head(dados)
## # A tibble: 6 × 14
## CD_MUN mun latitude longitude H14 P14 cad14 san14 cor.cad14 gpc14 edu14
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3100104 Abad… -18.5 -47.4 1 30.1 48.2 12.6 33.8 1.44 76.0
## 2 3100203 Abae… -19.2 -45.4 1 30.2 53.6 4.34 34.3 2.81 81.5
## 3 3100302 Abre… -20.3 -42.5 1 49.3 63.3 4.42 65.0 2.45 88.4
## 4 3100401 Acai… -20.4 -43.1 1 58.9 71.6 1.12 81.1 7.09 100
## 5 3100500 Açuc… -19.1 -42.5 3 48.3 67.8 3.63 79.6 4.38 88.5
## 6 3100609 Agua… -18.0 -42.4 0 65.5 75.0 7.38 76.6 0.78 100
## # ℹ 3 more variables: rend14 <dbl>, pop14 <dbl>, pmpc14 <dbl>
observed = dados$H14
prop <- dados$P14
population = dados$pop14
n=length(observed)
r = sum(observed)/sum(population)
expected = population * r
library(DCluster)
## Warning: pacote 'DCluster' foi compilado no R versão 4.4.1
## Carregando pacotes exigidos: boot
## Carregando pacotes exigidos: spdep
## Warning: pacote 'spdep' foi compilado no R versão 4.4.2
## Carregando pacotes exigidos: spData
## Warning: pacote 'spData' foi compilado no R versão 4.4.1
## To access larger datasets in this package, install the spDataLarge
## package with: `install.packages('spDataLarge',
## repos='https://nowosad.github.io/drat/', type='source')`
## Carregando pacotes exigidos: sf
## Warning: pacote 'sf' foi compilado no R versão 4.4.2
## Linking to GEOS 3.12.2, GDAL 3.9.3, PROJ 9.4.1; sf_use_s2() is TRUE
## Carregando pacotes exigidos: MASS
## Warning: pacote 'MASS' foi compilado no R versão 4.4.1
##
## Anexando pacote: 'MASS'
## O seguinte objeto é mascarado por 'package:patchwork':
##
## area
eb <- empbaysmooth(observed, expected)
EBPG <- eb$smthrr
eb$nu
## [1] 2.516455
eb$alpha
## [1] 3.929737
nu.alpha <- eb$nu/eb$alpha; nu.alpha
## [1] 0.640362
Especificações a priori
set.seed(1928301)
# nu Ga (a_nu b_nu) e alpha Ga(a_al , b_al):
a_nu = 0.1 ; b_nu = 0.1; a_al= 0.1; b_al= 0.1
Organizando em lista todos os elementos que o Stan vai usar
data = list(n=n , observed=observed, expected=expected,
a_nu=a_nu , b_nu=b_nu , a_al=a_al, b_al =b_al)
# Parametros a serem estimados
pars = c("mu","theta","nu","alpha")
# Chutes iniciais
initvals = list()
initvals[[1]] = list(theta=runif(n,0.5,1), nu=0.5, alpha=0.5)
# Aspectos relacionados ao MCMC
iter = 10000 # total de iteracoes (incluindo warm-up).
warmup = 2000
chains = 1
stanModel = rstan::stan_model("scriptSTAN.stan")
output = sampling(stanModel, data = data,
iter = iter, warmup = warmup, chains = chains,
pars = pars, init = initvals, verbose = FALSE)
##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 0.000498 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 4.98 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1:
## Chain 1:
## Chain 1: Iteration: 1 / 10000 [ 0%] (Warmup)
## Chain 1: Iteration: 1000 / 10000 [ 10%] (Warmup)
## Chain 1: Iteration: 2000 / 10000 [ 20%] (Warmup)
## Chain 1: Iteration: 2001 / 10000 [ 20%] (Sampling)
## Chain 1: Iteration: 3000 / 10000 [ 30%] (Sampling)
## Chain 1: Iteration: 4000 / 10000 [ 40%] (Sampling)
## Chain 1: Iteration: 5000 / 10000 [ 50%] (Sampling)
## Chain 1: Iteration: 6000 / 10000 [ 60%] (Sampling)
## Chain 1: Iteration: 7000 / 10000 [ 70%] (Sampling)
## Chain 1: Iteration: 8000 / 10000 [ 80%] (Sampling)
## Chain 1: Iteration: 9000 / 10000 [ 90%] (Sampling)
## Chain 1: Iteration: 10000 / 10000 [100%] (Sampling)
## Chain 1:
## Chain 1: Elapsed Time: 106.969 seconds (Warm-up)
## Chain 1: 210.385 seconds (Sampling)
## Chain 1: 317.354 seconds (Total)
## Chain 1:
## Warning in validityMethod(object): The following variables have undefined
## values: mu[1]. Many subsequent functions will not work correctly.
## Warning: There were 7777 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is NA, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
result = extract(output)
theta_estimate = result$theta
porteriori_estimate = apply(theta_estimate, 2, mean)
porteriori_estimate
## [1] -240.97326106 0.28614733 0.45283880 0.66918829 0.89068401
## [6] 0.26065717 0.49177929 0.69459642 1.97292175 0.25451281
## [11] 1.35548722 0.41892431 0.83016598 0.51147286 0.35992517
## [16] 0.38685167 0.62885862 0.87920455 0.86611542 0.77312724
## [21] 0.58331140 0.40949118 0.35291352 0.50789792 0.62774943
## [26] 0.29083058 0.39712075 0.48933056 0.46613656 0.71521817
## [31] 0.31149590 0.31569869 0.93563304 0.63546590 1.00868124
## [36] 0.57719665 1.44499554 0.96157553 0.52111301 0.40998774
## [41] 0.76397960 0.57944699 0.86842702 0.53149420 0.29973173
## [46] 0.42913829 0.20979744 0.53308557 0.52004289 0.86704649
## [51] 0.45001750 1.09566697 0.43842417 0.38150652 0.53739433
## [56] 0.44960802 0.39437763 0.37478942 0.44907219 0.53135416
## [61] 0.28599097 0.69507401 0.46830818 0.35498105 0.43198338
## [66] 1.54786598 1.16550309 0.36546860 0.25861371 0.43891614
## [71] 0.41384407 2.55783171 0.49946465 0.44244917 0.86351936
## [76] 0.36761032 0.48282348 0.94151118 0.69985915 0.68231596
## [81] 0.39063548 0.36549384 0.26472875 0.32818735 0.39122247
## [86] 0.43333777 0.39190550 0.68357691 0.25965867 0.36503438
## [91] 0.63082747 0.41727776 0.60017201 0.46069532 0.24662467
## [96] 0.63319031 1.43594055 0.34404448 0.64703267 0.64604982
## [101] 1.42705647 0.97362809 0.40726944 0.35101389 0.79229766
## [106] 0.28496148 0.59788711 0.57400761 0.57173978 0.35482994
## [111] 0.48824376 1.68755280 0.31061302 0.99767600 0.61891279
## [116] 0.31919425 0.42958574 0.43439659 0.23609514 0.51033647
## [121] 0.37151498 0.70944425 0.73270916 0.86226306 0.58130987
## [126] 1.02648830 0.35538133 0.55887930 0.42532226 0.75305671
## [131] 0.57123658 0.72027712 0.44620732 0.44802919 0.63394285
## [136] 0.65367202 0.57726443 0.74924077 0.37610948 0.46113917
## [141] 0.51411221 0.73122363 0.27535230 0.43839268 0.30432877
## [146] 1.38414042 0.91346034 1.03232712 0.31696481 0.70201184
## [151] 0.57812145 0.30354011 0.82331362 0.28479595 0.48576974
## [156] 0.47666077 0.49785516 0.42295843 0.30486762 0.39818338
## [161] 0.46421019 0.91736612 0.52220289 0.52864159 0.25603399
## [166] 0.44947920 0.52947685 0.73624907 0.75700441 0.63924097
## [171] 0.22911382 0.52734910 0.75459927 0.69315679 0.44722686
## [176] 0.42222434 0.28777030 0.47220717 0.48930526 0.39349766
## [181] 0.39310286 0.38083292 0.89316282 0.94063612 0.29544333
## [186] 0.71405982 0.68874226 0.60056430 0.49626786 0.79625294
## [191] 0.42163057 0.42031041 0.36982175 0.39807278 0.47224655
## [196] 0.32512364 0.87313355 1.78589591 0.29901586 0.36145824
## [201] 0.45430461 0.55616418 0.61356271 0.71881603 0.56907354
## [206] 1.78640945 0.60572434 0.59922927 0.65260114 0.48658310
## [211] 0.39571051 0.35005303 0.41577108 1.93097473 0.55629218
## [216] 0.40524629 0.53476509 0.50223150 0.42282246 0.34384497
## [221] 0.57512354 0.79337201 0.88899264 0.35804305 0.66372403
## [226] 0.54429867 0.36403112 0.51994494 0.47975636 0.29614997
## [231] 1.02456059 0.41697295 0.81158358 0.42133491 0.32705462
## [236] 0.60294805 0.54074401 0.42654696 0.34334007 0.48484718
## [241] 0.82682883 0.37396480 0.54549477 0.51208065 1.25471677
## [246] 1.70792446 0.34320522 0.67208329 0.59340942 0.71526877
## [251] 0.26648743 0.50847061 0.44942764 0.39874778 0.47475510
## [256] 0.63235535 0.40734834 0.28683686 0.42008631 0.24060243
## [261] 0.45405377 0.51752205 0.54497162 0.36010732 0.16330201
## [266] 0.96098023 0.77487059 0.71123705 0.57734410 0.82834731
## [271] 1.45587018 0.60729905 0.67400085 0.41271825 0.45325927
## [276] 0.54556729 0.48084008 0.33729660 0.27549389 0.76345000
## [281] 0.44391860 0.48070817 0.41659471 0.45487756 0.32888269
## [286] 0.77282905 0.52690474 1.08304709 1.12227940 0.83407524
## [291] 0.88089466 0.61880208 0.37168253 0.48481282 0.56221305
## [296] 0.38701014 0.43602627 0.47764754 0.43096199 0.52824574
## [301] 0.72621112 0.75877409 0.73117267 0.36950701 1.29207929
## [306] 0.69918657 1.05429338 0.47836222 0.61181160 0.53503646
## [311] 0.55311108 0.54320779 1.07114526 0.33264937 2.05517456
## [316] 0.55220418 0.49867457 0.35265199 0.45685730 0.33505295
## [321] 0.54757668 0.49098630 0.47710403 0.55455562 0.44136956
## [326] 0.49817708 0.35261909 1.34747001 0.56817760 0.57706120
## [331] 0.42842868 0.47443827 0.53289840 0.87638693 0.37592617
## [336] 0.65685661 0.51687685 1.04452738 0.46391794 0.44646937
## [341] 0.31612941 1.94496704 0.27965687 0.33242286 0.40587137
## [346] 0.29294997 0.79378635 0.36892411 0.75876551 0.40356028
## [351] 0.52625436 0.67579243 0.68973628 0.37737222 0.82526707
## [356] 1.31589495 0.91343900 0.45817257 0.30651349 1.28642383
## [361] 1.15579945 0.75959380 0.45671918 0.39178144 0.35140120
## [366] 0.46337280 1.64295005 0.52178314 0.55731986 0.54320139
## [371] 0.81531584 0.49359764 0.39472092 1.41703392 0.40399632
## [376] 0.88009594 1.35444599 0.50090227 0.59205201 0.33669662
## [381] 0.93040821 0.24382585 0.97461781 0.42421340 0.43149427
## [386] 0.60616978 1.06284339 0.43428554 0.96366758 0.45392560
## [391] 0.50333815 0.52016590 0.41261253 0.19221300 0.77031134
## [396] 0.94006003 0.39751253 1.56097088 0.52815570 0.36626738
## [401] 0.35622428 0.54422841 0.36183712 0.50227669 0.52168867
## [406] 0.44409836 0.66661059 0.56403230 1.22455256 0.41524841
## [411] 0.59340988 1.17240310 1.06953398 1.05010977 0.41461872
## [416] 1.15066323 0.88598273 1.88305972 1.11323043 0.40251896
## [421] 1.04945220 0.43826308 0.70292042 0.53058722 0.53710451
## [426] 0.61100988 0.27660423 0.38293469 0.58887396 0.09981696
## [431] 0.86572096 0.31851624 0.77449603 0.34455908 0.64672739
## [436] 0.88172618 0.70536531 0.53190121 0.27606638 0.42024525
## [441] 0.40201891 0.39797681 0.38066793 0.39947271 0.37988939
## [446] 0.51009967 0.25328104 0.65201502 0.34413861 0.44656945
## [451] 0.96223512 0.38758299 1.22821328 1.03834366 0.59252066
## [456] 1.27819468 0.31735944 0.33750269 0.26337005 0.72622440
## [461] 0.41686206 0.82423938 0.45938879 0.72165680 0.46950887
## [466] 0.68408590 0.67677326 0.75134187 0.44442731 1.01544805
## [471] 0.74140050 0.33011488 0.80826951 0.59410899 0.45262085
## [476] 1.44787901 0.42803482 0.46211847 1.34353682 0.67440259
## [481] 0.53548305 0.58703141 0.18546131 0.54531301 0.62393244
## [486] 1.04866986 0.25846860 1.05109600 0.43342027 0.43280183
## [491] 0.48381415 0.44813134 0.40814251 0.58684734 0.33777514
## [496] 0.64491118 0.78974612 0.45445082 0.43834494 0.35737566
## [501] 1.10599762 0.33407374 0.60379946 0.47097862 0.46002884
## [506] 0.35912149 1.24525378 1.45489579 0.38420495 0.55350580
## [511] 1.61883040 0.97232861 0.44780159 0.44876970 0.35857094
## [516] 0.19883776 0.35162503 0.48430329 0.42927379 0.55291435
## [521] 0.47793887 0.33404028 0.78801384 0.44100039 1.82478295
## [526] 0.40273274 0.48648902 0.68133692 0.36895587 0.47573371
## [531] 0.40254041 0.50200645 0.46404073 0.76709792 0.54725978
## [536] 0.68912543 0.75740708 0.41987607 0.43760784 0.52023551
## [541] 0.69894667 0.71646446 1.14627098 0.36184580 0.91925891
## [546] 0.35584212 0.47592475 0.35017086 0.62531995 0.82407117
## [551] 0.81049201 2.42622859 0.84560452 0.20470595 0.93371556
## [556] 0.52078458 0.38081856 0.66012531 0.50757574 0.85546151
## [561] 0.42091454 0.87570068 0.39005534 0.80048745 0.32065646
## [566] 0.43081349 0.69212461 1.13523054 0.82111711 0.40973345
## [571] 0.81347778 0.44074352 0.56759596 0.51100673 0.49345702
## [576] 0.68082083 1.12607418 0.52537493 0.54502314 1.03077295
## [581] 0.62968571 0.84895827 0.58931303 1.01722634 0.78080882
## [586] 0.41462632 0.33198238 0.44234391 0.73064100 0.48825663
## [591] 0.36461917 0.85212169 0.36122388 0.43448663 0.37237397
## [596] 0.98500536 0.45760618 0.35020582 0.34870009 1.32318040
## [601] 0.47368440 0.97723478 0.77997052 0.34299023 0.66904849
## [606] 0.28605902 0.98032577 0.79982265 1.18396817 0.43062521
## [611] 0.86117456 0.73465349 0.35916286 0.94658784 0.31188534
## [616] 0.35006385 0.31306369 0.96692522 0.60761982 0.46440614
## [621] 0.42055192 0.43064489 0.66712328 0.68984716 0.66967526
## [626] 0.73978339 0.58115222 0.22482610 0.49349040 0.32203029
## [631] 0.43339786 0.26955216 1.37665324 0.47619935 0.95121241
## [636] 0.88885276 2.05416916 0.69015505 0.97313970 1.09187746
## [641] 0.40248553 0.61688198 0.42001947 0.37168868 0.35296581
## [646] 1.80496910 0.60612297 0.27571974 0.22872528 0.52819226
## [651] 0.46818164 0.42229404 0.56765308 0.88597988 0.73189287
## [656] 0.67357253 0.45487730 0.33307542 1.43546085 0.56955544
## [661] 0.45250237 0.44685030 0.61981496 0.79393102 0.62563841
## [666] 0.47628406 0.57322928 1.20651645 0.52541163 0.45102578
## [671] 0.97215069 0.49019595 0.79022573 0.44046217 1.90591000
## [676] 0.67807375 0.65598558 0.37576362 1.11200835 0.49303734
## [681] 0.42420748 0.81000314 0.52503281 1.67396403 0.66402411
## [686] 0.52822115 1.60387527 0.33852424 0.45402778 0.75895936
## [691] 0.45438083 0.48559267 0.48357610 0.56491788 0.83960048
## [696] 0.53688346 0.47835654 0.24604762 0.52801518 0.49799359
## [701] 0.41209764 0.64833179 0.86235448 0.33992549 0.55734906
## [706] 0.56573159 0.33945312 0.36481730 0.35312269 0.85653352
## [711] 0.39364056 0.49088026 0.37028786 0.47785719 0.65841230
## [716] 0.48066127 0.77244798 0.49101267 0.98274922 0.86575433
## [721] 0.63445842 0.32360706 0.64851791 0.97138403 0.77213077
## [726] 0.81012890 0.44122154 0.50272442 0.59039485 0.46247970
## [731] 1.08939117 0.56268516 0.67722441 0.66929893 0.69361850
## [736] 0.17331945 0.43277886 0.48671478 2.75654077 0.57684970
## [741] 0.36875834 0.72525856 0.38241957 0.37914965 0.49401436
## [746] 0.66259956 0.62116591 0.44654609 0.85845558 0.80707889
## [751] 0.43499601 0.63153941 0.61137395 0.63891155 0.35788505
## [756] 0.41639901 0.49601989 0.63414140 1.31380880 0.38100829
## [761] 0.45197348 0.48000921 0.54975244 0.37132954 0.31045195
## [766] 0.38140978 0.59402864 0.36077969 0.37086696 0.39569549
## [771] 0.51332582 0.41938430 0.44990623 0.66102574 0.44251774
## [776] 0.54471734 0.90991043 0.43278189 0.27022293 0.37476843
## [781] 0.49339134 0.69039055 0.66900076 0.59101188 0.63157578
## [786] 0.58552855 0.40259750 0.54609304 0.47808132 1.49588197
## [791] 0.68659458 0.41893397 0.37197194 0.49333644 0.21775648
## [796] 0.37509126 0.41243758 0.46019752 0.85204194 0.67263039
## [801] 0.55256653 0.48081939 0.38004183 0.55521938 0.68129949
## [806] 1.14688768 1.55701036 0.60797714 0.88042319 0.69720016
## [811] 0.49855257 0.67819623 0.31815980 0.40574911 0.55243197
## [816] 0.24075235 0.66764953 0.51738223 0.66432920 0.38152524
## [821] 0.96795281 0.45933474 0.63529510 1.20029233 1.14482231
## [826] 0.79324826 0.80630733 0.40500946 0.50618352 0.47957314
## [831] 0.90263360 0.44246307 0.62996764 0.49943058 0.51582903
## [836] 0.33593231 1.09866690 0.66175263 0.24221528 0.94953859
## [841] 0.44235131 0.45613280 0.83023339 1.24609028 1.46690114
## [846] 0.35838110 0.86381687 0.30744261 0.75499478 0.66080848
## [851] 1.10800352 0.35650777 0.47907036
ts.plot(theta_estimate[,12], xlab="Interaction")
abline(h=mean(theta_estimate[,12]), lwd=2, col="red")
ts.plot(theta_estimate[,50], xlab="Interaction")
abline(h=mean(theta_estimate[,50]), lwd=2, col="red")
mean(theta_estimate[,12])
## [1] 0.4189243
mean(theta_estimate[,50])
## [1] 0.8670465
nu_estimado <- result$nu
mean(nu_estimado)
## [1] 1.728429
alpha_estimado <- result$alpha
mean(alpha_estimado)
## [1] 2.784216
par( mfrow= c(1,3) )
hist(theta_estimate[,25], main = "posterior distributin of theta_t|{y} when t = 25")
hist(theta_estimate[,50], main = "posterior distributin of theta_t|{y} when t = 50")
hist(theta_estimate[,853], main = "posterior distributin of theta_t|{y} when t = 853")
library(coda)
##
## Anexando pacote: 'coda'
## O seguinte objeto é mascarado por 'package:rstan':
##
## traceplot
HPD_theta <- coda::HPDinterval(as.mcmc(theta_estimate), prop = 0.95)
HPD_theta
## lower upper
## var1 -6.823502e+02 115.5624772
## var2 3.181240e-02 0.6869027
## var3 4.620490e-02 0.9254081
## var4 5.702433e-02 1.3052625
## var5 2.186346e-01 1.6853492
## var6 4.163330e-03 0.5875205
## var7 8.380352e-03 1.0766307
## var8 5.098582e-02 1.4866874
## var9 9.106514e-01 3.1742416
## var10 4.308907e-03 0.6054590
## var11 6.079145e-01 1.9925532
## var12 2.396997e-03 1.1421768
## var13 1.276981e-01 1.6909855
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