.3420392517463, 0.766060805908607, -0.532028206443727, 
-0.204691173967602, 0.400597209605507, -1.37955303639807, 1.10376664253894, 
0.0726680172766116, -0.0806600490319542, 1.26876658802488, 1.72805226150727, 
2.04490815156605, -0.860646640956996, 0.927781727736906, -0.497672005944157, 
-0.658042626192458, 0.54533482718949, -0.964318551896509, 0.850777837635649, 
1.11428969841371, 1.11747465332548, 0.586393753192318, 1.94594852542083, 
-0.723852759482358, -0.103302075130573, 0.435881113177011, 1.15579979651882, 
0.0508840333617564, 1.14996569866337, 0.770572295778458, 1.25542992560847, 
-0.366718144612776, 1.83781661002386, 0.765149370099074, 0.320539511340124, 
0.529981485263611, 1.32918423545406, 0.054758045804175, -1.18658815020598, 
0.0150788656175678, -0.469988377597531, -0.271687925678611, -0.330259446726219, 
0.166650696315088, 0.460458293013768, 0.861971623230067, 0.783734997015681, 
0.347241549853463, -1.78546753449955, 0.0513714964954858, 2.24246344679807, 
-1.32991343421457, -1.78849284718788, -0.987565115077859, 0.315357684648374, 
-0.28664647368686, 0.225415723430126, -0.178511911588058, -1.0557886897221, 
-0.925698834762394, -0.642547969007825, 0.395632357029575, -0.176595031896436, 
0.122122966141956, -0.755179792456776, 0.234613454265532, 1.23426397936396, 
-0.868245651255047, -0.860926835986438, -0.265095506439507, 1.07285886355033, 
0.59909497303871, -0.41072007709135, -0.701450752845329, -0.114503910890831, 
-1.52229748513794, -1.03408243954282, -0.921942202651887, -1.76992185137235, 
-2.17482341693102, -0.178091438545776, -0.265400564568077, -0.661212392203144, 
0.753467644794517, 0.310351193280275, 0.701328842963796, 0.131311803944741, 
0.922038322725174, -1.17015321377127, 0.526871461112958, -0.362990782394625, 
0.48069374274964, -1.32397661694465, -0.184945847272509, 0.455559348302312, 
0.785694770916118, 0.919022020152805, 0.123488728325526, 0.348117718290177, 
0.550948411645754, 1.37498399656156, 1.5058778161582, -0.593660277830187, 
-0.867116621018196, 0.86142293469716, 1.59391951348085, -0.666401967302745, 
-0.44716298837626, 0.190564815272732, -0.249595543940657, 0.0861674173481018, 
-0.720911310731819, 0.58414436271256, -0.732108276510831, 1.19033814101515, 
0.52378066006685, -0.90819664247322, -0.560170352878871, -0.448984676742932, 
0.715985031629499, -0.258609106628965, 0.619323688498881, -0.324761208856213, 
-0.97524601581721, 0.322405147727671, -0.142196692673644, -0.19943214327786, 
0.556962929606084, 0.352737752730922, 0.404651073587142, 0.0137305473187293, 
-2.43892888432837, 0.867501172570773, 0.572588793010019, 0.383479790161704, 
-0.934493859037078, -0.780782770300908, -0.379519468112453, -0.10023477658886, 
-0.635240053905356, 0.362621295273774, -1.57274311167859, -0.0118501431860321, 
-2.21684447371063, 0.634078048723694, -1.11447499967841, 1.03568688805334, 
0.436407321552343, -0.508632869186697, -1.30923584406219, -1.1799794107768, 
1.57525216150922, -0.201857422215394, 0.129887039710908, 0.666480115799847, 
-1.1974807386992, 0.511467858769015, 0.309129710307985, -0.0318695456678357, 
-0.728909779092582, -0.262100090248981, -0.33340959305878, -0.147145713429717, 
-1.77232151208644, 0.68184900166618, 1.33769928728615)), class = "data.frame", row.names = c(NA, 
-240L))