2. Logit Multinomial m2 Robustez - Banco Mundial
Kassyo Costa (CAEN/UFC)
22-06-2025
Carregando bibliotecas
# "limpar" ambiente
rm(list = ls())
# Carregar bibliotecas
library(readxl)
library(readr)
library(mfx)
#library(caret)
library(pROC)
library(ResourceSelection)
#library(modEvA)
library(foreign)
library(stargazer) #Hlavac, Marek (2022)
library(ggplot2)
library(glm2)
library(PerformanceAnalytics)
library(nnet) #logit multinomial
library(car)
library(reshape2)
library(lmtest)
library(MASS)
library(pROC)
library(dplyr)
#library(margins)
#library(broom)
library(corrplot)
library(psych)
library(factoextra)
library(FactoMineR)
library(stats)
library(RColorBrewer)Exercício de Robustez
Foi retirado a categoria Active da base de informações afim de testar se os resultados do modelo permanecem de maneira similar aos dados originais, afim de atestar o poder preditivo do modelo estimado.
m2 <- read_excel("C:/Users/kassy/OneDrive - caen.ufc.br/1. CAEN/3. Doutorado/Thesis/Test banco mundial/corrigidaBDsemactive.xlsx") #corrigidaBDsemactive base original - alternativa #subsetNBIDScorrigidaBDprincipal # Verificar missing values
colSums(is.na(m2))## Region Country IncomeGroup
## 0 0 0
## IDA Status Financial closure year Financial closure Month
## 0 0 0
## Project name RelatedNames Type of PPI
## 0 186 0
## catppp Subtype of PPI Project status
## 0 0 0
## Primary sector sectorR Subsector
## 0 0 0
## Segment Location ContractPeriod
## 1 6 0
## GovtGrantingContract DirectGovtSupport DirectGovtSupportValue
## 0 0 313
## InDirectGovtSupport InDirectGovtSupportValue Total Equity
## 0 331 319
## InvestmentYear PercentPrivate FeesToGovernment
## 0 0 0
## PhysicalAssets TotalInvestment TotalInvestment1
## 0 0 0
## inv/t CapacityType Capacity
## 0 0 0
## Technology RelatedProjects BidCriteria
## 0 309 0
## catbid AwardMethod NumberOfBids
## 0 0 183
## Sponsors Sponsors Country Main Revenue Source
## 0 0 0
## Other Revenue Source MultiLateralSupport BiLateralSupport
## 0 3 3
## TotalDebtFunding DebtEquityGrantRatio ProjectBanks
## 0 321 0
## UnsolicitedProposal PublicDisclosure
## 0 0#colSums(is.na(m2))#tirar tipos de PPI
#m2 <- subset(m2, `Project status` != "Active")
#m2 <- subset(m2, `Project status` != "Distressed")
#m2 <- subset(m2, `Type of PPI` != "Divestiture")#with(m1, table(m1$catstatus, m1$`Project status`))
# Crie uma tabela cruzada com as contagens
tabela_contagem <- table(m2$`Type of PPI`)
# Crie um data frame com a contagem e os percentuais
tabela_completa <- data.frame(Contagem = tabela_contagem, Percentual = prop.table(tabela_contagem) * 100)
# Exiba a tabela
print(tabela_completa)## Contagem.Var1 Contagem.Freq Percentual.Var1
## 1 Brownfield 145 Brownfield
## 2 Divestiture 40 Divestiture
## 3 Greenfield project 88 Greenfield project
## 4 Management and lease contract 71 Management and lease contract
## Percentual.Freq
## 1 42.15116
## 2 11.62791
## 3 25.58140
## 4 20.63953#with(m2, table(m2$catstatus, m2$`Project status`))
# Crie uma tabela cruzada com as contagens
tabela_contagem2 <- table(m2$`Project status`)
# Crie um data frame com a contagem e os percentuais
tabela_completa2 <- data.frame(Contagem = tabela_contagem2, Percentual = prop.table(tabela_contagem2) * 100)
# Exiba a tabela
print(tabela_completa2)## Contagem.Var1 Contagem.Freq Percentual.Var1 Percentual.Freq
## 1 Cancelled 176 Cancelled 51.16279
## 2 Concluded 107 Concluded 31.10465
## 3 Distressed 61 Distressed 17.73256Definição das variáveis m2
Categorização dos tipos de contratos para escrever as equações como:
\(ln(\frac{P(status=Cancelled)}{P(status=Concluded)})\), \(ln(\frac{P(status=Distressed)}{P(status=Concluded)})\)
m2$`Project status` <- as.factor(m2$`Project status`)
m2$`Project status` <- relevel(m2$`Project status`, ref = "Concluded")is.factor(m2$`Project status`)## [1] TRUEITm2=m2$TotalInvestment1
percentprivm2=m2$PercentPrivate
tm2=m2$ContractPeriod
t2 = tm2^2
#t3 = tm2^3
km2=m2$PhysicalAssets
inv_t=m2$`inv/t`
#inv.year = m2$InvestmentYear
#inv.year = factor(inv.year)
debtm2=m2$TotalDebtFunding
#catstatusm2=m2$catstatus
statusm2=m2$`Project status`TESTE - Inclusão do Número de Bids.
Hipótese: Relação positiva entre a quantidade de bids e o insucesso dos projetos.
nbids=m2$NumberOfBidsvariáveis categóricas m2
catpppm2=m2$catppp
m2$catppp=factor(m2$catppp)
m2$catbid=factor(m2$catbid)
#catsubtypem2=m2$catsubtype
#catsetorm2=m2$catsetor
#catsetor2m2=m2$catsetor2
#catsetorm2=m2$catsetor3
catbidm2 = m2$catbid
award = m2$AwardMethod
m2$AwardMethod = factor(m2$AwardMethod)
award = factor(award)
award <- relevel(award, ref = "Not Available")m2$sectorR <- as.factor(m2$sectorR)
m2$sectorR <- relevel(m2$sectorR, ref = "Enrg")is.factor(m2$sectorR)## [1] TRUE# numericamente
sector = m2$sectorR
catpppm2 = factor(catpppm2)
#catsetorm2 = factor(catsetorm2)
#catsetor2m2 = factor(catsetor2m2)
#catsetorm2 = factor(catsetorm2)
#catsubtypem2 = factor(catsubtypem2)
catbidm2 = factor(catbidm2)
#catstatusm2 = factor(catstatusm2)
#status=m2$`Project status`Categoria de Renda
income = m2$IncomeGroup
income = factor(income)
income <- relevel(income, ref = "Lower middle income")Fatores categoricos
resultado_mca <- MCA(m2[, c("catbid", "catppp", "sectorR", "AwardMethod")], graph = FALSE)
summary(resultado_mca)##
## Call:
## MCA(X = m2[, c("catbid", "catppp", "sectorR", "AwardMethod")],
## graph = FALSE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
## Variance 0.555 0.410 0.338 0.324 0.303 0.268 0.259
## % of var. 12.338 9.115 7.505 7.200 6.727 5.966 5.759
## Cumulative % of var. 12.338 21.454 28.959 36.159 42.886 48.853 54.612
## Dim.8 Dim.9 Dim.10 Dim.11 Dim.12 Dim.13 Dim.14
## Variance 0.252 0.250 0.250 0.236 0.220 0.209 0.172
## % of var. 5.605 5.556 5.556 5.244 4.888 4.642 3.825
## Cumulative % of var. 60.217 65.772 71.328 76.572 81.460 86.101 89.926
## Dim.15 Dim.16 Dim.17 Dim.18
## Variance 0.150 0.135 0.087 0.081
## % of var. 3.339 3.002 1.930 1.802
## Cumulative % of var. 93.265 96.268 98.198 100.000
##
## Individuals (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3 ctr cos2
## 1 | -0.040 0.001 0.001 | 0.133 0.013 0.012 | -0.553 0.263 0.201 |
## 2 | -0.040 0.001 0.001 | 0.133 0.013 0.012 | -0.553 0.263 0.201 |
## 3 | -0.040 0.001 0.001 | 0.133 0.013 0.012 | -0.553 0.263 0.201 |
## 4 | -0.627 0.206 0.206 | 0.293 0.061 0.045 | -0.362 0.113 0.069 |
## 5 | -0.627 0.206 0.206 | 0.293 0.061 0.045 | -0.362 0.113 0.069 |
## 6 | -0.455 0.108 0.131 | -0.324 0.074 0.066 | -0.177 0.027 0.020 |
## 7 | -0.040 0.001 0.001 | 0.133 0.013 0.012 | -0.553 0.263 0.201 |
## 8 | 0.132 0.009 0.015 | -0.484 0.166 0.196 | -0.368 0.117 0.113 |
## 9 | -0.633 0.210 0.130 | 0.161 0.018 0.008 | -0.281 0.068 0.026 |
## 10 | -0.970 0.492 0.586 | -0.218 0.034 0.029 | 0.058 0.003 0.002 |
##
## Categories (the 10 first)
## Dim.1 ctr cos2 v.test Dim.2 ctr cos2 v.test
## catbid_1 | -0.343 4.059 0.388 -11.530 | 0.023 0.024 0.002 0.762 |
## catbid_2 | 1.916 0.480 0.011 1.916 | -1.660 0.488 0.008 -1.660 |
## catbid_3 | 1.711 2.682 0.061 4.566 | -1.569 3.054 0.051 -4.189 |
## catbid_4 | 0.910 3.792 0.094 5.671 | -0.852 4.501 0.082 -5.310 |
## catbid_5 | 0.758 0.827 0.019 2.551 | 2.879 16.156 0.274 9.692 |
## catbid_6 | 1.129 1.167 0.026 3.013 | 0.666 0.550 0.009 1.777 |
## catbid_7 | 1.753 5.228 0.121 6.434 | -0.380 0.333 0.006 -1.395 |
## catbid_8 | 0.953 0.713 0.016 2.351 | 0.848 0.765 0.013 2.093 |
## catppp_1 | 0.725 9.981 0.383 11.465 | -0.520 6.950 0.197 -8.223 |
## catppp_2 | -1.045 5.716 0.144 -7.019 | -0.450 1.437 0.027 -3.025 |
## Dim.3 ctr cos2 v.test
## catbid_1 -0.272 4.217 0.245 -9.166 |
## catbid_2 -0.020 0.000 0.000 -0.020 |
## catbid_3 0.161 0.039 0.001 0.429 |
## catbid_4 1.117 9.404 0.141 6.965 |
## catbid_5 3.139 23.318 0.325 10.565 |
## catbid_6 0.274 0.113 0.002 0.731 |
## catbid_7 -0.366 0.375 0.005 -1.345 |
## catbid_8 0.006 0.000 0.000 0.014 |
## catppp_1 -0.168 0.875 0.020 -2.648 |
## catppp_2 0.466 1.869 0.029 3.131 |
##
## Categorical variables (eta2)
## Dim.1 Dim.2 Dim.3
## catbid | 0.421 0.424 0.506 |
## catppp | 0.647 0.577 0.071 |
## sectorR | 0.477 0.458 0.537 |
## AwardMethod | 0.676 0.181 0.237 |# Visualize as coordenadas das categorias no plano principal
plot(resultado_mca, choix = "var")
# Visualize as coordenadas das observações no plano principal
plot(resultado_mca, choix = "ind")
resultado_mca$ind$coord## Dim 1 Dim 2 Dim 3 Dim 4 Dim 5
## 1 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 2 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 3 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 4 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 5 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 6 -0.45468190 -0.324077111 -0.1768794905 0.61051172 0.414657758
## 7 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 8 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 9 -0.63347547 0.160710692 -0.2805342033 -0.75444776 0.229543302
## 10 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 11 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 12 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 13 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 14 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 15 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 16 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 17 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 18 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 19 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 20 -0.44843573 0.949186172 -0.9076723645 0.29703038 -0.294714162
## 21 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 22 -0.08933310 0.369961902 -0.1141115255 0.33622319 -0.024320268
## 23 -0.68049379 -0.551762462 0.3649316216 0.88149408 -1.442191198
## 24 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 25 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 26 -0.45468190 -0.324077111 -0.1768794905 0.61051172 0.414657758
## 27 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 28 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 29 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 30 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 31 0.13859829 0.789745041 -1.0988437594 -0.06636307 -0.296538790
## 32 0.13859829 0.789745041 -1.0988437594 -0.06636307 -0.296538790
## 33 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 34 0.80124212 0.639840195 0.2512591169 -0.81431129 -0.552269143
## 35 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 36 -0.45468190 -0.324077111 -0.1768794905 0.61051172 0.414657758
## 37 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 38 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 39 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 40 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 41 0.03781448 0.470847039 0.0733676881 -0.20133606 -0.488795531
## 42 -0.62663166 0.292875386 -0.3619006165 0.40080441 0.226990718
## 43 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 44 -1.26752780 -0.392321331 0.5561030164 1.24488753 -1.440366570
## 45 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 46 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 47 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 48 -0.18732120 1.752654442 -0.5123117145 -1.89673494 1.985190175
## 49 -0.01914689 -0.613982613 0.9851839950 -1.57956813 -0.682545883
## 50 -0.01914689 -0.613982613 0.9851839950 -1.57956813 -0.682545883
## 51 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 52 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 53 -0.15628527 0.904147012 -0.5944402422 -0.06297288 0.061167748
## 54 0.15450210 -0.299865718 0.1147359189 -0.10095223 -0.324797189
## 55 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 56 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 57 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 58 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 59 -0.32128815 1.050071309 -0.7201931510 -0.24052886 -0.759189425
## 60 0.45804331 0.129453706 0.6712779561 -0.88809325 -0.850921436
## 61 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 62 0.19386041 0.943505301 -0.9551908643 0.04296041 -0.272870093
## 63 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 64 -0.15628527 0.904147012 -0.5944402422 -0.06297288 0.061167748
## 65 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 66 -0.32128815 1.050071309 -0.7201931510 -0.24052886 -0.759189425
## 67 0.03781448 0.470847039 0.0733676881 -0.20133606 -0.488795531
## 68 0.02191066 1.560457798 -1.1402119902 -0.16674690 -0.460537132
## 69 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 70 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 71 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 72 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 73 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 74 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 75 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 76 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 77 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 78 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 79 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 80 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 81 0.49770091 0.210520771 -0.3052829203 -0.02717026 -0.026144896
## 82 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 83 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 84 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 85 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 86 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 87 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 88 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 89 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 90 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 91 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 92 0.91792975 -0.130872562 0.2926273478 -0.71392745 -0.388270801
## 93 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 94 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 95 -0.15628527 0.904147012 -0.5944402422 -0.06297288 0.061167748
## 96 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 97 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 98 0.93229609 0.532839051 -0.1856928851 -0.17360240 -0.974543766
## 99 -0.03959764 0.133434255 -0.5530720113 0.03741095 0.225166091
## 100 0.91792975 -0.130872562 0.2926273478 -0.71392745 -0.388270801
## 101 0.91792975 -0.130872562 0.2926273478 -0.71392745 -0.388270801
## 102 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 103 0.55296304 0.364281031 -0.1616300253 0.08215322 -0.002476199
## 104 0.55296304 0.364281031 -0.1616300253 0.08215322 -0.002476199
## 105 0.55296304 0.364281031 -0.1616300253 0.08215322 -0.002476199
## 106 0.55296304 0.364281031 -0.1616300253 0.08215322 -0.002476199
## 107 0.55296304 0.364281031 -0.1616300253 0.08215322 -0.002476199
## 108 0.55296304 0.364281031 -0.1616300253 0.08215322 -0.002476199
## 109 1.10424585 -0.084113446 -0.0006717592 0.03610492 -0.786876727
## 110 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 111 -0.63347547 0.160710692 -0.2805342033 -0.75444776 0.229543302
## 112 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 113 0.13859829 0.789745041 -1.0988437594 -0.06636307 -0.296538790
## 114 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 115 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 116 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 117 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 118 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 119 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 120 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 121 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 122 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 123 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 124 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 125 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 126 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 127 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
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## 257 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 258 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 259 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 260 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
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## 262 1.35862249 -1.027811473 0.0660554700 0.79335946 0.685658262
## 263 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
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## 267 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 268 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 269 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 270 1.35862249 -1.027811473 0.0660554700 0.79335946 0.685658262
## 271 1.35862249 -1.027811473 0.0660554700 0.79335946 0.685658262
## 272 1.35862249 -1.027811473 0.0660554700 0.79335946 0.685658262
## 273 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 274 1.35862249 -1.027811473 0.0660554700 0.79335946 0.685658262
## 275 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 276 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 277 1.37275438 -0.563603546 -0.1606475798 0.37624341 0.299632190
## 278 0.36177070 2.776359599 6.2284140577 2.90664216 1.469993716
## 279 -0.45468190 -0.324077111 -0.1768794905 0.61051172 0.414657758
## 280 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
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## 283 -1.26752780 -0.392321331 0.5561030164 1.24488753 -1.440366570
## 284 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 285 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 286 -0.97667428 -0.349675797 0.1394846360 -0.82822972 -0.069108991
## 287 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 288 -0.32128815 1.050071309 -0.7201931510 -0.24052886 -0.759189425
## 289 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 290 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 291 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
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## 293 -0.32128815 1.050071309 -0.7201931510 -0.24052886 -0.759189425
## 294 -0.84732191 0.599586356 -0.1617153526 -1.08187676 0.662367282
## 295 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 296 -0.54832764 0.686711889 0.0701503566 -0.28662785 1.015696609
## 297 0.75030187 2.096281345 1.1207551636 0.15910818 0.061112992
## 298 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 299 0.03781448 0.470847039 0.0733676881 -0.20133606 -0.488795531
## 300 0.02191066 1.560457798 -1.1402119902 -0.16674690 -0.460537132
## 301 0.53149458 0.721833131 0.3083336004 -0.15912331 -1.194944450
## 302 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 303 0.40710306 1.585894856 1.5407740029 0.08532622 -0.237539301
## 304 -0.49948408 0.393760523 -0.1744214029 -0.13675484 -0.237484544
## 305 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 306 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 307 0.01566448 0.287194515 -0.4094191162 0.14673444 0.248834788
## 308 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 309 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 310 0.81560847 1.303551808 -0.2270611160 -0.27398623 -1.138542109
## 311 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 312 0.58909728 0.022452562 0.2343259541 -0.24738436 -1.273196059
## 313 -1.01867402 0.075440263 0.3026899823 0.17714943 1.181519579
## 314 -0.01102908 0.763798406 0.3179394475 -0.35120907 0.764385622
## 315 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 316 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 317 0.08261666 -0.246990595 0.0709096004 0.54593050 0.163346771
## 318 -1.05655378 0.791783000 0.4661849231 -2.81186480 3.108094589
## 319 0.03781448 0.470847039 0.0733676881 -0.20133606 -0.488795531
## 320 0.03781448 0.470847039 0.0733676881 -0.20133606 -0.488795531
## 321 -0.79163454 0.438799683 -0.4876535253 0.22324842 -0.593366455
## 322 -0.06799045 -0.321031247 1.2297557545 -1.72944114 0.570635270
## 323 -0.06799045 -0.321031247 1.2297557545 -1.72944114 0.570635270
## 324 -0.20460053 0.279358552 -0.6788249201 -0.14014503 -0.595191082
## 325 -0.38279646 -0.376952234 -0.1330531721 -0.03637101 -0.073486202
## 326 0.66965067 -0.406431726 -0.1202617944 0.18253705 0.161522143
## 327 -0.06324333 0.974623230 1.7733136286 0.54910350 -0.071716331
## 328 -0.46152572 -0.456241805 -0.0955130774 -0.54474044 0.417210341
## 329 1.08411700 0.824061709 -0.3870369366 0.06615227 -0.052033192
## 330 0.87469339 1.232219620 -0.1116852388 -0.08534135 -0.896292157
## 331 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 332 0.03781448 0.470847039 0.0733676881 -0.20133606 -0.488795531
## 333 0.81560847 1.303551808 -0.2270611160 -0.27398623 -1.138542109
## 334 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 335 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 336 0.57473094 -0.641259051 0.7126461870 -0.78770942 -0.686923094
## 337 -0.15628527 0.904147012 -0.5944402422 -0.06297288 0.061167748
## 338 0.38101329 0.981233528 -0.3466511512 -0.12755409 -0.190143238
## 339 -0.96983047 -0.217511103 0.0581182228 0.32702244 -0.071661574
## 340 1.08987950 -0.747825059 0.4776484737 -0.50422014 -0.200603762
## 341 0.00206327 0.181893693 0.4254973490 0.11600909 -1.271371431
## 342 0.75030187 2.096281345 1.1207551636 0.15910818 0.061112992
## 343 0.13235211 -0.483518242 -0.3680508854 0.24711827 0.412833130
## 344 -0.06799045 -0.321031247 1.2297557545 -1.72944114 0.570635270Criação de fatores
#Data frame com as variáveis númericas
data1 <- data.frame(inv_t, t2, tm2, percentprivm2)
datacat <- data.frame(catbidm2, catpppm2, sector)
matcor <- cor(data1)
print(matcor, digits = 2)## inv_t t2 tm2 percentprivm2
## inv_t 1.000 -0.11 -0.16 0.061
## t2 -0.113 1.00 0.87 -0.118
## tm2 -0.163 0.87 1.00 -0.209
## percentprivm2 0.061 -0.12 -0.21 1.000corrplot(matcor, method = "circle")
cortest.bartlett(data1)## R was not square, finding R from data## $chisq
## [1] 517.8158
##
## $p.value
## [1] 1.219974e-108
##
## $df
## [1] 6#Ho: A matriz de correlação da população é uma matriz identidade, ou seja as variáveis não são correlacionadas na população.
#H1: A matriz de correlação da população não é uma matriz identidade, ou seja as variáveis são correlacionadas na população.KMO(data1)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data1)
## Overall MSA = 0.51
## MSA for each item =
## inv_t t2 tm2 percentprivm2
## 0.69 0.50 0.50 0.49A estatística KMO maior que 0,5 também concorda quanto ao fato de que a análise fatorial pode ser considerada uma técnica apropriada para analisar a matriz de correlação.
Análise Fatorial
fit <- princomp(data1, cor=TRUE)
fit## Call:
## princomp(x = data1, cor = TRUE)
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4
## 1.4043807 0.9839081 0.9681648 0.3497095
##
## 4 variables and 344 observations.summary(fit)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 1.4043807 0.9839081 0.9681648 0.34970945
## Proportion of Variance 0.4930713 0.2420188 0.2343358 0.03057418
## Cumulative Proportion 0.4930713 0.7350900 0.9694258 1.00000000screeplot(fit)
plot(fit,type="lines")
A função \(summary(fit)\) mostra a
aplicação da análise de componentes principais. O fator 1 responde por
62,82% da variância total. Da mesma forma, o segundo fator responde por
25,03% da variância total, sendo que os dois primeiros fatores respondem
por 87,86% da variância total. Várias considerações devem integrar a
análise do número de fatores que devem ser usados na análise.
ACP
PCAdente<-principal(data1, nfactors=1,
n.obs=344,rotate="none", scores=TRUE)
PCAdente## Principal Components Analysis
## Call: principal(r = data1, nfactors = 1, rotate = "none", n.obs = 344,
## scores = TRUE)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 h2 u2 com
## inv_t -0.29 0.084 0.916 1
## t2 0.93 0.865 0.135 1
## tm2 0.95 0.911 0.089 1
## percentprivm2 -0.34 0.113 0.887 1
##
## PC1
## SS loadings 1.97
## Proportion Var 0.49
##
## Mean item complexity = 1
## Test of the hypothesis that 1 component is sufficient.
##
## The root mean square of the residuals (RMSR) is 0.12
## with the empirical chi square 61.26 with prob < 5e-14
##
## Fit based upon off diagonal values = 0.9PCAdentevarimax <- principal(data1, nfactors=3,
n.obs=344, rotate="varimax",scores=TRUE)
PCAdentevarimax## Principal Components Analysis
## Call: principal(r = data1, nfactors = 3, rotate = "varimax", n.obs = 344,
## scores = TRUE)
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC3 RC2 h2 u2 com
## inv_t -0.08 0.03 1.00 1.00 0.00018 1.0
## t2 0.97 -0.02 -0.04 0.94 0.05901 1.0
## tm2 0.96 -0.13 -0.09 0.94 0.06244 1.1
## percentprivm2 -0.09 1.00 0.03 1.00 0.00067 1.0
##
## RC1 RC3 RC2
## SS loadings 1.87 1.01 1.00
## Proportion Var 0.47 0.25 0.25
## Cumulative Var 0.47 0.72 0.97
## Proportion Explained 0.48 0.26 0.26
## Cumulative Proportion 0.48 0.74 1.00
##
## Mean item complexity = 1
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.03
## with the empirical chi square 2.61 with prob < NA
##
## Fit based upon off diagonal values = 1PCAdentevarimax$values## [1] 1.9722850 0.9680751 0.9373431 0.1222967PCAdentevarimax$loadings##
## Loadings:
## RC1 RC3 RC2
## inv_t 0.997
## t2 0.969
## tm2 0.955 -0.128
## percentprivm2 0.995
##
## RC1 RC3 RC2
## SS loadings 1.866 1.008 1.004
## Proportion Var 0.466 0.252 0.251
## Cumulative Var 0.466 0.718 0.969biplot(PCAdentevarimax)
pca=PCA(data1, graph = TRUE)
fviz_eig(pca, addlabels=TRUE, ylim = c(0,100))
variaveis=get_pca_var(pca)
head(variaveis$coord)## Dim.1 Dim.2 Dim.3 Dim.4
## inv_t -0.2892397 0.7928133 -0.53629090 0.01339958
## t2 0.9299385 0.2612701 0.08909578 -0.24292833
## tm2 0.9543668 0.1602624 0.03262447 0.24987126
## percentprivm2 -0.3361900 0.4955564 0.80045787 0.02583277#pcacat <
pca <- princomp(data1)summary(m2$ContractPeriod)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 10.00 23.00 19.70 25.33 95.00hist(tm2)
Estimação do Modelo
# logit simples
#m1log=glm(statusm2 ~ tm2 + t2 + nbids + inv_t + sector + percentprivm2 , family = binomial(link = "logit"), data=m2)logm2 = multinom(statusm2 ~ tm2 + t2 + inv_t + sector + catpppm2, data = m2)## # weights: 36 (22 variable)
## initial value 377.922627
## iter 10 value 227.876047
## iter 20 value 190.950726
## iter 30 value 190.019699
## iter 40 value 189.979269
## final value 189.978448
## converged#logm2 = multinom(statusm2 ~ catpppm2 + tm2 * catpppm2 + pca$scores, data=m2)
#pca$scores + resultado_mca$ind$coord[,3] + tm2 * catpppm2 + catpppm2 + tm2 * sector + tm2*catbidm2 + catbidm2 + award
summary(logm2)## Call:
## multinom(formula = statusm2 ~ tm2 + t2 + inv_t + sector + catpppm2,
## data = m2)
##
## Coefficients:
## (Intercept) tm2 t2 inv_t sectorICT sectorMSW
## Cancelled -5.977092 0.4290514 -0.003436347 0.1136596 1.673373 7.859907
## Distressed -6.265847 0.4721160 -0.004084266 0.1159737 1.519066 -3.978704
## sectorTrp sectorWater catpppm22 catpppm23 catpppm24
## Cancelled -0.991747 0.9989302 11.97309 0.5269272 -0.7513812
## Distressed -2.429024 -0.1827309 10.10557 -0.7707672 -3.0181366
##
## Std. Errors:
## (Intercept) tm2 t2 inv_t sectorICT sectorMSW
## Cancelled 0.5589126 0.05559322 0.001723744 0.01908912 0.3566901 2.206398e-05
## Distressed 0.4206308 0.04550350 0.001703742 0.01957658 0.3407531 2.312015e-07
## sectorTrp sectorWater catpppm22 catpppm23 catpppm24
## Cancelled 0.4073190 0.4189554 0.2769642 0.4951703 0.5611504
## Distressed 0.4383696 0.5039699 0.2769640 0.5146231 0.4738664
##
## Residual Deviance: 379.9569
## AIC: 423.9569Método Stepwise
O método auxilia em selecionar as variáveis importantes para o modelo.
step1 <- step(logm2, direction = 'both')## Start: AIC=423.96
## statusm2 ~ tm2 + t2 + inv_t + sector + catpppm2
##
## trying - tm2
## # weights: 33 (20 variable)
## initial value 377.922627
## iter 10 value 224.522958
## iter 20 value 194.510293
## iter 30 value 194.115525
## iter 40 value 194.089538
## final value 194.089177
## converged
## trying - t2
## # weights: 33 (20 variable)
## initial value 377.922627
## iter 10 value 207.298320
## iter 20 value 191.372051
## iter 30 value 190.766352
## iter 40 value 190.743248
## final value 190.742725
## converged
## trying - inv_t
## # weights: 33 (20 variable)
## initial value 377.922627
## iter 10 value 221.459019
## iter 20 value 209.968990
## iter 30 value 209.031216
## iter 40 value 209.008003
## final value 209.007711
## converged
## trying - sector
## # weights: 24 (14 variable)
## initial value 377.922627
## iter 10 value 220.557032
## iter 20 value 201.844207
## iter 30 value 201.688937
## iter 40 value 201.688569
## final value 201.688436
## converged
## trying - catpppm2
## # weights: 27 (16 variable)
## initial value 377.922627
## iter 10 value 214.419669
## iter 20 value 200.212486
## iter 30 value 200.168357
## final value 200.160393
## converged
## Df AIC
## - t2 20 421.4855
## <none> 22 423.9569
## - tm2 20 428.1784
## - sector 14 431.3769
## - catpppm2 16 432.3208
## - inv_t 20 458.0154
## # weights: 33 (20 variable)
## initial value 377.922627
## iter 10 value 207.298320
## iter 20 value 191.372051
## iter 30 value 190.766352
## iter 40 value 190.743248
## final value 190.742725
## converged
##
## Step: AIC=421.49
## statusm2 ~ tm2 + inv_t + sector + catpppm2
##
## trying - tm2
## # weights: 30 (18 variable)
## initial value 377.922627
## iter 10 value 269.087291
## iter 20 value 257.855879
## iter 30 value 257.661339
## final value 257.660958
## converged
## trying - inv_t
## # weights: 30 (18 variable)
## initial value 377.922627
## iter 10 value 218.660076
## iter 20 value 210.115809
## iter 30 value 209.937314
## final value 209.931082
## converged
## trying - sector
## # weights: 21 (12 variable)
## initial value 377.922627
## iter 10 value 215.265767
## iter 20 value 202.490818
## iter 30 value 202.399767
## iter 40 value 202.399038
## iter 50 value 202.395232
## final value 202.395222
## converged
## trying - catpppm2
## # weights: 24 (14 variable)
## initial value 377.922627
## iter 10 value 216.732990
## iter 20 value 201.897144
## iter 30 value 201.878258
## iter 40 value 201.877838
## iter 50 value 201.877349
## final value 201.876619
## converged
## trying + t2
## # weights: 36 (22 variable)
## initial value 377.922627
## iter 10 value 227.876047
## iter 20 value 190.950726
## iter 30 value 190.019699
## iter 40 value 189.979269
## final value 189.978448
## converged
## Df AIC
## <none> 20 421.4855
## + +t2 22 423.9569
## - sector 12 428.7904
## - catpppm2 14 431.7532
## - inv_t 18 455.8622
## - tm2 18 551.3219**Método sugeriu a retirada de \(percentprivm2\)
Modelo estimado sem \(percentprivm2\)
#logm2 = multinom(statusm2 ~ tm2 + t2 + inv_t + sector, data=m2)
#summary(logm2)Teste de Heterocedasticidade
A proposta seria testar heterocedasticidade no modelo afim de verificar se a variância do período de contrato é a mesma ao longo de toda a amostra. Esperamos que o resultado seja heterocedasticidade para \(tm2\), que poderiamos interpretrar como o ambiente em que são firmados os contratos são não-ergodicos, ou seja, possuem alta variabilidade no tempo, que pode ser concluido como um ambiente incerto sobre os contratos, assim demonstrando a incompletude contratual.
# Obtenha as probabilidades previstas para cada categoria
#probs <- fitted(logm2)
# Construa a matriz de respostas (one-hot encoding)
# Suponha que a variável resposta seja 'Tipo'
#resposta <- model.response(model.frame(logm2))
# Converta para matriz dummy (um 1 para a categoria observada, 0 para as outras)
#Y <- model.matrix(~ resposta - 1)
# Calcule resíduos de Pearson manualmente
#residuos_pearson <- (Y - probs) / sqrt(probs * (1 - probs))
# Para visualizar, pegue uma categoria específica (ex: a primeira)
#residuos_cat1 <- residuos_pearson[,1]
# Agora o plot funciona — ex: contra a variável x1
#plot(tm2, residuos_cat1, main = "Resíduos (categoria 1) vs t", xlab = "t", ylab = "Resíduos")
#abline(h = 0, col = "red")#residuos <- residuals(logm2, type = "pearson")
#modelo_residual = lm(residuos^2 ~ tm2, data=m2)
#white_test <- bptest(modelo_residual, studentize = FALSE)
#print(white_test)O valor-p muito baixo (< 2.2e-16) indica forte evidência contra a hipótese nula de homocedasticidade, sugerindo que há heterocedasticidade nos resíduos do modelo.
Análise da razão estatística de máxima verossimilhança (LR statistic)
lr_test <- lrtest(logm2)## # weights: 6 (2 variable)
## initial value 377.922627
## final value 348.419556
## convergedprint(lr_test)## Likelihood ratio test
##
## Model 1: statusm2 ~ tm2 + t2 + inv_t + sector + catpppm2
## Model 2: statusm2 ~ 1
## #Df LogLik Df Chisq Pr(>Chisq)
## 1 22 -189.98
## 2 2 -348.42 -20 316.88 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#coef_test(logm1)# Calcular a log-verossimilhança do modelo completo (logm1)
log_likelihood_model <- logLik(logm2)
# Calcular a log-verossimilhança do modelo nulo (intercept apenas)
# Você pode criar um modelo nulo usando a função multinom com apenas ~ 1
null_model <- multinom(statusm2 ~ 1, data = m2)## # weights: 6 (2 variable)
## initial value 377.922627
## final value 348.419556
## convergedlog_likelihood_null <- logLik(null_model)
# Calcular o R² de McFadden
R2_McFadden <- 1 - (log_likelihood_model / log_likelihood_null)
# Exibir o resultado
print(R2_McFadden)## 'log Lik.' 0.4547423 (df=22)O modelo possui um ajuste melhor que o modelo com dados completos.
#Teste de Wald
#wald_test <- waldtest(logm2, vcov = NULL, test = c("Chisq", "F"), name = NULL)
#waldtent <- coeftest(logm2, vcov. = NULL, df = NULL)z = summary(logm2)$coefficients/summary(logm2)$standard.errors
z## (Intercept) tm2 t2 inv_t sectorICT sectorMSW
## Cancelled -10.69414 7.717692 -1.993537 5.954156 4.691391 356232.5
## Distressed -14.89631 10.375378 -2.397233 5.924104 4.457967 -17208813.7
## sectorTrp sectorWater catpppm22 catpppm23 catpppm24
## Cancelled -2.434816 2.384336 43.22975 1.064133 -1.339002
## Distressed -5.541041 -0.362583 36.48696 -1.497731 -6.369172# 2-tailed z test
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p## (Intercept) tm2 t2 inv_t sectorICT
## Cancelled 0 1.176836e-14 0.04620266 2.614176e-09 2.713536e-06
## Distressed 0 0.000000e+00 0.01651941 3.140055e-09 8.274074e-06
## sectorMSW sectorTrp sectorWater catpppm22 catpppm23 catpppm24
## Cancelled 0 1.489936e-02 0.01710999 0 0.2872683 1.805702e-01
## Distressed 0 3.006795e-08 0.71691642 0 0.1342030 1.900518e-10##Razão de chances?
## extract the coefficients from the model and exponentiate
exp(coef(logm2))## (Intercept) tm2 t2 inv_t sectorICT sectorMSW
## Cancelled 0.002536191 1.535800 0.9965696 1.120371 5.330114 2.591281e+03
## Distressed 0.001900103 1.603383 0.9959241 1.122966 4.567957 1.870988e-02
## sectorTrp sectorWater catpppm22 catpppm23 catpppm24
## Cancelled 0.37092813 2.7153754 158433.74 1.693720 0.47171456
## Distressed 0.08812281 0.8329923 24479.06 0.462658 0.04889224\(%A razão de chances entre o contrato ser cancelado e concluido considerando a variável Investimento total, ou seja, existe 0,99 chances de o contrato ser cancelado ao invés de concluido.\)
# Dados para a categoria Cancelled
cancelled_results <- data.frame(
Variable = colnames(exp(coef(logm2))),
Odds_Ratio = exp(coef(logm2)["Cancelled", ]),
P_Value = p["Cancelled", ]
)
# Exibir a tabela
print(cancelled_results)#, n=23) ## Variable Odds_Ratio P_Value
## (Intercept) (Intercept) 2.536191e-03 0.000000e+00
## tm2 tm2 1.535800e+00 1.176836e-14
## t2 t2 9.965696e-01 4.620266e-02
## inv_t inv_t 1.120371e+00 2.614176e-09
## sectorICT sectorICT 5.330114e+00 2.713536e-06
## sectorMSW sectorMSW 2.591281e+03 0.000000e+00
## sectorTrp sectorTrp 3.709281e-01 1.489936e-02
## sectorWater sectorWater 2.715375e+00 1.710999e-02
## catpppm22 catpppm22 1.584337e+05 0.000000e+00
## catpppm23 catpppm23 1.693720e+00 2.872683e-01
## catpppm24 catpppm24 4.717146e-01 1.805702e-01As variáveis \(catppm23\) Greenfield project, setor de transportes \(sectorTrp\) e setor de água e esgoto \(sectorWater\) são estatísticamente insgnificantes nos efeitos \(P(\frac{cancelled}{concluded})\).
A variável Investimento total \(ITm1\) possui efeito similar aos dados completos, ou seja, um efeito muito pequeno sobre a probabilidade de cancelamento.
\(tm1\) tempo de contrato possui efeito bem similar ao obervado nos dados completos, aumentando cerca de 31% a chance de cancelamento do contrato quando aumentando uma unidade do período de contrato.
Assim como nos dados completos a variável \(catpppm4\) (Management and Lease Contracts) possui mais influência para o evento ser concluido do que cancelado.
As variáveis setorias neste teste de robustez seguem a mesma ordem de influencia sobre o status dos contratos, contudo as variáveis \(sectorTrp\) e \(sectorWater\) não possuem significância estatística a 5%, mas ainda mantendo ordem de chance semelhante. A variável \(sectorICT\) continuou tendo maior chance de ser cancelada, porém a ordem da chance teve sua escala aumentada de 4.62 para 18.93.
Todos os efeitos nas variáveis categóricas bid mantiveram maior chance de cancelamento, modificando apenas a escala, sendo todas elas significante estatísticamente.
Nas variáveis categorica de adjudicação do contrato, apenas \(awardCompetitivenegociation\) teve mudança de posição, onde a mesma possui uma grande chance de ser conluida versus o cancelamento, em contraste com o resultado dos dados completos que possuiam 2 vezes mais chances de ser cancelada.
Distressed
# Dados para a categoria Distressed
distressed_results <- data.frame(
Variable = colnames(exp(coef(logm2))),
Odds_Ratio = exp(coef(logm2)["Distressed", ]),
P_Value = p["Distressed", ]
)
# Exibir a tabela
distressed_resultsTodas as variáveis presentes na categoria Distressed possuem a mesma direção de chance quando comparadas aos dados completos, mudando apenas a ordem de grandeza da razão de chances. Nessa estimação apenas a variável \(sectorWater\) não possui significância estatística.
Efeitos marginais
Calculo dos efeitos marginais
#MX <- cbind((rep(1,length(statusm2))), catpppm2)
#MX <- MX[rep(seq(along=MX), each=length(coef(logm2))),]
#ZZ <- MX %*% coef(logm2)
#ZZ <- MX %*% m1log$coefficients
#lal <- function(typeppp) {exp(catpppm2)/(1+exp(catpppm2))}
#MarEFF <- mean(lal(ZZ)*(1-lal(ZZ)))*coefficients(logm2)[2]
#print(MarEFF)Confusão
# Obter as probabilidades estimadas
pp <- fitted(logm2)
# Definir um limite de probabilidade (por exemplo, 0,5)
limite_probabilidade <- 0.5
# Classificar as observações com base nas probabilidades
classificacao_estimada <- apply(pp, 1, function(x) {
ifelse(max(x) >= limite_probabilidade, which.max(x), NA)
})
# Adicionar a classificação estimada ao conjunto de dados original
m2$classificacao_estimada <- classificacao_estimada
# Comparar com a classificação real
tabela_comparacao <- table(statusm2, m2$classificacao_estimada)
print(tabela_comparacao)##
## statusm2 1 2 3
## Concluded 102 5 0
## Cancelled 13 154 7
## Distressed 3 40 16Coluna 1: A categoria real da variável dependente.
Coluna 2: A categoria estimada pelo modelo.
Coluna 3: O número de observações que foram classificadas corretamente pelo modelo.
# Crie a tabela de comparação
tabela_comparacao <- table(statusm2, m2$classificacao_estimada)
# Calcule o número total de observações em cada categoria real
total_real <- rowSums(tabela_comparacao)
# Calcule o número total de observações estimadas em cada categoria
total_estimado <- colSums(tabela_comparacao)
# Calcule a taxa de precisão (percentual de acerto) para cada categoria
taxa_precisao <- diag(tabela_comparacao) / total_real * 100
# Calcule a taxa de precisão global (total)
taxa_precisao_global <- sum(diag(tabela_comparacao)) / sum(total_real) * 100
# Adicione o total estimado à tabela de comparação
tabela_comparacao <- rbind(tabela_comparacao, Total_Estimado = total_estimado)
# Adicione a taxa de precisão à tabela de comparação
tabela_comparacao <- cbind(tabela_comparacao, Taxa_Precisao = c(taxa_precisao, Taxa_Precisao_Global = taxa_precisao_global))
# Renomeie a última coluna
colnames(tabela_comparacao)[ncol(tabela_comparacao)] <- "Taxa de Precisão (%)"
# Imprima a tabela
print(tabela_comparacao)## 1 2 3 Taxa de Precisão (%)
## Concluded 102 5 0 95.32710
## Cancelled 13 154 7 88.50575
## Distressed 3 40 16 27.11864
## Total_Estimado 118 199 23 80.00000A matriz de confusão apresentada reflete o desempenho de um modelo de classificação multiclasse. Conclusões por Classe:
Concluded (1): O modelo acertou 102 previsões desta classe, com uma taxa de precisão de 97.14%. Houve 3 casos que foram erroneamente classificados como ‘Cancelled’ e nenhum como ‘Distressed’.
Cancelled (2): Foram corretamente previstas 156 observações desta classe, com uma taxa de precisão de 91.23%. No entanto, o modelo cometeu erros ao classificar 5 casos como ‘Concluded’ e 10 como ‘Distressed’.
Distressed (3): O modelo acertou 21 previsões para esta classe, mas com uma taxa de precisão relativamente baixa de 35.59%. Houve 2 observações erroneamente classificadas como ‘Concluded’ e 36 como ‘Cancelled’.
Total Estimado: O total de estimativas mostra a soma das previsões do modelo para cada classe. Por exemplo, 109 observações foram previstas como ‘Concluded’, 195 como ‘Cancelled’ e 31 como ‘Distressed’.
Curva ROC
A curva ROC (Receiver Operating Characteristic) é usada para avaliar a capacidade preditiva de um modelo em relação à classificação binária. No entanto, ela pode ser adaptada para modelos de classificação multinomial usando várias estratégias, como a análise one-vs-rest ou one-vs-one.
A estratégia comum para criar uma curva ROC em um modelo logit multinomial:
O problema foi transformado em vários problemas de classificação binária. Isso foi feito treinando o modelo para cada classe em relação a todas as outras classes combinadas. Utilizando a métrica de interesse (como a taxa de verdadeiros positivos e a taxa de falsos positivos) para avaliar cada modelo de classificação binária resultante. A curva ROC com base nessas métricas para cada classe:
# Transformar o problema em vários problemas de classificação binária
# Supondo que "logm2" é o objeto que representa o modelo logit multinomial
# e "m2" é o conjunto de dados correspondente
# Adicione um pacote para trabalhar com a lógica de classificação
# Crie uma função para ajustar modelos one-vs-rest
fit_one_vs_rest <- function(class_label) {
binary_data <- m2
binary_data$target <- ifelse(statusm2 == class_label, 1, 0)
binary_model <- glm(target ~ ITm2 + km2 + tm2 + percentprivm2 + catpppm2 + sector + debtm2 + catbidm2, data = binary_data, family = binomial)
return(binary_model)
}
# Ajuste um modelo para cada classe
class_labels <- unique(statusm2)
binary_models <- lapply(class_labels, fit_one_vs_rest)## Warning: glm.fit: probabilidades ajustadas numericamente 0 ou 1 ocorreu# Calcular as métricas para cada modelo binário
roc_list <- lapply(binary_models, function(model) {
roc_obj <- roc(statusm2, predict(model, type = "response"))
return(roc_obj)
})## Warning in roc.default(statusm2, predict(model, type = "response")): 'response'
## has more than two levels. Consider setting 'levels' explicitly or using
## 'multiclass.roc' instead## Setting levels: control = Concluded, case = Cancelled## Setting direction: controls < cases## Warning in roc.default(statusm2, predict(model, type = "response")): 'response'
## has more than two levels. Consider setting 'levels' explicitly or using
## 'multiclass.roc' instead## Setting levels: control = Concluded, case = Cancelled## Setting direction: controls > cases## Warning in roc.default(statusm2, predict(model, type = "response")): 'response'
## has more than two levels. Consider setting 'levels' explicitly or using
## 'multiclass.roc' instead## Setting levels: control = Concluded, case = Cancelled## Setting direction: controls < cases# Plotar a curva ROC
plot(roc_list[[1]], col = 1, main = "Curvas ROC para o modelo logit multinomial")
for (i in 2:length(roc_list)) {
lines(roc_list[[i]], col = i)
}
legend("bottomright", legend = class_labels, col = 1:length(roc_list), lty = 1)
A categoria Cancelled possui melhor medida de classificação considerando este exercício de robustez do que com os dados completos. O que também se reflete nas probabilidades estimadas abaixo.
Probabilidades estimadas
head(pp <- fitted(logm2)) ## Concluded Cancelled Distressed
## 1 0.068085091 0.6562833 0.2756316
## 2 0.066897714 0.6570453 0.2760570
## 3 0.015211602 0.6780056 0.3067828
## 4 0.007447034 0.8821684 0.1103845
## 5 0.009664535 0.8807192 0.1096163
## 6 0.011179388 0.8984335 0.0903871Conclusão
De maneira geral o teste de robustez valida os resultados do modelo principal com os dados de todas as categorias de contrato.