Predição de Votação de Deputados
José Ivan Silva da Cruz Júnior
7 de novembro de 2018
library(tidyverse)## ── Attaching packages ────────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──## ✔ ggplot2 3.1.0 ✔ purrr 0.2.5
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## ✖ dplyr::lag() masks stats::lag()library(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## liftInicialmente, precisamos fazer um limpeza nos dados e sem seguida tratá-los para podermos utilizá-los nos modelos que queremos.
dadosBrutos <- read.csv("train.csv")
dadosLimpos <- dadosBrutos %>%
mutate(comites = recursos_de_outros_candidatos.comites) %>%
select(-sequencial_candidato, -uf, -partido, - estado_civil, -ano, -recursos_de_outros_candidatos.comites)
test <- read.csv("test.csv") %>%
mutate(comites = recursos_de_outros_candidatos.comites)Questão 1) Usando todas as variáveis disponíveis, tune (usando validação cruzada): (i) um modelo de regressão Ridge, (ii) um modelo de regressão Lasso e (iii) um modelo KNN. Para os modelos de regressão linear, o parâmetro a ser tunado é o lambda (penalização dos coeficientes) e o KNN o número de vizinhos.
Inicialmente, para o modelo Ridge , utilizo a função “train()” do pacote caret para efetuar o treino do modelo com o parâmetro “lambdas”.
lambdas <- expand.grid(lambda = seq(10^-2, 10^-9, length=20))
validacao <- trainControl(method = "cv", number = 10)
voto.modelRidge <- train(votos ~ media_despesa + total_despesa + quantidade_fornecedores + quantidade_despesas + recursos_de_partido_politico + recursos_proprios + recursos_de_pessoas_juridicas + recursos_de_pessoas_fisicas + media_receita + total_receita + quantidade_doadores + quantidade_doacoes, data = dadosLimpos, method = "ridge", tuneGrid = lambdas, preProc = c("center", "scale"), trControl = validacao)
plot(voto.modelRidge)
voto.modelRidge## Ridge Regression
##
## 7476 samples
## 12 predictors
##
## Pre-processing: centered (12), scaled (12)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6728, 6729, 6728, 6728, 6729, 6729, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0000000010 37374.80 0.4151208 16886.27
## 0.0005263167 37329.55 0.4156585 16884.69
## 0.0010526325 37298.12 0.4160471 16884.20
## 0.0015789482 37275.29 0.4163390 16883.86
## 0.0021052639 37258.11 0.4165649 16883.43
## 0.0026315797 37244.81 0.4167442 16882.97
## 0.0031578954 37234.29 0.4168898 16882.68
## 0.0036842112 37225.79 0.4170103 16882.44
## 0.0042105269 37218.82 0.4171117 16882.03
## 0.0047368426 37213.02 0.4171985 16881.54
## 0.0052631584 37208.13 0.4172738 16881.10
## 0.0057894741 37203.97 0.4173399 16880.50
## 0.0063157898 37200.39 0.4173987 16879.76
## 0.0068421056 37197.28 0.4174516 16878.92
## 0.0073684213 37194.57 0.4174994 16877.98
## 0.0078947371 37192.19 0.4175432 16877.49
## 0.0084210528 37190.09 0.4175835 16877.15
## 0.0089473685 37188.23 0.4176209 16876.77
## 0.0094736843 37186.58 0.4176556 16876.27
## 0.0100000000 37185.11 0.4176882 16875.66
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.01.Para o modelo lasso, mudarei farei a mesma coisa que para o modelo Ridge, mudando apenas o método e o range do lambda.
lambdas <- expand.grid(fraction = seq(0.01, 10^-8, length=20))
voto.modelLasso <- train(votos ~ media_despesa + total_despesa + quantidade_fornecedores + quantidade_despesas + recursos_de_partido_politico + recursos_proprios + recursos_de_pessoas_juridicas + recursos_de_pessoas_fisicas + media_receita + total_receita + quantidade_doadores + quantidade_doacoes, data = dadosLimpos, method = "lasso", tuneGrid = lambdas, preProc = c("center", "scale"), trControl = validacao)
plot(voto.modelLasso)
voto.modelLasso## The lasso
##
## 7476 samples
## 12 predictors
##
## Pre-processing: centered (12), scaled (12)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6728, 6728, 6730, 6728, 6728, 6728, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.0000000100 47083.79 0.4056267 28628.09
## 0.0005263253 47045.06 0.4056267 28597.09
## 0.0010526405 47006.38 0.4056267 28566.10
## 0.0015789558 46967.76 0.4056267 28535.11
## 0.0021052711 46929.18 0.4056267 28504.12
## 0.0026315863 46890.65 0.4056267 28473.13
## 0.0031579016 46852.17 0.4056267 28442.18
## 0.0036842168 46813.74 0.4056267 28411.25
## 0.0042105321 46775.36 0.4056267 28380.31
## 0.0047368474 46737.04 0.4056267 28349.39
## 0.0052631626 46698.76 0.4056267 28318.48
## 0.0057894779 46660.53 0.4056267 28287.58
## 0.0063157932 46622.36 0.4056267 28256.68
## 0.0068421084 46584.23 0.4056267 28225.82
## 0.0073684237 46546.16 0.4056267 28195.09
## 0.0078947389 46508.13 0.4056267 28164.42
## 0.0084210542 46470.16 0.4056267 28133.75
## 0.0089473695 46432.24 0.4056267 28103.08
## 0.0094736847 46394.37 0.4056267 28072.42
## 0.0100000000 46356.55 0.4056267 28041.78
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.01.Para o modelo KNN, v será o parâmetro que indicará a quantidade de vizinhos
v <- expand.grid(k = seq(20, 100, length=81))
voto.modelKNN <- train(votos ~ media_despesa + total_despesa + quantidade_fornecedores + quantidade_despesas + recursos_de_partido_politico + recursos_proprios + recursos_de_pessoas_juridicas + recursos_de_pessoas_fisicas + media_receita + total_receita + quantidade_doadores + quantidade_doacoes, data = dadosLimpos, method = "knn", tuneGrid = v, preProc = c("center", "scale"), trControl = validacao)
plot(voto.modelKNN)
voto.modelKNN## k-Nearest Neighbors
##
## 7476 samples
## 12 predictors
##
## Pre-processing: centered (12), scaled (12)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6729, 6728, 6728, 6728, 6729, 6728, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 20 31954.95 0.5532855 11994.64
## 21 31927.76 0.5539429 11998.97
## 22 31934.18 0.5535787 11995.61
## 23 31885.82 0.5549657 11965.35
## 24 31880.68 0.5552237 11941.58
## 25 31880.82 0.5553687 11938.63
## 26 31893.63 0.5550897 11939.11
## 27 31954.28 0.5532697 11954.84
## 28 31966.31 0.5526655 11958.43
## 29 31959.57 0.5528570 11951.54
## 30 31942.00 0.5534179 11933.45
## 31 31917.61 0.5542903 11910.11
## 32 31933.28 0.5537208 11895.89
## 33 31898.51 0.5548182 11868.73
## 34 31868.08 0.5557970 11862.96
## 35 31833.86 0.5568055 11834.16
## 36 31847.29 0.5565151 11846.99
## 37 31841.89 0.5566632 11834.08
## 38 31829.92 0.5570650 11826.49
## 39 31822.91 0.5573007 11825.15
## 40 31834.23 0.5569197 11829.61
## 41 31821.23 0.5573675 11824.13
## 42 31824.14 0.5574038 11826.45
## 43 31833.12 0.5571810 11825.03
## 44 31861.06 0.5563622 11830.76
## 45 31866.88 0.5562660 11829.25
## 46 31865.18 0.5564498 11821.84
## 47 31873.03 0.5562712 11822.58
## 48 31850.64 0.5569809 11803.98
## 49 31861.52 0.5566986 11809.24
## 50 31884.61 0.5559902 11828.02
## 51 31882.66 0.5560988 11829.73
## 52 31889.60 0.5560168 11837.52
## 53 31908.79 0.5555201 11834.68
## 54 31920.36 0.5552880 11834.23
## 55 31933.13 0.5549958 11838.46
## 56 31958.99 0.5543511 11842.65
## 57 31966.63 0.5541358 11846.85
## 58 32002.19 0.5531627 11850.97
## 59 31996.60 0.5533797 11853.57
## 60 32008.58 0.5530595 11855.12
## 61 32006.03 0.5532140 11852.06
## 62 32010.17 0.5531755 11841.13
## 63 32012.82 0.5530985 11844.00
## 64 32010.37 0.5532259 11841.35
## 65 32007.19 0.5533020 11838.64
## 66 32025.81 0.5527921 11842.78
## 67 32031.35 0.5526537 11849.69
## 68 32038.45 0.5525221 11842.06
## 69 32033.92 0.5528079 11839.46
## 70 32043.35 0.5526029 11843.15
## 71 32052.09 0.5523746 11841.97
## 72 32062.85 0.5520963 11844.30
## 73 32060.29 0.5522170 11842.71
## 74 32050.65 0.5525876 11840.92
## 75 32052.55 0.5526094 11836.45
## 76 32051.89 0.5526765 11834.77
## 77 32057.25 0.5526292 11844.87
## 78 32063.06 0.5525082 11845.76
## 79 32055.63 0.5527907 11837.44
## 80 32055.82 0.5528282 11829.50
## 81 32064.10 0.5526558 11831.94
## 82 32066.68 0.5527048 11831.26
## 83 32068.46 0.5527172 11830.43
## 84 32067.91 0.5527852 11830.09
## 85 32084.00 0.5524188 11838.47
## 86 32094.02 0.5521519 11836.66
## 87 32103.71 0.5518705 11842.24
## 88 32106.14 0.5518530 11838.84
## 89 32113.18 0.5517128 11835.04
## 90 32110.17 0.5518825 11834.65
## 91 32108.85 0.5520165 11830.74
## 92 32119.60 0.5517278 11832.72
## 93 32129.17 0.5515479 11838.66
## 94 32120.48 0.5518541 11835.04
## 95 32120.24 0.5519756 11832.12
## 96 32104.08 0.5525285 11830.03
## 97 32112.63 0.5523369 11828.42
## 98 32121.62 0.5520823 11830.04
## 99 32123.86 0.5521010 11826.66
## 100 32121.84 0.5522065 11826.49
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 41.Questão 2) Compare os três modelos em termos do erro RMSE de validação cruzada.
summary(resamples(list(RIDGE= voto.modelRidge, LASSO = voto.modelLasso, KNN = voto.modelKNN)))##
## Call:
## summary.resamples(object = resamples(list(RIDGE = voto.modelRidge, LASSO
## = voto.modelLasso, KNN = voto.modelKNN)))
##
## Models: RIDGE, LASSO, KNN
## Number of resamples: 10
##
## MAE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## RIDGE 15070.91 16417.31 16778.86 16875.66 17269.44 18728.43 0
## LASSO 25489.93 26993.72 28440.28 28041.78 28796.31 30275.00 0
## KNN 10388.10 11299.97 11739.32 11824.13 12462.64 13711.15 0
##
## RMSE
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## RIDGE 28023.57 29829.15 34386.77 37185.11 40035.93 67189.98 0
## LASSO 35215.24 39714.23 47394.25 46356.55 49842.69 63710.80 0
## KNN 23190.61 25934.33 28065.97 31821.23 34503.30 52544.63 0
##
## Rsquared
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## RIDGE 0.1262740 0.3494130 0.4358193 0.4176882 0.4991854 0.6234080 0
## LASSO 0.2546338 0.3560434 0.4180349 0.4056267 0.4707850 0.4896826 0
## KNN 0.3266019 0.4992167 0.5839067 0.5573675 0.6224054 0.7041570 0Após realizar a mesma validação cruzada para os três modelos, observando o erro RMSE de cada um vemos que pelo modelo KNN obtemos o menor valor, seguido do modelo ridge e por último, o lasso.
Questão 3) Quais as variáveis mais importantes segundo o modelo de regressão Ridge e Lasso? Variáveis foram descartadas pelo Lasso? Quais?
ridgeImportancia <- ggplot(varImp(voto.modelRidge))
lassoImportancia <- ggplot(varImp(voto.modelLasso))
#grid.arrange(ridgeImportancia, lassoImportancia, nrow = 1)Para os dois modelos, a variável “total_despesa” revela grande importância. Isto parece algo bem lógico, já que, em uma campanha eleitoral, quanto mais se gastar, mais votos se tende obter. O modelo lasso também eliminou as variáveis que podemos considerar como desnecessárias. Podemos obter as variáveis utilizadas como preditoras pelo seguinte comando:
pre <- predictors(voto.modelLasso)
pre## [1] "total_despesa"O restante das variáveis foram todas descartadas.
Questão 4) Re-treine o melhor modelo (usando os melhores valores de parâmetros encontrados em todos os dados, sem usar validação cruzada).
Para poder retreinar o modelo, estarei removendo as variávies que foram apontadas na questão acima. Usarei o preditor feito na útima questão.
dadosRetreinados <- dadosLimpos %>% select(pre, votos)Como o modelo KNN foi aquele que apresentou o menor valor de RMSE retreinaremos o mesmo.
voto.modelKNNRetreinado <- train(votos ~ ., data = dadosRetreinados, method = "knn",trControl = validacao,
preProcess = c("center","scale"), tuneGrid = v)
plot(voto.modelKNNRetreinado)
voto.modelKNNRetreinado## k-Nearest Neighbors
##
## 7476 samples
## 1 predictors
##
## Pre-processing: centered (1), scaled (1)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6729, 6728, 6728, 6729, 6729, 6728, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 20 33160.69 0.5181140 12768.36
## 21 33086.52 0.5200607 12711.93
## 22 33082.76 0.5202307 12704.51
## 23 33033.16 0.5215315 12661.28
## 24 33096.16 0.5198532 12673.75
## 25 33051.67 0.5211026 12653.13
## 26 33029.37 0.5215968 12624.68
## 27 33029.49 0.5215059 12617.24
## 28 33024.07 0.5215140 12606.78
## 29 32947.53 0.5235482 12586.79
## 30 32933.30 0.5238704 12566.34
## 31 32906.05 0.5245892 12548.22
## 32 32881.76 0.5252100 12548.68
## 33 32844.68 0.5261848 12510.91
## 34 32818.79 0.5269849 12502.10
## 35 32831.03 0.5265211 12490.01
## 36 32813.23 0.5270111 12488.12
## 37 32818.48 0.5268957 12483.72
## 38 32762.12 0.5284481 12459.66
## 39 32762.84 0.5285331 12469.86
## 40 32758.70 0.5286731 12454.74
## 41 32714.20 0.5299121 12439.54
## 42 32707.61 0.5300983 12432.67
## 43 32702.43 0.5302548 12431.18
## 44 32712.04 0.5299323 12431.46
## 45 32718.83 0.5297895 12426.26
## 46 32721.80 0.5297143 12427.99
## 47 32705.80 0.5301275 12424.01
## 48 32677.57 0.5309173 12427.04
## 49 32665.37 0.5312598 12427.78
## 50 32640.78 0.5319842 12417.44
## 51 32639.68 0.5320580 12409.63
## 52 32644.85 0.5318876 12406.49
## 53 32630.83 0.5322929 12404.03
## 54 32650.05 0.5317523 12400.92
## 55 32626.23 0.5324041 12398.04
## 56 32606.49 0.5329662 12395.40
## 57 32602.58 0.5331140 12392.69
## 58 32595.19 0.5333053 12391.83
## 59 32585.61 0.5336051 12382.60
## 60 32566.21 0.5341416 12368.69
## 61 32572.71 0.5339488 12382.06
## 62 32555.11 0.5344214 12376.90
## 63 32545.20 0.5347155 12375.89
## 64 32549.94 0.5345730 12376.30
## 65 32551.94 0.5344667 12369.41
## 66 32551.35 0.5344939 12362.82
## 67 32543.98 0.5346612 12348.78
## 68 32536.13 0.5349271 12351.64
## 69 32546.91 0.5345816 12350.68
## 70 32557.00 0.5343071 12349.85
## 71 32561.39 0.5341855 12357.58
## 72 32557.64 0.5342914 12361.25
## 73 32554.48 0.5344244 12354.07
## 74 32563.28 0.5341445 12355.85
## 75 32560.55 0.5341966 12348.16
## 76 32563.39 0.5341572 12357.29
## 77 32548.98 0.5345950 12351.10
## 78 32544.08 0.5347352 12347.22
## 79 32535.94 0.5349858 12349.79
## 80 32521.37 0.5353858 12344.51
## 81 32520.63 0.5354870 12344.45
## 82 32499.77 0.5361127 12346.47
## 83 32500.50 0.5360907 12345.64
## 84 32504.03 0.5359877 12339.79
## 85 32491.88 0.5363521 12333.55
## 86 32490.59 0.5364136 12337.06
## 87 32476.04 0.5368294 12323.89
## 88 32489.77 0.5364392 12329.08
## 89 32483.70 0.5366205 12325.41
## 90 32477.35 0.5367978 12324.50
## 91 32487.46 0.5364949 12326.27
## 92 32485.07 0.5365521 12325.84
## 93 32491.33 0.5363735 12331.36
## 94 32494.15 0.5363234 12330.26
## 95 32481.77 0.5366813 12325.69
## 96 32482.36 0.5366747 12323.66
## 97 32482.60 0.5366544 12322.38
## 98 32481.24 0.5367094 12320.78
## 99 32482.71 0.5366846 12321.81
## 100 32498.51 0.5362040 12326.32
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 87.Questão 5) Use esse último modelo treinado para prever os dados de teste disponíveis no challenge que criamos na plataforma Kaggle.
prediction <- predict(voto.modelKNNRetreinado, test)
return <- data.frame(ID=test$sequencial_candidato, votos = prediction)
return$ID <- as.character(return$ID)
return## ID votos
## 1 10000000135 1503.3596
## 2 10000000142 1601.9310
## 3 10000000158 64120.1839
## 4 10000000161 58260.2529
## 5 10000000163 93939.9770
## 6 10000000164 6277.1839
## 7 10000000166 67361.0115
## 8 10000000169 92166.9425
## 9 10000000170 16126.9425
## 10 10000000171 67682.7701
## 11 10000000172 44067.5057
## 12 10000000173 75228.2989
## 13 10000000176 10239.0690
## 14 10000000177 35252.4138
## 15 10000000178 65634.1379
## 16 10000000179 30865.6782
## 17 10000000180 12742.4483
## 18 10000000327 1009.1889
## 19 10000000347 3355.3448
## 20 10000000348 3732.1609
## 21 10000000349 12751.2644
## 22 10000000358 5725.9425
## 23 10000000363 2823.0345
## 24 10000000365 914.6552
## 25 10000000366 1945.9425
## 26 10000000367 1526.3333
## 27 10000000368 54390.2644
## 28 10000000369 1334.1839
## 29 10000000370 1382.7816
## 30 10000000371 1979.1264
## 31 10000000602 5064.3793
## 32 10000000603 4016.4368
## 33 10000000607 39240.3563
## 34 10000000608 8353.0920
## 35 10000000609 13156.6322
## 36 10000000610 9111.1954
## 37 10000000611 1546.4831
## 38 10000000613 114366.4483
## 39 10000000614 117025.7586
## 40 10000000615 66923.9770
## 41 10000000616 115494.3678
## 42 10000000617 19858.4943
## 43 10000000618 10661.9195
## 44 10000000619 2212.8851
## 45 10000000620 20612.0230
## 46 10000000624 31819.2644
## 47 10000000721 1503.3596
## 48 10000000761 66196.6437
## 49 20000000009 1255.0690
## 50 20000000010 893.8621
## 51 20000000019 5038.3793
## 52 20000000023 1272.5632
## 53 20000000024 662.5747
## 54 20000000043 67036.6092
## 55 20000000044 55092.7471
## 56 20000000045 9431.5402
## 57 20000000046 12715.9885
## 58 20000000047 2579.2759
## 59 20000000050 1987.7159
## 60 20000000052 1663.5057
## 61 20000000054 11097.7126
## 62 20000000059 1439.0805
## 63 20000000060 12592.2759
## 64 20000000082 2408.7241
## 65 20000000083 1136.8851
## 66 20000000085 1458.1149
## 67 20000000086 1458.1149
## 68 20000000119 999.6322
## 69 20000000126 2470.7126
## 70 20000000127 113980.4368
## 71 20000000128 32112.4138
## 72 20000000153 121394.6897
## 73 20000000156 66532.3218
## 74 20000000157 2863.1149
## 75 20000000158 1336.0115
## 76 20000000159 1821.9540
## 77 20000000160 7120.4598
## 78 20000000167 121807.4828
## 79 20000000169 5786.9540
## 80 20000000170 33505.4598
## 81 20000000172 27549.0575
## 82 20000000198 1280.3182
## 83 20000000265 2537.3523
## 84 20000000266 87169.8736
## 85 20000000267 12513.2759
## 86 20000000269 121246.0920
## 87 20000000270 1439.0805
## 88 20000000271 2710.6629
## 89 20000000272 1439.0805
## 90 20000000273 50667.1494
## 91 20000000274 77867.9195
## 92 20000000277 32426.0805
## 93 20000000278 41268.6092
## 94 20000000280 12517.2644
## 95 20000000281 35247.5517
## 96 20000000282 36903.5862
## 97 20000000283 19798.0909
## 98 20000000284 30321.0920
## 99 20000000286 9389.6897
## 100 20000000287 103983.4023
## 101 20000000289 40977.7011
## 102 20000000364 8836.0115
## 103 20000000367 2936.4943
## 104 20000000369 68217.5057
## 105 20000000373 16283.7931
## 106 20000000380 108151.7241
## 107 20000000381 1900.0575
## 108 20000000382 108100.9310
## 109 20000000385 12506.3103
## 110 20000000391 4841.4828
## 111 20000000393 936.6092
## 112 20000000444 5046.2989
## 113 20000000446 1491.1149
## 114 20000000449 1714.4253
## 115 20000000468 1049.4023
## 116 20000000474 2536.8276
## 117 20000000482 1219.0460
## 118 20000000484 1049.4023
## 119 20000000485 1049.4023
## 120 20000000503 41734.9080
## 121 20000000541 14665.0115
## 122 30000000004 1897.1724
## 123 30000000005 1411.5632
## 124 30000000022 13304.5862
## 125 30000000029 51580.5517
## 126 30000000033 2662.4253
## 127 30000000084 40202.5402
## 128 30000000085 4265.9310
## 129 30000000086 3795.1379
## 130 30000000087 16374.3103
## 131 30000000089 2697.4713
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