DHARMa
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Published
20 hours ago •
florianhartig
florianhartig
Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions.
Hi, I am pretty new to DHARMa and model diagnostics in general so please bear with me if I have made a simple correctable error. I am trying to diagnose the following model that I have fit with glmmTMB, to correct for overdispersion:
glmmTMB(cbind(actual, time_not_wear) ~ 1 + reason + age_c + sex + (1|id),
family = betabinomial(), data = outmlm)
The proportional response data was obtained via daily diaries so the daily diary entries (approximately 1202 observations) are nested within 47 individuals. I should also mention that a most responses were clustered around prop = 0.0 and 1.0. However, I have not been able to generate the red quantile lines in the residual vs. predicted plot, due to the following error after plotting the simulated residuals (I encountered the same error with my overdispersed model fit with the binomial family):
res <- simulateResiduals(model2)
plot(res)
Unable to calculate quantile regression for quantile 0.25. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
Unable to calculate quantile regression for quantile 0.5. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
Unable to calculate quantile regression for quantile 0.75. Possibly to few (unique) data points / predictions. Will be ommited in plots and significance calculations.
This is the resulting plot:
Here are the tests of overdispersion and zero inflation (just in case they are relevant):
testZeroInflation(res)
testDispersion(res)
I have looked through the vignette but I have not found a solution to this. Is this a problem with my data structure or am I missing something with my diagnosis?
Hi @cirxi, thanks for reporting this.
This error is created by the qgam package, and as it says, it's usually a problem of not having enough residuals, which is obviously not the problem in your case.
I have no idea why the quantile plots fail - if your data is not secret, you could maybe paste it (or only the residuals) via a dput here, then I could investigate further.
Best, F
p.s.: are you fitting continous or discrete proportions here? For continous proportions, the betabinomial is probably not the most appropriate choice.
Hi Florian,
Thanks for checking on this.
Correct me if I am wrong, but I am fitting discrete proportions here. Maybe to give a little context...
actual = successes = time spent outside wearing the device (in minutes)
time_not_wear = failures = time spent outside wearing the device (in minutes) that the device was not worn
time_not_wear was calculated by subtracting actual from time_out_minutes (which is the total number of minutes spent outside for the day). Given that the total number of trials is a known value time_out_minutes, I believe that I am fitting discrete proportions. Could this whole issue be caused by me treating each minute as a trial?
I have tried fitting the resulting proportion directly actual / time_out_minutes = adh_score by specifying time_out_minutes in the weights argument but i encountered the following error. Interestingly, I do not encounter this error if use successes/failures to specify the proportions.
model2 <- glmmTMB(adh_score ~ 1 + reason + age_c + sex + (1|id),
family = betabinomial(), weights = time_out_minutes, data = outmlm)
res <- simulateResiduals(model2)
Warning messages:
1: In securityAssertion("nKcase - wrong dimensions of response") :
Message from DHARMa: During the execution of a DHARMa function, some unexpected conditions occurred. Even if you didn't get an error, your results may not be reliable. Please check with the help if you use the functions as intended. If you think that the error is not on your side, I would be grateful if you could report the problem at https://github.com/florianhartig/DHARMa/issues
Unfortunately, I cannot share my data, so here are the residuals of my fitted model via dput.
> dput(residuals(model2))
c(`1` = 0.376641662164871, `2` = -0.1947869092637, `3` = -0.1947869092637,
`4` = -0.134084036754832, `5` = -0.0583425430483765, `6` = -0.1947869092637,
`7` = -0.1947869092637, `8` = -0.0455202487563408, `9` = -0.1947869092637,
`10` = -0.1947869092637, `11` = -0.1947869092637, `12` = -0.0983697510405467,
`13` = 0.227207023970932, `14` = -0.0455202487563408, `15` = 0.954479751243659,
`16` = -0.1947869092637, `17` = -0.186464989135785, `18` = -0.1947869092637,
`19` = -0.062655465326261, `20` = -0.0455202487563408, `21` = -0.0455202487563408,
`22` = 0.954479751243659, `23` = -0.1947869092637, `24` = -0.0455202487563408,
`25` = -0.1947869092637, `26` = -0.0455202487563408, `27` = -0.0455202487563408,
`28` = -0.0351829378537335, `29` = -0.109453494882911, `30` = -0.1947869092637,
`31` = 0.133491928566721, `32` = -0.743174738099945, `33` = 0.133491928566721,
`34` = 0.133491928566721, `35` = -0.624083829009036, `36` = -0.357259590974586,
`37` = 0.133491928566721, `38` = 0.133491928566721, `39` = 0.133491928566721,
`40` = 0.133491928566721, `41` = 0.133491928566721, `42` = -0.357259590974586,
`43` = 0.133491928566721, `44` = 0.133491928566721, `45` = 0.133491928566721,
`46` = -0.299647412159274, `47` = 0.133491928566721, `48` = 0.700352587840726,
`49` = 0.0739681190429119, `50` = 0.133491928566721, `51` = -0.866508071433279,
`52` = -0.799841404766612, `53` = 0.133491928566721, `54` = 0.133491928566721,
`55` = 0.133491928566721, `56` = 0.133491928566721, `57` = 0.133491928566721,
`58` = -0.0269817936424095, `59` = 0.0667682063575905, `60` = 0.0667682063575905,
`61` = 0.0667682063575905, `62` = 0.0667682063575905, `63` = 0.0667682063575905,
`64` = 0.0667682063575905, `65` = 0.0667682063575905, `66` = 0.0667682063575905,
`67` = 0.0667682063575905, `68` = 0.0667682063575905, `69` = 0.0667682063575905,
`70` = 0.0667682063575905, `71` = -0.0582317936424095, `72` = -0.479516164184682,
`73` = 0.0667682063575905, `74` = 0.0667682063575905, `75` = 0.0667682063575905,
`76` = 0.0667682063575905, `77` = 0.0667682063575905, `78` = 0.0667682063575905,
`79` = 0.446194966149935, `80` = 0.0795317477491697, `81` = 0.0795317477491697,
`82` = -0.432739771610829, `83` = -0.553805033850065, `84` = 0.567260228389171,
`85` = 0.567260228389171, `86` = -0.432739771610829, `87` = 0.0795317477491697,
`88` = 0.0795317477491697, `89` = 0.0795317477491697, `90` = 0.567260228389171,
`91` = 0.0795317477491697, `92` = -0.553805033850065, `93` = 0.0795317477491697,
`94` = -0.432739771610829, `95` = -0.432739771610829, `96` = -0.92046825225083,
`97` = 0.0795317477491697, `98` = 0.567260228389171, `99` = 0.0795317477491697,
`100` = 0.0795317477491697, `101` = -0.432739771610829, `102` = -0.553805033850065,
`103` = 0.446194966149935, `104` = 0.0795317477491697, `105` = 0.0795317477491697,
`106` = 0.0795317477491697, `107` = 0.0795317477491697, `108` = 0.302007275269811,
`109` = -0.198624749154388, `110` = -0.198624749154388, `111` = 0.302007275269811,
`112` = -0.198624749154388, `113` = -0.198624749154388, `114` = -0.198624749154388,
`115` = 0.801375250845612, `116` = 0.239507275269811, `117` = -0.198624749154388,
`118` = -0.198624749154388, `119` = 0.801375250845612, `120` = -0.198624749154388,
`121` = -0.198624749154388, `122` = 0.410236383064586, `123` = -0.0460704961055441,
`124` = -0.700509780474627, `125` = 0.0438392676111035, `126` = 0.0438392676111035,
`127` = 0.120596170561122, `128` = 0.0438392676111035, `129` = 0.0438392676111035,
`130` = 0.0296870796520315, `131` = 0.120596170561122, `132` = 0.120596170561122,
`133` = 0.410236383064586, `134` = -0.481991261956108, `135` = 0.0438392676111035,
`136` = 0.120596170561122, `137` = 0.0705961705611224, `138` = 0.0494902195253732,
`139` = 0.120596170561122, `140` = 0.256390229218432, `141` = -0.839403829438877,
`142` = 0.0438392676111035, `143` = 0.0438392676111035, `144` = 0.120596170561122,
`145` = 0.120596170561122, `146` = 0.299490219525373, `147` = 0.120596170561122,
`148` = -0.00161527784344195, `149` = 0.299490219525373, `150` = 0.120596170561122,
`151` = 0.0438392676111035, `152` = -0.467926678636467, `153` = 0.1987399880302,
`154` = -0.0869742976840862, `155` = 0.1987399880302, `156` = -0.242845831735301,
`157` = -0.0639277038217465, `158` = 0.1987399880302, `159` = 0.41826527937581,
`160` = -0.12226103715508, `161` = -0.217926678636467, `162` = 0.436072296178253,
`163` = 0.557154168264699, `164` = -0.563927703821747, `165` = -0.563927703821747,
`166` = -0.130345831735301, `167` = -0.563927703821747, `168` = 0.436072296178253,
`169` = 0.0194056295115869, `170` = -0.0261791650686344, `171` = 0.436072296178253,
`172` = 0.358647637237603, `173` = 0.436072296178253, `174` = 0.1987399880302,
`175` = -0.563927703821747, `176` = -0.563927703821747, `177` = 0.436072296178253,
`178` = -0.6012600119698, `179` = 0.436072296178253, `180` = 0.245269071780905,
`181` = 0.264866141377974, `182` = 0.258089584601417, `183` = 0.323794712806546,
`184` = 0.0657818922937251, `185` = 0.342355318867152, `186` = 0.23116650767834,
`187` = 0.372405823917657, `188` = 0.24323915725099, `189` = 0.290140866652699,
`190` = 0.21823915725099, `191` = 0.302961379473212, `192` = -0.0881793023180498,
`193` = -0.108029188429401, `194` = -0.108029188429401, `195` = 0.297405823917657,
`196` = 0.323474199986033, `197` = 0.145818522330355, `198` = 0.316850268362101,
`199` = 0.262683601695434, `200` = -0.0748941213761362, `201` = 0.448786477321129,
`202` = 0.448786477321129, `203` = -0.551213522678871, `204` = 0.448786477321129,
`205` = 0.448786477321129, `206` = -0.551213522678871, `207` = -0.0748941213761362,
`208` = 0.448786477321129, `209` = 0.448786477321129, `210` = -0.551213522678871,
`211` = -0.551213522678871, `212` = 0.448786477321129, `213` = -0.291104795838652,
`214` = -0.551213522678871, `215` = 0.448786477321129, `216` = -0.551213522678871,
`217` = -0.116387395181139, `218` = -0.0748941213761362, `219` = 0.448786477321129,
`220` = 0.448786477321129, `221` = -0.0748941213761362, `222` = -0.551213522678871,
`223` = -0.551213522678871, `224` = -0.551213522678871, `225` = -0.116387395181139,
`226` = -0.0748941213761362, `227` = 0.448786477321129, `228` = 0.448786477321129,
`229` = -0.551384899931594, `230` = -0.733203081749776, `231` = 0.809501408689399,
`232` = -0.545703081749776, `233` = -0.483203081749776, `234` = -0.478846520345605,
`235` = -0.227631342574954, `236` = 0.772368657425046, `237` = 0.772368657425046,
`238` = -0.227631342574954, `239` = 0.521153479654395, `240` = 0.521153479654395,
`241` = 0.521153479654395, `242` = 0.521153479654395, `243` = -0.227631342574954,
`244` = 0.846638103119098, `245` = -0.190498591310601, `246` = -0.190498591310601,
`247` = -0.478846520345605, `248` = -0.153361896880902, `249` = -0.524869748416443,
`250` = -0.227631342574954, `251` = 0.52211537402867, `252` = -0.329720575164352,
`253` = -0.444551292637996, `254` = 0.018161281255851, `255` = -0.444551292637996,
`256` = 0.118161281255851, `257` = 0.118161281255851, `258` = 0.118161281255851,
`259` = 0.118161281255851, `260` = -0.444551292637996, `261` = 0.118161281255851,
`262` = -0.444551292637996, `263` = 0.118161281255851, `264` = 0.455448707362004,
`265` = 0.305448707362004, `266` = 0.118161281255851, `267` = 0.610104136228933,
`268` = 0.118161281255851, `269` = -0.881838718744149, `270` = 0.555448707362004,
`271` = 0.118161281255851, `272` = 0.555448707362004, `273` = 0.0499794630740328,
`274` = 0.305448707362004, `275` = 0.670279424835649, `276` = -0.131838718744149,
`277` = 0.118161281255851, `278` = 0.118161281255851, `279` = -0.389895863771067,
`280` = 0.118161281255851, `281` = 0.21210218332232, `282` = 0.0280594333339355,
`283` = 0.0280594333339355, `284` = 0.0280594333339355, `285` = 0.0280594333339355,
`286` = 0.0280594333339355, `287` = 0.0280594333339355, `288` = 0.0280594333339355,
`289` = 0.0280594333339355, `290` = 0.304584288426828, `291` = -0.0287490449065049,
`292` = 0.0280594333339355, `293` = -0.024572145613433, `294` = 0.0280594333339355,
`295` = 0.0280594333339355, `296` = 0.304584288426828, `297` = 0.0280594333339355,
`298` = 0.137917621760162, `299` = 0.304584288426828, `300` = 0.0280594333339355,
`301` = 0.0280594333339355, `302` = 0.304584288426828, `303` = -0.150511995237493,
`304` = 0.0280594333339355, `305` = -0.78789781667768, `306` = 0.304584288426828,
`307` = 0.0280594333339355, `308` = 0.769959813656764, `309` = 0.769959813656764,
`310` = -0.538430292128569, `311` = -0.272287974840761, `312` = 0.362470608772332,
`313` = 0.616600914048128, `314` = -0.272287974840761, `315` = -0.777234829812661,
`316` = -0.230040186343235, `317` = 0.222765170187339, `318` = 0.228236374538097,
`319` = -0.138430292128569, `320` = -0.538430292128569, `321` = 0.461569707871431,
`322` = 0.461569707871431, `323` = 0.757468915216642, `324` = 0.813024470772197,
`325` = 0.0282363745380974, `326` = -0.538430292128569, `327` = -0.186578440276717,
`328` = -0.538430292128569, `329` = 0.461569707871431, `330` = -0.538430292128569,
`331` = -0.538430292128569, `332` = 0.453993950295673, `333` = 0.699934247381461,
`334` = 0.294903041204764, `335` = 0.0460536384940282, `336` = 0.072826394287398,
`337` = 0.0460536384940282, `338` = 0.072826394287398, `339` = 0.0460536384940282,
`340` = 0.00515064077164717, `341` = 0.072826394287398, `342` = 0.072826394287398,
`343` = 0.072826394287398, `344` = 0.00515064077164717, `345` = 0.072826394287398,
`346` = 0.00515064077164717, `347` = 0.072826394287398, `348` = 0.00515064077164717,
`349` = -0.0382847168237131, `350` = 0.00515064077164717, `351` = 0.072826394287398,
`352` = 0.0172346653274243, `353` = 0.100567998660758, `354` = 0.100567998660758,
`355` = 0.100567998660758, `356` = 0.100567998660758, `357` = 0.566302061831499,
`358` = 0.566302061831499, `359` = 0.100567998660758, `360` = 0.0783457764385355,
`361` = 0.100567998660758, `362` = 0.19179241575994, `363` = -0.433697938168501,
`364` = 0.100567998660758, `365` = 0.100567998660758, `366` = 0.064853712946472,
`367` = 0.566302061831499, `368` = 0.100567998660758, `369` = 0.100567998660758,
`370` = 0.100567998660758, `371` = 0.100567998660758, `372` = 0.100567998660758,
`373` = 0.0767584748512339, `374` = -0.749384054828295, `375` = 0.0131026046300967,
`376` = 0.0131026046300967, `377` = 0.0381932176510945, `378` = 0.0381932176510945,
`379` = 0.0131026046300967, `380` = 0.0381932176510945, `381` = -0.0868973953699033,
`382` = 0.0131026046300967, `383` = 0.134232111180065, `384` = 0.134232111180065,
`385` = 0.0131026046300967, `386` = 0.0131026046300967, `387` = 0.0131026046300967,
`388` = 0.0131026046300967, `389` = 0.0131026046300967, `390` = 0.0131026046300967,
`391` = 0.0131026046300967, `392` = 0.0131026046300967, `393` = -0.12326103173354,
`394` = 0.0131026046300967, `395` = 0.134232111180065, `396` = 0.0131026046300967,
`397` = 0.0381932176510945, `398` = 0.0381932176510945, `399` = 0.0381932176510945,
`400` = 0.0131026046300967, `401` = 0.110162186142565, `402` = 0.0131026046300967,
`403` = 0.0131026046300967, `404` = 0.0131026046300967, `405` = 0.261457221112999,
`406` = -0.111313892430817, `407` = -0.111313892430817, `408` = 0.65535277423585,
`409` = 0.114021323677102, `410` = -0.655209445553667, `411` = -0.111313892430817,
`412` = -0.111313892430817, `413` = -0.111313892430817, `414` = 0.229405939061717,
`415` = 0.344790554446333, `416` = 0.0447905544463326, `417` = 0.344790554446333,
`418` = 0.253881463537242, `419` = 0.344790554446333, `420` = -0.117061213254409,
`421` = 0.332067482722179, `422` = 0.332067482722179, `423` = -0.117061213254409,
`424` = -0.117061213254409, `425` = -0.117061213254409, `426` = 0.332067482722179,
`427` = -0.177435375599139, `428` = 0.329984149388846, `429` = -0.117061213254409,
`430` = 0.332067482722179, `431` = 0.332067482722179, `432` = -0.117061213254409,
`433` = -0.177435375599139, `434` = 0.332067482722179, `435` = 0.327900816055513,
`436` = 0.332067482722179, `437` = -0.117061213254409, `438` = -0.117061213254409,
`439` = -0.117061213254409, `440` = -0.117061213254409, `441` = -0.117061213254409,
`442` = -0.117061213254409, `443` = -0.177435375599139, `444` = -0.146933207780213,
`445` = -0.177435375599139, `446` = -0.117061213254409, `447` = 0.332067482722179,
`448` = -0.167932517277821, `449` = -0.117061213254409, `450` = 0.165923519895242,
`451` = 0.0687012976730196, `452` = 0.19370129767302, `453` = -0.80629870232698,
`454` = 0.691370114220967, `455` = 0.19370129767302, `456` = -0.215299705105217,
`457` = 0.19370129767302, `458` = -0.80629870232698, `459` = -0.308629885779033,
`460` = 0.19370129767302, `461` = 0.19370129767302, `462` = 0.19370129767302,
`463` = 0.19370129767302, `464` = 0.19370129767302, `465` = 0.19370129767302,
`466` = 0.19370129767302, `467` = 0.19370129767302, `468` = 0.19370129767302,
`469` = -0.80629870232698, `470` = 0.19370129767302, `471` = 0.19370129767302,
`472` = -0.215299705105217, `473` = 0.127034631006353, `474` = -0.80629870232698,
`475` = 0.19370129767302, `476` = 0.0572892833445665, `477` = 0.415096168620987,
`478` = 0.4797016460919, `479` = 0.0572892833445665, `480` = 0.361703899846063,
`481` = 0.0572892833445665, `482` = 0.0572892833445665, `483` = 0.0572892833445665,
`484` = 0.0572892833445665, `485` = -0.276044049988767, `486` = 0.0572892833445665,
`487` = 0.0572892833445665, `488` = 0.0572892833445665, `489` = -0.0538218277665446,
`490` = 0.4797016460919, `491` = 0.0572892833445665, `492` = -0.0260440499887669,
`493` = -0.0538218277665446, `494` = -0.0427107166554335, `495` = 0.0572892833445665,
`496` = 0.368590534980789, `497` = -0.299189545664727, `498` = 0.2922016460919,
`499` = 0.0572892833445665, `500` = 0.0572892833445665, `501` = -0.0965568705015873,
`502` = 0.153807315054622, `503` = 0.0572892833445665, `504` = 0.296729040289133,
`505` = 0.106700404911349, `506` = 0.106700404911349, `507` = -0.417556673996581,
`508` = 0.106700404911349, `509` = 0.207443326003419, `510` = -0.0182995950886514,
`511` = 0.106700404911349, `512` = -0.0182995950886514, `513` = 0.0297773279882717,
`514` = 0.106700404911349, `515` = 0.106700404911349, `516` = 0.106700404911349,
`517` = 0.263220291521978, `518` = 0.106700404911349, `519` = 0.106700404911349,
`520` = 0.106700404911349, `521` = 0.106700404911349, `522` = 0.106700404911349,
`523` = 0.106700404911349, `524` = -0.417556673996581, `525` = -0.473082932866538,
`526` = 0.106700404911349, `527` = 0.163220291521978, `528` = 0.263220291521978,
`529` = 0.106700404911349, `530` = 0.106700404911349, `531` = 0.132443326003419,
`532` = 0.136110433671845, `533` = 0.123289920851332, `534` = 0.0478792760476235,
`535` = 0.136110433671845, `536` = 0.0591873567487683, `537` = -0.294956950811417,
`538` = 0.136110433671845, `539` = -0.352120723952377, `540` = 0.136110433671845,
`541` = 0.136110433671845, `542` = 0.705043049188583, `543` = 0.136110433671845,
`544` = 0.136110433671845, `545` = -0.294956950811417, `546` = 0.136110433671845,
`547` = -0.294956950811417, `548` = 0.136110433671845, `549` = 0.136110433671845,
`550` = 0.136110433671845, `551` = 0.136110433671845, `552` = -0.294956950811417,
`553` = -0.352120723952377, `554` = 0.136110433671845, `555` = -0.294956950811417,
`556` = 0.136110433671845, `557` = -0.0187873906190432, `558` = -0.294956950811417,
`559` = -0.294956950811417, `560` = -0.294956950811417, `561` = 0.705043049188583,
`562` = 0.0196595210004176, `563` = 0.0196595210004176, `564` = 0.0196595210004176,
`565` = 0.0196595210004176, `566` = 0.0196595210004176, `567` = 0.0196595210004176,
`568` = 0.0196595210004176, `569` = 0.0196595210004176, `570` = 0.0196595210004176,
`571` = 0.0196595210004176, `572` = 0.0244994741534372, `573` = 0.0315965793332158,
`574` = 0.00214598632618423, `575` = 0.0196595210004176, `576` = 0.0315965793332158,
`577` = 0.0196595210004176, `578` = 0.0244994741534372, `579` = 0.0196595210004176,
`580` = 0.0244994741534372, `581` = 0.0196595210004176, `582` = 0.0196595210004176,
`583` = 0.0196595210004176, `584` = 0.0196595210004176, `585` = 0.00214598632618423,
`586` = 0.0196595210004176, `587` = 0.249614040932675, `588` = 0.154614040932675,
`589` = -0.745385959067325, `590` = -0.238937002218901, `591` = 0.758285220003321,
`592` = 0.761062997781099, `593` = -0.161751348513867, `594` = 0.594396331114432,
`595` = 0.251836263154898, `596` = 0.761062997781099, `597` = 0.154614040932675,
`598` = -0.200438601442918, `599` = 0.254614040932675, `600` = -0.238937002218901,
`601` = 0.838248651486133, `602` = -0.161751348513867, `603` = -0.745385959067325,
`604` = 0.251280707599342, `605` = -0.200438601442918, `606` = 0.252947374266009,
`607` = 0.761062997781099, `608` = -0.306604540321407, `609` = 0.162238366795653,
`610` = 0.162238366795653, `611` = 0.162238366795653, `612` = -0.306604540321407,
`613` = 0.062238366795653, `614` = 0.393395459678593, `615` = 0.166777248400974,
`616` = 0.0083922129494991, `617` = -0.356404852034978, `618` = 0.162238366795653,
`619` = -0.253933775248024, `620` = 0.643595147965022, `621` = 0.162238366795653,
`622` = 0.162238366795653, `623` = -0.306604540321407, `624` = 0.366777248400974,
`625` = -0.306604540321407, `626` = 0.162238366795653, `627` = 0.162238366795653,
`628` = -0.306604540321407, `629` = 0.162238366795653, `630` = 0.162238366795653,
`631` = 0.446066224751976, `632` = 0.062238366795653, `633` = 0.366777248400974,
`634` = -0.253933775248024, `635` = 0.0404434950007811, `636` = 0.162238366795653,
`637` = 0.162238366795653, `638` = 0.0318076881888133, `639` = 0.234503669851498,
`640` = 0.0318076881888133, `641` = 0.0318076881888133, `642` = 0.0318076881888133,
`643` = 0.0318076881888133, `644` = 0.0318076881888133, `645` = 0.234503669851498,
`646` = 0.0318076881888133, `647` = -0.0931923118111867, `648` = 0.0318076881888133,
`649` = 0.0318076881888133, `650` = 0.234503669851498, `651` = 0.234503669851498,
`652` = 0.0318076881888133, `653` = 0.0318076881888133, `654` = 0.0318076881888133,
`655` = 0.0318076881888133, `656` = -0.0237478673667423, `657` = 0.0318076881888133,
`658` = 0.0318076881888133, `659` = 0.234503669851498, `660` = -0.722724006682928,
`661` = 0.0318076881888133, `662` = -0.0616174816482832, `663` = 0.438382518351717,
`664` = -0.172728592759394, `665` = -0.561617481648283, `666` = -0.371141291172093,
`667` = -0.291245842213252, `668` = 0.438382518351717, `669` = -0.793036784650808,
`670` = 0.708754157786748, `671` = -0.561617481648283, `672` = 0.438382518351717,
`673` = -0.0199508149816165, `674` = 0.438382518351717, `675` = -0.249117481648283,
`676` = -0.27828414831495, `677` = 0.355049185018383, `678` = 0.798360578729089,
`679` = 0.438382518351717, `680` = 0.438382518351717, `681` = 0.438382518351717,
`682` = 0.438382518351717, `683` = -0.0949508149816165, `684` = -0.793036784650808,
`685` = 0.438382518351717, `686` = -0.12828414831495, `687` = -0.275903195933997,
`688` = -0.793036784650808, `689` = -0.0616174816482832, `690` = -0.201639421270911,
`691` = -0.793036784650808, `692` = -0.0286127719303944, `693` = -0.0286127719303944,
`694` = -0.0286127719303944, `695` = -0.0286127719303944, `696` = -0.0286127719303944,
`697` = -0.0286127719303944, `698` = -0.0286127719303944, `699` = -0.00193776610533472,
`700` = -0.0286127719303944, `701` = -0.0286127719303944, `702` = -0.00193776610533472,
`703` = -0.0286127719303944, `704` = -0.0286127719303944, `705` = -0.0286127719303944,
`706` = -0.0286127719303944, `707` = -0.00193776610533472, `708` = -0.0286127719303944,
`709` = -0.00193776610533472, `710` = -0.0286127719303944, `711` = -0.00193776610533472,
`712` = -0.0286127719303944, `713` = -0.0286127719303944, `714` = -0.0286127719303944,
`715` = -0.0286127719303944, `716` = -0.00193776610533472, `717` = -0.0286127719303944,
`718` = -0.00314892105277025, `719` = -0.0286127719303944, `720` = -0.0286127719303944,
`721` = -0.0286127719303944, `722` = 0.0409476096653328, `723` = 0.112376181093904,
`724` = 0.112376181093904, `725` = 0.0945190382367613, `726` = 0.112376181093904,
`727` = 0.112376181093904, `728` = 0.112376181093904, `729` = 0.112376181093904,
`730` = -0.403473550451983, `731` = 0.0498761810939042, `732` = 0.112376181093904,
`733` = 0.112376181093904, `734` = 0.112376181093904, `735` = 0.112376181093904,
`736` = 0.112376181093904, `737` = 0.112376181093904, `738` = 0.112376181093904,
`739` = 0.00126506998279308, `740` = 0.112376181093904, `741` = -0.636225181962031,
`742` = -0.636225181962031, `743` = 0.363774818037969, `744` = -0.157937878313839,
`745` = 0.24612775921444, `746` = 0.363774818037969, `747` = 0.363774818037969,
`748` = -0.157937878313839, `749` = 0.363774818037969, `750` = -0.157937878313839,
`751` = 0.304951288626205, `752` = -0.157937878313839, `753` = -0.157937878313839,
`754` = 0.20307665164942, `755` = 0.363774818037969, `756` = 0.363774818037969,
`757` = -0.636225181962031, `758` = -0.636225181962031, `759` = -0.133420440382588,
`760` = -0.210343517305665, `761` = -0.0513691583313063, `762` = -0.24720249166464,
`763` = 0.366579559617412, `764` = 0.615717530515643, `765` = -0.0513691583313063,
`766` = -0.0716072535694015, `767` = -0.518035824997973, `768` = 0.21529750833536,
`769` = -0.0894643964265444, `770` = 0.148630841668694, `771` = -0.0894643964265444,
`772` = -0.26907749166464, `773` = -0.0661597441212203, `774` = -0.451369158331306,
`775` = -0.232321539283687, `776` = 0.339107032144884, `777` = 0.12482131785917,
`778` = -0.118035824997973, `779` = -0.43470249166464, `780` = -0.160892967855116,
`781` = -0.0842824694843566, `782` = -0.18470249166464, `783` = 0.12482131785917,
`784` = 0.12482131785917, `785` = -0.0513691583313063, `786` = 0.328118021155873,
`787` = 0.481964175002027, `788` = 0.00797716226313461, `789` = -0.205030164215358,
`790` = 0.29369144797742, `791` = -0.342672188386216, `792` = 0.252024781310754,
`793` = 0.554304192521241, `794` = 0.261399781310754, `795` = -0.205030164215358,
`796` = 0.29369144797742, `797` = -0.205030164215358, `798` = -0.70630855202258,
`799` = 0.29369144797742, `800` = 0.16869144797742, `801` = -0.205030164215358,
`802` = -0.234086329800357, `803` = 0.419969835784642, `804` = -0.70630855202258,
`805` = 0.29369144797742, `806` = 0.248236902522875, `807` = -0.205030164215358,
`808` = 0.29369144797742, `809` = 0.0436914479774203, `810` = -0.205030164215358,
`811` = -0.205030164215358, `812` = 0.816410374624344, `813` = 0.29369144797742,
`814` = 0.29369144797742, `815` = 0.29369144797742, `816` = 0.29369144797742,
`817` = 0.0436914479774203, `818` = 0.0625367580014273, `819` = -0.302091690112839,
`820` = 0.00710312088328768, `821` = 0.0209489932723173, `822` = 0.00710312088328768,
`823` = 0.0771023988848099, `824` = 0.00710312088328768, `825` = 0.0209489932723173,
`826` = 0.00710312088328768, `827` = 0.00710312088328768, `828` = 0.0771023988848099,
`829` = 0.00710312088328768, `830` = 0.0979083098871607, `831` = 0.0625367580014273,
`832` = 0.0771023988848099, `833` = -0.0138066920242811, `834` = 0.0625367580014273,
`835` = 0.0771023988848099, `836` = 0.0209489932723173, `837` = 0.0771023988848099,
`838` = 0.0209489932723173, `839` = 0.00710312088328768, `840` = 0.0209489932723173,
`841` = 0.0771023988848099, `842` = 0.0625367580014273, `843` = 0.0771023988848099,
`844` = 0.0209489932723173, `845` = 0.0625367580014273, `846` = 0.0771023988848099,
`847` = 0.0771023988848099, `848` = 0.362283795008087, `849` = -0.537716204991913,
`850` = 0.0360937847950291, `851` = 0.0360937847950291, `852` = 0.362283795008087,
`853` = 0.0360937847950291, `854` = 0.0360937847950291, `855` = 0.102283795008087,
`856` = -0.0543828716585791, `857` = 0.0360937847950291, `858` = -0.588906215204971,
`859` = 0.0360937847950291, `860` = -0.512716204991913, `861` = 0.0360937847950291,
`862` = 0.162283795008088, `863` = 0.0360937847950291, `864` = 0.0289504616747541,
`865` = 0.0360937847950291, `866` = 0.0360937847950291, `867` = 0.0360937847950291,
`868` = 0.0360937847950291, `869` = 0.0360937847950291, `870` = 0.0360937847950291,
`871` = 0.0360937847950291, `872` = 0.0360937847950291, `873` = 0.179244923754071,
`874` = 0.0360937847950291, `875` = 0.0360937847950291, `876` = 0.0360937847950291,
`877` = -0.511918870326145, `878` = 0.0595097011024268, `879` = 0.0595097011024268,
`880` = 0.371078582137706, `881` = 0.0595097011024268, `882` = 0.0595097011024268,
`883` = 0.0595097011024268, `884` = 0.371078582137706, `885` = 0.371078582137706,
`886` = 0.0595097011024268, `887` = 0.371078582137706, `888` = -0.0313993898066641,
`889` = -0.840862906357626, `890` = 0.0595097011024268, `891` = -0.628921417862294,
`892` = -0.40715696556424, `893` = 0.371078582137706, `894` = 0.0595097011024268,
`895` = -0.288921417862294, `896` = 0.371078582137706, `897` = 0.0595097011024268,
`898` = 0.0595097011024268, `899` = -0.628921417862294, `900` = 0.424933421491569,
`901` = 0.133955693705007, `902` = -0.866044306294993, `903` = 0.0130718569655852,
`904` = 0.167321874405864, `905` = 0.0130718569655852, `906` = 0.133955693705007,
`907` = 0.0130718569655852, `908` = 0.133955693705007, `909` = 0.133955693705007,
`910` = -0.832678125594136, `911` = 0.109929041123825, `912` = 0.167321874405864,
`913` = 0.133955693705007, `914` = 0.167321874405864, `915` = 0.0130718569655852,
`916` = 0.0130718569655852, `917` = 0.109929041123825, `918` = 0.133955693705007,
`919` = 0.133955693705007, `920` = 0.133955693705007, `921` = 0.133955693705007,
`922` = 0.0130718569655852, `923` = 0.0130718569655852, `924` = -0.0535948097010814,
`925` = -0.890070958876175, `926` = 0.133955693705007, `927` = 0.0130718569655852,
`928` = 0.323675500086474, `929` = -0.100287573946261, `930` = -0.398546722135748,
`931` = -0.509657833246859, `932` = -0.509657833246859, `933` = 0.440342166753141,
`934` = -0.0817298350815849, `935` = 0.935882445242684, `936` = 0.742109795319327,
`937` = -0.0641175547573164, `938` = -0.0817298350815849, `939` = -0.100287573946261,
`940` = 0.935882445242684, `941` = -0.0817298350815849, `942` = -0.509657833246859,
`943` = 0.0317200885873054, `944` = 0.0317200885873054, `945` = 0.0317200885873054,
`946` = 0.233992751353997, `947` = 0.0317200885873054, `948` = -0.766007248646003,
`949` = -0.766007248646003, `950` = 0.0317200885873054, `951` = 0.0317200885873054,
`952` = 0.0317200885873054, `953` = 0.0317200885873054, `954` = 0.0317200885873054,
`955` = 0.0317200885873054, `956` = 0.0317200885873054, `957` = 0.0317200885873054,
`958` = 0.233992751353997, `959` = 0.0317200885873054, `960` = -0.766007248646003,
`961` = 0.0317200885873054, `962` = 0.0317200885873054, `963` = 0.0317200885873054,
`964` = 0.0317200885873054, `965` = 0.0317200885873054, `966` = 0.0317200885873054,
`967` = 0.0317200885873054, `968` = 0.0317200885873054, `969` = 0.233992751353997,
`970` = 0.0317200885873054, `971` = 0.0317200885873054, `972` = 0.0317200885873054,
`973` = 0.0917473909831028, `974` = 0.147302946538658, `975` = 0.341747390983103,
`976` = 0.0500807243164362, `977` = 0.225080724316436, `978` = 0.175080724316436,
`979` = 0.425080724316436, `980` = 0.0750807243164362, `981` = 0.225080724316436,
`982` = 0.0917473909831028, `983` = 0.175080724316436, `984` = 0.0917473909831028,
`985` = -0.0193637201280082, `986` = 0.177858502094214, `987` = 0.425080724316436,
`988` = 0.147302946538658, `989` = 0.0361918354275473, `990` = 0.14915479839051,
`991` = 0.239895539131251, `992` = 0.225080724316436, `993` = 0.25841405764977,
`994` = 0.239895539131251, `995` = 0.13936643860215, `996` = 0.391747390983103,
`997` = 0.0616963254768566, `998` = 0.00700209757004633, `999` = -0.173917895133345,
`1000` = 0.0616963254768566, `1001` = 0.0616963254768566, `1002` = -0.123917895133345,
`1003` = 0.0616963254768566, `1004` = 0.0206551451808251, `1005` = 0.0616963254768566,
`1006` = 0.0616963254768566, `1007` = 0.0616963254768566, `1008` = 0.0616963254768566,
`1009` = 0.0760821048666546, `1010` = 0.00700209757004633, `1011` = 0.0206551451808251,
`1012` = 0.0616963254768566, `1013` = 0.00700209757004633, `1014` = 0.0616963254768566,
`1015` = 0.0616963254768566, `1016` = 0.0616963254768566, `1017` = 0.00700209757004633,
`1018` = 0.00700209757004633, `1019` = 0.00700209757004633, `1020` = 0.0616963254768566,
`1021` = 0.0616963254768566, `1022` = 0.0206551451808251, `1023` = 0.0760821048666546,
`1024` = 0.0760821048666546, `1025` = 0.0760821048666546, `1026` = 0.00700209757004633,
`1027` = 0.139491354384717, `1028` = 0.326529999082812, `1029` = 0.06256827746164,
`1030` = 0.100602465495828, `1031` = 0.118658021051383, `1032` = 0.113850328743691,
`1033` = 0.118658021051383, `1034` = 0.139491354384717, `1035` = 0.139491354384717,
`1036` = 0.139491354384717, `1037` = 0.139491354384717, `1038` = 0.139491354384717,
`1039` = 0.139491354384717, `1040` = 0.139491354384717, `1041` = 0.139491354384717,
`1042` = 0.139491354384717, `1043` = 0.118658021051383, `1044` = 0.139491354384717,
`1045` = 0.139491354384717, `1046` = 0.139491354384717, `1047` = -0.289073763945616,
`1048` = 0.160764859786535, `1049` = 0.373910231173135, `1050` = 0.160764859786535,
`1051` = 0.160764859786535, `1052` = 0.160764859786535, `1053` = 0.361229760471748,
`1054` = -0.626089768826865, `1055` = -0.626089768826865, `1056` = 0.373910231173135,
`1057` = -0.130901806880132, `1058` = -0.626089768826865, `1059` = -0.422568473546799,
`1060` = 0.151688008950913, `1061` = 0.160764859786535, `1062` = 0.160764859786535,
`1063` = 0.290576897839802, `1064` = -0.572103572861586, `1065` = 0.160764859786535,
`1066` = 0.160764859786535, `1067` = 0.160764859786535, `1068` = -0.626089768826865,
`1069` = 0.373910231173135, `1070` = 0.373910231173135, `1071` = 0.373910231173135,
`1072` = 0.373910231173135, `1073` = 0.160764859786535, `1074` = -0.084423102160198,
`1075` = 0.0837593794784431, `1076` = -0.0829072871882235, `1077` = 0.0284871614905152,
`1078` = 0.0284871614905152, `1079` = 0.0837593794784431, `1080` = 0.0837593794784431,
`1081` = 0.0837593794784431, `1082` = 0.0837593794784431, `1083` = 0.0284871614905152,
`1084` = 0.129476815173992, `1085` = 0.0837593794784431, `1086` = -0.138179505176151,
`1087` = -0.0829072871882235, `1088` = 0.102726397654094, `1089` = 0.0284871614905152,
`1090` = 0.0837593794784431, `1091` = 0.0284871614905152, `1092` = 0.0837593794784431,
`1093` = 0.129476815173992, `1094` = 0.0837593794784431, `1095` = 0.0284871614905152,
`1096` = 0.0837593794784431, `1097` = 0.0837593794784431, `1098` = 0.0837593794784431,
`1099` = 0.652631530043108, `1100` = 0.445570065542534, `1101` = -0.512763267790799,
`1102` = -0.505818823346355, `1103` = 0.0481341681066367, `1104` = -0.554429934457466,
`1105` = -0.505818823346355, `1106` = -0.477506857534389, `1107` = 0.445570065542534,
`1108` = 0.0609546809271496, `1109` = 0.153903398875868, `1110` = 0.424736732209201,
`1111` = -0.498019678047209, `1112` = -0.554429934457466, `1113` = -0.49887437890191,
`1114` = 0.445570065542534, `1115` = 0.445570065542534, `1116` = -0.540541045568577,
`1117` = -0.519707712235244, `1118` = -0.47387437890191, `1119` = 0.00401917798910445,
`1120` = 0.00401917798910445, `1121` = 0.00401917798910445, `1122` = 0.00401917798910445,
`1123` = 0.0362643777731282, `1124` = 0.0576904175536409, `1125` = 0.00401917798910445,
`1126` = 0.00401917798910445, `1127` = 0.00401917798910445, `1128` = 0.00401917798910445,
`1129` = 0.00401917798910445, `1130` = 0.00401917798910445, `1131` = 0.00401917798910445,
`1132` = 0.00401917798910445, `1133` = 0.00401917798910445, `1134` = 0.00401917798910445,
`1135` = 0.00401917798910445, `1136` = 0.00401917798910445, `1137` = 0.0119258292984928,
`1138` = 0.00401917798910445, `1139` = 0.00401917798910445, `1140` = 0.00401917798910445,
`1141` = 0.00401917798910445, `1142` = 0.0119258292984928, `1143` = 0.00401917798910445,
`1144` = 0.00401917798910445, `1145` = 0.00401917798910445, `1146` = 0.00401917798910445,
`1147` = 0.00401917798910445, `1148` = 0.00401917798910445, `1149` = 0.0244715517611499,
`1150` = 0.0244715517611499, `1151` = 0.0244715517611499, `1152` = 0.226573830251397,
`1153` = 0.0244715517611499, `1154` = 0.0244715517611499, `1155` = 0.0244715517611499,
`1156` = 0.275666482147827, `1157` = 0.0244715517611499, `1158` = 0.0244715517611499,
`1159` = 0.0244715517611499, `1160` = 0.0244715517611499, `1161` = 0.0244715517611499,
`1162` = 0.0244715517611499, `1163` = 0.0244715517611499, `1164` = 0.0244715517611499,
`1165` = 0.0244715517611499, `1166` = 0.0244715517611499, `1167` = 0.0244715517611499,
`1168` = 0.0244715517611499, `1169` = 0.0244715517611499, `1170` = 0.0244715517611499,
`1171` = -0.724333517852173, `1172` = 0.0244715517611499, `1173` = -0.724333517852173,
`1174` = 0.0244715517611499, `1175` = 0.58556833197041, `1176` = -0.0170673192288852,
`1177` = 0.107932680771115, `1178` = 0.0694711423095764, `1179` = -0.352658472552792,
`1180` = 0.107932680771115, `1181` = 0.107932680771115, `1182` = 0.107932680771115,
`1183` = 0.107932680771115, `1184` = 0.107932680771115, `1185` = 0.107932680771115,
`1186` = 0.107932680771115, `1187` = 0.107932680771115, `1188` = 0.107932680771115,
`1189` = -0.352658472552792, `1190` = 0.647341527447208, `1191` = 0.107932680771115,
`1192` = -0.352658472552792, `1193` = -0.352658472552792, `1194` = -0.352658472552792,
`1195` = -0.41443166802959, `1196` = 0.107932680771115, `1197` = 0.107932680771115,
`1198` = 0.107932680771115, `1199` = 0.107932680771115, `1200` = 0.107932680771115,
`1201` = 0.107932680771115, `1202` = -0.352658472552792)
Again, please do let me know if I have made an easily correctable mistake. Thank you!
Regards, Utek
Hi Utek,
just from the theoretical side, what you describe sounds more like continuous proportions than a k/n binomial process to me, but with near certainty, this has nothing to do with the plots and in the end it's up to you what model you want to fit.
About the residuals: I need the DHARMa residuals, not the model residuals (the model residuals are useless). So, residuals(res).
Hi Florian,
Here are the DHARMa residuals:
> dput(residuals(res))
c(0.264, 0.148573131445795, 0.052896301433444, 0.104, 0.144807734161615,
0.0347340918080881, 0.144213027246296, 0.0960572091573849, 0.0573501304388046,
0.000714320719242096, 0.0587746998742223, 0.124, 0.48, 0.273922465667129,
0.831321206184104, 0.131019222646952, 0.152, 0.116063548015431,
0.164, 0.347289138257504, 0.174419575466774, 0.913563089312054,
0.038343763563782, 0.162773686090484, 0.0421402595676482, 0.0252567971218377,
0.244489019662142, 0.14, 0.16, 0.167941471645609, 0.654245762632228,
0.324, 0.689256176287308, 0.645887244958431, 0.316, 0.359774041358382,
0.713801730699837, 0.942531933540478, 0.824020865034312, 0.711051007024944,
0.673307002663612, 0.112310483098961, 0.501319775474258, 0.543778247658163,
0.609262305142358, 0.612230427800678, 0.918598642711528, 0.94794175744988,
0.424, 0.908874171189032, 0.20909894621931, 0.256, 0.66541963236779,
0.781509081721306, 0.486855502286926, 0.563461286487058, 0.572979526878335,
0.282109905190766, 0.385139843722805, 0.955298232659697, 0.619545819688588,
0.802379825358279, 0.890191148929298, 0.915386697757989, 0.524101244427264,
0.569590357623994, 0.436184268938377, 0.852460162879899, 0.442430190459825,
0.5635359286163, 0.228, 0.253959779340774, 0.647857793226838,
0.661688047610223, 0.597623759100214, 0.954568323716521, 0.662056447420269,
0.420553711290471, 0.930057042840868, 0.777284991873428, 0.802457452286035,
0.254268425837159, 0.304115434653126, 0.981906942697242, 0.975340183218941,
0.454984499290586, 0.893073470696807, 0.48167505470477, 0.606791982799768,
0.915724535988644, 0.372828364646062, 0.294627582684159, 0.92338137418963,
0.162320812951773, 0.0644569171182811, 0.137060892596841, 0.810507204197347,
0.940887507907115, 0.912442828550003, 0.523249233001843, 0.21236200502608,
0.32721545515582, 0.780917272856459, 0.570058659315109, 0.902031267199665,
0.802237480729818, 0.471013148488477, 0.394859552099369, 0.190385933220387,
0.365190493129194, 0.506544250991195, 0.363800012296997, 0.332460799701512,
0.213288537407294, 0.770638034947216, 0.252, 0.370109149094671,
0.443068787008524, 0.733361267697066, 0.247839368696325, 0.0579701418410987,
0.876173617448658, 0.188, 0.053589738923125, 0.272877568230033,
0.939745768591762, 0.549344369266182, 0.648331866534427, 0.826817641141824,
0.204, 0.453625658260658, 0.443655690437183, 0.98846366481483,
0.244, 0.308398005571216, 0.996522573370487, 0.24500601126533,
0.328, 0.631233786498197, 0.384, 0.148, 0.360492278495803, 0.333327471200377,
0.577158056226559, 0.759594258381985, 0.922022665151395, 0.378427025559358,
0.104, 0.784732271288522, 0.499405817330815, 0.877478158855811,
0.364, 0.743353627718985, 0.376, 0.691264337878674, 0.592, 0.552,
0.899299416067079, 0.682074969493784, 0.524, 0.416, 0.754419157125056,
0.990384378563613, 0.438099164664745, 0.162053166786209, 0.608,
0.167193218506873, 0.970294051194563, 0.544, 0.596, 0.784617117855698,
0.61776313243527, 0.973870973970741, 0.849762387018651, 0.226288476604968,
0.282445109661669, 0.761603587649763, 0.272, 0.862911293376237,
0.32, 0.32, 0.263932383911684, 0.324, 0.288, 0.308414085354656,
0.32, 0.348, 0.32, 0.316, 0.274120333668776, 0.276, 0.360351232690737,
0.0335246472805738, 0.342252408756875, 0.315631537610665, 0.34,
0.28, 0.336, 0.32, 0.468624704740942, 0.551090939890593, 0.486960449498147,
0.155519950892776, 0.905207663943991, 0.518314882567152, 0.114583445709199,
0.342154786262661, 0.876043462646194, 0.972927158117294, 0.152509565927088,
0.0879697447260842, 0.44570893054828, 0.0617725699059665, 0.0259644620679319,
0.666947999717668, 0.0350265203369781, 0.222320938683115, 0.326799000940286,
0.974932177720591, 0.864684296483174, 0.0365039308145642, 0.00428699134290218,
0.0291897192969918, 0.144478474158794, 0.0450180945107713, 0.578090961397626,
0.500083503020927, 0.580228248119354, 0.184, 0.039416947722435,
0.999420351846144, 0.152, 0.164, 0.0653875207081437, 0.100569160664454,
0.729792999100871, 0.96112607568223, 0.0724810322867706, 0.576141042839736,
0.526324795207009, 0.810987653851509, 0.936395117962733, 0.303217599042691,
0.875094317844138, 0.0232749732397497, 0.0186984631028026, 0.0369502243939787,
0.077010289429687, 0.16, 0.0299407028853893, 0.636, 0.340567698022351,
0.0299208321869373, 0.252, 0.235707201445475, 0.504098200479522,
0.516694195661694, 0.572080211830325, 0.623372815862298, 0.0620022936612368,
0.421665675608441, 0.208156366825104, 0.333078795956448, 0.608,
0.536, 0.956301934949122, 0.7560415815413, 0.382753194980323,
0.0911274392874911, 0.932488372451626, 0.482437640525401, 0.946630462732166,
0.26, 0.548, 0.790422738417983, 0.208, 0.449894595570862, 0.964712650982663,
0.196785302728415, 0.84939386415109, 0.87147766316589, 0.605887091311626,
0.741520722365007, 0.889110935005359, 0.533115814992227, 0.831969109851867,
0.514774562686682, 0.942397669204511, 0.977486899141222, 0.821787766294554,
0.724, 0.54103151217103, 0.34, 0.890014013722539, 0.73562632724829,
0.831682650011033, 0.557304362675175, 0.768, 0.877318263763562,
0.581727775388397, 0.416673369500786, 0.921990588354878, 0.28,
0.601940313860774, 0.404323194045573, 0.912007918022573, 0.503438361652195,
0.884767416215502, 0.852777965754271, 0.237504390478134, 0.0495172826759517,
0.502575608394109, 0.751396272470243, 0.329667655041441, 0.0513092222157866,
0.461017856797203, 0.488442242575809, 0.52, 0.476, 0.221079924004152,
0.776908277103677, 0.758048487151042, 0.772, 0.960852452754974,
0.476, 0.109787419863045, 0.48, 0.0767963702064007, 0.638856650829315,
0.0893874916713685, 0.306795011609793, 0.596, 0.729704238901846,
0.528089327369817, 0.786617090069689, 0.553300748769194, 0.707758359142579,
0.999905068119057, 0.552955256970599, 0.592140197837725, 0.673142271082848,
0.806252887890674, 0.63126500314381, 0.538447078973055, 0.618471513075754,
0.701490483859554, 0.83496948716417, 0.269382770732977, 0.512,
0.740454311642796, 0.625894425958395, 0.416, 0.83579227632843,
0.966036877140403, 0.587397767114453, 0.697885818636045, 0.973024269188754,
0.881649467768148, 0.900933626759797, 0.468, 0.963957917684689,
0.628, 0.00576529160141945, 0.511152378632687, 0.648170166873373,
0.456, 0.894034785415977, 0.791037054694258, 0.799217310448177,
0.784398618258536, 0.775416806815192, 0.99404729899019, 0.444,
0.237814155975357, 0.424241482602432, 0.560612052380107, 0.578048578430899,
0.584901013915427, 0.791689014746808, 0.550700735979713, 0.068,
0.380199038356543, 0.581289433147758, 0.567522496555001, 0.757069277594797,
0.302061338275671, 0.987275709141046, 0.718899740956724, 0.611633794136345,
0.408716152476147, 0.978040051570162, 0.594129319470376, 0.068,
0.594021573830396, 0.909784586060792, 0.768817603874952, 0.345117120883428,
0.342134587660432, 0.721541509073228, 0.221657490623184, 0.843127764100209,
0.934525801725686, 0.810559762297198, 0.419776917240582, 0.248,
0.0669442113703117, 0.338135780900717, 0.628, 0.204, 0.0268486514696851,
0.00513319233432412, 0.168873594783247, 0.267449972167611, 0.196,
0.69756508214213, 0.188, 0.502611963640898, 0.196, 0.417556343945675,
0.367142258442938, 0.29159021716658, 0.612230421025306, 0.19241504477337,
0.419732008181512, 0.250947001738474, 0.566815522775054, 0.363210950158536,
0.244832706034184, 0.0653923301082104, 0.602633126950823, 0.840590527774766,
0.124444519113749, 0.163585366874933, 0.418279968719929, 0.286297008268535,
0.957041731376201, 0.135952198550105, 0.242834505036473, 0.0801034728772938,
0.16796200620383, 0.186004247810692, 0.0141297215949744, 0.0449624276161194,
0.250845633493736, 0.101548213034868, 0.388391802415252, 0.879210411757231,
0.168, 0.254449022382498, 0.228, 0.276, 0.571800382425077, 0.0139603370167315,
0.897484818067402, 0.774651248786598, 0.0929268816243857, 0.881445589680225,
0.0635036554094404, 0.0977519768476486, 0.885861082795076, 0.857980385731906,
0.328650451298803, 0.529334105014801, 0.758572384351864, 0.550583774263971,
0.37693532047607, 0.91347997206822, 0.723958935502917, 0.0697163785183802,
0.711111226743087, 0.515478654127568, 0.347711997214705, 0.296,
0.0717123785689473, 0.930542584076524, 0.240136425100267, 0.4604109413689,
0.981984261646867, 0.609729283098131, 0.779781488328241, 0.618297688257881,
0.626278048058972, 0.35146939072758, 0.59578694949951, 0.088,
0.600467284796759, 0.852914429761469, 0.601944298008457, 0.104,
0.85728884710744, 0.228596291791648, 0.104, 0.116, 0.144, 0.237169502520002,
0.4, 0.308, 0.422178809581324, 0.452697855841368, 0.507404206284322,
0.12, 0.929798217757605, 0.767137076528743, 0.816, 0.596836035876535,
0.999173479959369, 0.66854948859103, 0.731203337199986, 0.768,
0.472, 0.609530354619026, 0.464, 0.476, 0.60101402843371, 0.961521647274494,
0.955605239671655, 0.821583336136304, 0.976001135803759, 0.620150113810785,
0.91694354660809, 0.570112564638257, 0.742735408794135, 0.785106026635505,
0.537551356726326, 0.19444205121696, 0.586430993691087, 0.604,
0.792554481159896, 0.725737253398634, 0.7619376309691, 0.788,
0.973420108312741, 0.27158867343422, 0.488, 0.863527828156948,
0.196, 0.134797853022814, 0.446143939540722, 0.201492481422611,
0.742355890067294, 0.567543326799758, 0.737812597776763, 0.799730244535021,
0.677271046280861, 0.0182246061805636, 0.614565356015228, 0.211793760616332,
0.708358583506197, 0.481256488039158, 0.447904720373452, 0.554797805854119,
0.29711443326436, 0.114323287788779, 0.899021913398057, 0.371295465135947,
0.736668310593814, 0.552, 0.0255506191402674, 0.332191411044449,
0.00534543976187706, 0.737414743932895, 0.95235238256678, 0.722487516879104,
0.90617590562813, 0.963243110924959, 0.869828064113855, 0.972248883627355,
0.815600438134745, 0.945759192660451, 0.817122454822063, 0.695783167991787,
0.801906168047339, 0.858385029812343, 0.642119642868638, 0.973792211309075,
0.833022914240137, 0.815535245249048, 0.860702479740605, 0.79546878835652,
0.696332056135871, 0.827839491423219, 0.699005407826044, 0.780030949378386,
0.878259603586048, 0.836229626977816, 0.797011480935849, 0.212200598307885,
0.18, 0.0233556863069534, 0.335169788723811, 0.607666980346665,
0.599710503265262, 0.301344121458009, 0.544, 0.252, 0.798070589866489,
0.208, 0.192242873601615, 0.510976048979908, 0.150078876434825,
0.788852560818195, 0.290891806527972, 0.0323039871454239, 0.272262744002044,
0.016503616631031, 0.256976346150041, 0.694443789999932, 0.226044367975555,
0.941372850257903, 0.619995731489733, 0.777904637241736, 0.199949599605054,
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