### These are three data sets I simulated with K=2, 3 and 4
### Level 2 parameters are based on MLEs from one of the timing log data sets.



K2simdat <-
structure(list(Y = structure(c(-0.691520963538924, -0.646549571303902,
-1.27112031982827, -1.39525767855597, -0.0204279822769189, -0.957533196116045,
-1.17536203290469, -0.0982836377030618, 2.28630382367926, -0.3615817375965,
-0.976692789287333, -0.273205078999369, -0.670475723118683, -1.25778767854458,
0.0349477182538223, -0.140229903186339, -0.0706402487062028,
0.308959280957061, -0.312945010656802, -0.258551953111972, 1.72442022653569,
-0.0825559852440352, -1.39021932072005, -0.967559238612189, -0.467732490273794,
-0.592239723288642, -0.308080103109746, 0.00696993879722219,
-0.815275078970943, -0.79704171260379, 2.91825149305256, 0.807801246070109,
-1.34686358673519, -0.585854719889991, -0.0545731896047363, -1.10665519122134,
0.100043283630478, 0.174232603434439, -1.00980152944373, 1.08363939964445,
-0.278636149166826, 0.290299110305383, 1.58177236054855, -0.872238205585216,
1.81682977470787, -0.250724445833832, -0.366519113773939, 0.500910143050219,
1.21630097480551, 0.101699107522297, -0.802314347781113, -0.395273271464517,
-1.38882518339937, -0.90330244951331, 0.0713469932066501, -0.340694151331695,
-1.83720371933802, -0.388922159962595, 1.02547043148414, -0.700425697728525,
-0.663828307675379, 1.51359474725204, -1.49629120926653, -1.00349980182501,
-0.556655803056848, -0.993105728501385, 1.46358545403506, 0.624370100052483,
1.04210408826334, 0.136580609707994, -2.11910333602056, -0.54530722578936,
-1.44340691799409, -1.44759299502962, 0.631957752887941, 2.17640241478349,
-0.661933483960101, 0.636294067564279, 1.5726647390963, 0.256054016046008,
-0.405448387959392, -0.490753928903767, -1.40357263903656, -1.10324193631791,
2.5483056633685, -0.680281984974522, 0.209050259645299, 0.626202911623476,
0.72561467286304, -0.125156510454902, -0.479226488919731, -0.550621781299768,
-0.17861266880203, -1.06968162117991, 0.848889529685236, -0.353802582665426,
0.00117424702547247, 0.898495943598046, -0.0797181439910587,
-0.612159460585906, -0.46025391324431, -0.353254461290235, -1.70236740328018,
-0.61462485542785, 1.31813175671534, 0.298139782498618, -0.514747431434601,
-0.0808961397896844, 0.716179175157106, -1.96548837010368, 5.34499091787991,
-0.205082352118617, -1.54091214654254, -0.484167471188918, -0.164806539009913,
-0.658160347373182, -0.570586620574461, 0.816262488994784, -0.526366482099895,
0.495431689325966, -0.68875585400758, 0.158067639861203, -1.64569665238175,
-0.813923498662041, 1.22581086856738, -0.842993233627105, -0.0874457051812166,
-0.0850348960432378, 1.55124481805907, -0.369754994093119, -1.29997688179893,
1.04175028671407, -0.184420386009667, -1.72600425797648, -0.507801571759608,
3.14688677888675, -2.88479463423809, 0.975455843489998, 2.45899619559819,
0.250236208624441, -0.121627528712256, -0.170765504697191, 0.669511374303859,
-1.52774732731917, 0.00326343795561335, 2.84954311608219, -0.420610235159158,
0.321668722023694, -1.16337348670088, 0.11496793537279, -1.04784344036883,
-0.13102661569061, -1.129907692869, 3.07944619630577, -0.151333722084411,
-0.506756826947858, -0.873471566161367, 0.396646417041313, -0.84118983857253,
0.660387252657287, -0.770904762823911, -0.317282123215412, -1.09496608273032,
-0.882666610068115, -0.661856911194601, 0.689257634049814, -0.934111068990796,
0.0257401426834626, -0.474715793019976, -0.474519907862965, -0.475506249516053,
-0.203801579166575, 0.967799817511032, 1.78277644943244, -0.237615725652568,
3.76636687089813, -0.763506687148709, 1.03720104516545, -0.502851081413968,
-0.0420956535372058, -0.964520704160567, -0.0122648150243608,
-1.10605515367579, 3.15513020999258, -0.27570594377143, -1.01333810780094,
0.615606739657325, -0.401379143253036, -0.161837971754709, -1.26466585485374,
-0.0351936706814557, 0.195513648302894, -1.13960274265874, -0.306635309232015,
1.01916954031467, -0.582971399009827, -0.442528431074983, -1.42318392110259,
0.588586990566905, 0.0825790044456288, -0.600080077329688, -0.368473418893898,
-1.6582152800336, -0.828806276656578, -0.764800808915893, -1.50161406233878,
0.131135807137642, 0.106582518577111, 1.72658749833719, 0.921673802147435,
-1.31847767392863, -0.297727717815845, -1.3266510413607, -4.24414525969146,
0.262619601011909, 0.585893775295789, -0.040200767529075, 0.420520579972909,
-0.338543605731236, 0.203111047052196, -0.3251365501921, -0.0393320517266578,
-1.17893410290429, -0.877149722395545, 1.36828295583606, -0.125119114197204,
0.0791465896626968, -0.0992695354801909, 1.87914661344172, 0.293768120948978,
-0.692984291873183, 0.0211725181007818, -0.999021975630723, -1.7782357508028,
-0.405640080907159, -1.14092670841051, -0.720445015667024, 0.0152924011892841,
1.93860058214393, -1.21043322593174, -0.321171880817282, -0.493197448903818,
-1.49106144292813, -0.438359992029669, -0.561731736693306, -0.41157808102112,
-0.716164819205324, -0.750621419300787, 1.81500873844884, 0.529736085237207,
-0.398231182236588, -0.454179398743864, -1.17864175216226, -4.48595427861317,
0.662974478506723, 4.24100253918337, -0.214519402039945, -2.38691144630846,
2.19674788590205, 0.822684230786997, -0.511191412616962, -0.215628146359102,
-1.4273774779302, -1.14762191873765, 0.159663050018401, 4.6587973708419,
-0.24213418603221, -0.702452694110264, -0.195943903493526, 0.295322340967871,
-0.79215940119631, 0.507447746619229, 1.42914352426392, -1.18619586736305,
-0.349655861088985, 5.3854153666433, -0.652230615896926, -1.27314066683517,
0.647712016574016, 0.431345080600413, -0.994761457400611, 0.198478514358706,
-1.10088300158481, -1.29153682469922, 1.13217803602485, 7.87417549051372,
0.828090626433144, 0.688684231963583, -1.17948524486106, 0.551451456376687,
-0.490740062858698, -0.0168664291512929, -1.46542976235012, -0.950186829092933,
-0.522605160128575, -1.13515121357178, -0.713593826975319, -1.04523983814055,
1.55339655466592, -0.427355194577193, -0.222677883784124, -0.246335251059032,
1.37399687121665, -0.81418453667275, -0.649458000150331, -0.22228204883011,
-0.0956927771163243, 0.747628857801545, 0.247472947049019, 0.222666971627825,
-0.489320485357171, -0.491863768486494, -1.64745914880906, -1.18761230680194,
-0.280596968149779, -0.138540678396331, -0.101625560712549, 0.354388858875798,
1.61499433717038, 1.01196740419392, -0.96166563047603, -0.308120387571862,
-1.05883279138453, -0.677098166327808, -0.334676726872005, -0.970546047062385,
0.389332585938832, 0.464057924510814, -0.154601805371438, 0.651725998915063,
1.83833597511157, -0.564261396478341, -1.09381465858085, -2.11411492361914,
1.5756743644019, -0.790079486211289, -0.0348471446889219, 0.233562873595103,
2.42340947287424, 0.742537506533992, -0.581216472396803, -0.164698761576187,
-1.27307118068626, -1.42044873216493, -0.121953749966832, 5.59066553763152,
-0.419993049071406, 1.32640321558019, -0.78908050026596, 0.8629877574627,
5.62318584002019, -0.260748474760296, -1.10448196709558, -0.934516841643153,
-0.0809664874431404, 1.22329584074044, 0.100576712362193, 0.00725078013277941,
-1.65657020575526, 1.12895492431261, -4.05109137150507, -0.296638157039288,
-1.37392938995957, -0.505859310929695, 0.208333262167783, -0.467850217125456,
-0.711393881229378, -2.9201559250931, 1.23079646690861, -1.09379092061406,
-0.37435853615688, -0.176373885582769, -1.17380369579113, -1.02736811631466,
0.848826741914512, -0.210229724741439, 0.112832315099956, -0.0715598377534119,
NA, 0.621866457185314, -0.787742570507034, -0.185161531594784,
-1.41789325054877, -1.39653054148943, -0.288275185711181, -3.50259766951007,
1.19433370250419, 1.40671408463504, NA, 0.506469148992293, -0.648251218614132,
-0.131708584318399, -1.46708132557438, -1.21032929484355, 0.133335248760401,
-0.892338621086601, -0.581423302097572, 1.49285533825841, NA,
0.537230631912468, -0.500275201208814, -0.32216621764767, 1.45260339075564,
-1.49764841811491, -0.57333183801558, 1.09187519192735, 0.0538534224621972,
0.0744231438168921, NA, -1.22925057388823, 1.43673035896895,
-0.202257344251577, -1.44042297483632, -3.07664953454407, -0.245590026352454,
-0.927829988636327, 0.0364910138203445, -0.177321843238538, NA,
-0.341070016243098, -0.592076288891206, -0.284051449052862, -1.32525446457441,
-1.27140759209403, -0.335229405271334, -0.274482720344822, -0.630223599102072,
-0.382067477190496, NA, -0.0891309244095678, 3.67609362430795,
-0.197854743154372, -1.63091517694485, -1.54611173326082, 1.4319040417402,
-0.713698355780381, -0.704586124984528, 0.78251937584467, NA,
0.732264151638679, -0.71634505201562, NA, -1.38475423213142,
-0.853841569886105, 0.948897040266849, -0.528276903915852, -0.197699398615147,
0.42325362328939, NA, 0.422441804449746, -0.654935703704536,
NA, -3.14162695655357, -1.40851932679202, -0.371025063893518,
4.2518955170061, -0.593071164098331, -0.440310903736675, NA,
1.42709393150812, -0.688317470492579, NA, -1.13806971457739,
NA, -0.0168197835277371, -1.11981485135747, -0.216075945662066,
0.489441021172834, NA, 0.970788597945605, -0.294193087833086,
NA, -1.36461091023413, NA, -0.415467858048657, -1.32293918882298,
-0.456333945835698, 0.515426956579196, NA, NA, -0.528283636926371,
NA, -1.02721468582137, NA, -0.309024136739698, -1.58260583008218,
-0.246315861185704, 0.545391005059254, NA, NA, -0.686734458432947,
NA, -1.20872061102083, NA, -0.32788298689154, -0.989398715454311,
0.71017737965993, -1.58733244699517, NA, NA, 4.0190980702835,
NA, -1.17198227691088, NA, -0.557558391609772, 1.00953525928919,
0.326742319743261, 0.50170921192888, NA, NA, 0.865857783357414,
NA, 0.898218552832772, NA, -0.092417733860861, 0.45402325096896,
0.219003942871412, -0.261567333333383, NA, NA, -0.520090527827431,
NA, -1.19318621208488, NA, 0.0362414282356845, -1.12091296912548,
-0.795046812430041, NA, NA, NA, -0.197773487362791, NA, -1.27273465160642,
NA, NA, -0.00740837793881499, -0.679592437440116, NA, NA, NA,
1.17897682447842, NA, -1.44055897509944, NA, NA, -1.55090143767784,
-2.15389874431914, NA, NA, NA, -0.79628021039484, NA, -1.3312287205903,
NA, NA, -1.33848712887422, -0.12709039797963, NA, NA, NA, -3.61265337839578,
NA, -1.33921398848134, NA, NA, NA, NA, NA, NA, NA, -0.456102432674905,
NA, -0.441808971326462, NA, NA, NA, NA, NA, NA, NA, -0.567839604846627,
NA, -0.70492389171573, NA, NA, NA, NA, NA, NA, NA, 0.204377246484258,
NA, NA, NA, NA, NA, NA, NA, NA, NA, -0.495900349025564, NA, NA,
NA, NA, NA, NA, NA, NA, NA, 1.08735358131288, NA, NA, NA, NA,
NA, NA, NA, NA, NA, -0.760748895961475, NA, NA, NA, NA, NA, NA,
NA, NA, NA), .Dim = c(10L, 63L)), J = c(63L, 44L, 59L, 46L, 53L,
56L, 56L, 52L, 37L, 47L), I = 10, pi = structure(c(0.631331717955818,
0.689682899269878, 0.752753058045683, 0.784165245358942, 0.710796067215372,
0.704158535954631, 0.719445677582892, 0.685033920595269, 0.585040008317498,
0.688588552413736, 0.368668282044182, 0.310317100730122, 0.247246941954317,
0.215834754641057, 0.289203932784627, 0.295841464045369, 0.280554322417107,
0.314966079404732, 0.414959991682502, 0.311411447586264), .Dim = c(10L,
2L)), mu = structure(c(-0.592367336565177, -0.295451967735407,
-1.26549772419415, -1.05435641593114, -0.282071051916399, -0.669779566935783,
-0.261911268248762, 0.33556686460064, -0.130259575952076, -0.426508668085031,
0.592734076511357, 0.230666425997801, -0.0104754294400033, -0.389927091323119,
1.32548185175963, 0.805742713416505, 0.173534923796682, -0.458994009061964,
1.50627188612908, 0.796359533190784), .Dim = c(10L, 2L)), tau = structure(c(22.4771284925446,
34.992960802432, 23.1564736985979, 9.11021030920965, 17.1233212521505,
3.00165952744889, 6.28088613288906, 4.3542360160839, 2.91155918792529,
1.58432603013348, 0.188884177204475, 1.75641766153547, 0.775138679201308,
0.0662989348713583, 2.33744870903953, 0.11489166859445, 0.364826739216831,
0.864090471618329, 4.07382153430732, 3.37403900992499), .Dim = c(10L,
2L)), alpha0 = c(0.689409859623227, 0.310590140376773), mu0 = c(-0.542165533726129,
0.510930199253648), beta0 = c(0.395113597768731, 0.800636736160821
), tau0 = c(1.69060560845033, 0.0941040008696826), gamma0 = c(0.943158883420632,
1.52664647150361), alphaN = 50), .Names = c("Y", "J", "I", "pi",
"mu", "tau", "alpha0", "mu0", "beta0", "tau0", "gamma0", "alphaN"
))
K3simdat <-
structure(list(Y = structure(c(-3.46249611508687, -1.23479367714478,
1.78166066031741, 0.627523628931001, -0.340223302982872, -1.02632545751557,
-0.965916706555726, -0.498161691856074, -1.57426458396308, -0.681020609240536,
-1.21963384107893, -0.700333915952907, -0.697687451612136, 0.448705862888922,
-0.629819288655705, -1.95993604928104, -1.15046576201488, -0.449571773035135,
2.24090601363179, -1.0862694778596, 1.96006744573062, -0.732176330328052,
1.93369591586199, -1.20079670800151, -0.566618627683424, -0.87620259301327,
-0.314970951515519, -1.07759571202537, -1.3177405892571, -0.549163749762601,
1.17354430219582, -0.902782381902179, -0.666680832636536, -0.862688307597872,
-0.166031533013116, 1.43897231061399, -0.250680732144537, -1.17765855644761,
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-0.532093344207663, 2.26751395926646, -0.160410777424628, -1.03805634641967,
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1.54677669884893, 1.0591115137425, -0.509027049110476, -2.0969457302406,
-0.273165167976479, -1.22727294295052, -0.959345349378276, 0.0215103404234058,
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-1.23630430533876, -1.81998557914267, 0.294900404666016, 0.808136147839817,
2.65451592677531, -0.742247586448716, -0.838162395385733, -0.637936992584452,
-1.65600709743665, 3.70499007808053, -0.426415345292686, -0.890256738340459,
0.426329200438289, 0.583366190274771, -2.11064934287763, -1.1106479050313,
2.47951344303607, -0.548993993633681, -1.23126400730698, -0.119350902656416,
0.0934107371381512, -1.25833978587413, -1.88558550920806, -1.47086812591297,
-0.806819980881281, -1.76727371578612, 0.80747795509375, 2.29373102632506,
0.582808585361783, -0.145770146048089, -1.05732541921175, -0.525691160204818,
0.0118020324167561, 0.37663209592023, 0.219874344956386, -0.693213872528571,
-0.930337554589762, 2.47721020323592, -0.727548289903182, -1.10302415068735,
-0.558989885350989, -1.28893851005009, 0.0464153624246917, -0.195035448049405,
-1.01486003606676, 0.180692531164616, 0.451679722834613, 0.62280141355877,
-2.34360168260673, -0.514664968959054, 1.48255520066864, -1.36163094641339,
-0.371435837194132, 0.145324691066497, -1.28966381230837, 2.06131197143149,
0.528969143094808, -1.10330962606297, -1.19438787623631, -0.147369712223882,
-0.302004834724846, -1.48615169985527, -0.470079175544392, -0.308053658800883,
0.349174079962382, -0.789905672445428, 0.624096276119517, -0.766056955966303,
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60L, 50L, 53L, 40L, 43L, 43L, 65L), I = 10, pi = structure(c(0.410598660738122,
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"J", "I", "pi", "mu", "tau", "alpha0", "mu0", "beta0", "tau0",
"gamma0", "alphaN"))
K4simdat <-
structure(list(Y = structure(c(-0.871686993142966, -0.222821384305109,
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