Resposta dicotômica
# Pacotes.
library(lattice)
library(latticeExtra)
# Carrega os dados.
url <- paste0("http://archive.ics.uci.edu/ml/machine-learning-databases",
"/credit-screening/crx.data")
cre <- read.csv(url, header = FALSE, na.string = "?")
names(cre)[16] <- "y"
summary(cre)
## V1 V2 V3 V4 V5
## a :210 Min. :13.75 Min. : 0.000 l : 2 g :519
## b :468 1st Qu.:22.60 1st Qu.: 1.000 u :519 gg : 2
## NA's: 12 Median :28.46 Median : 2.750 y :163 p :163
## Mean :31.57 Mean : 4.759 NA's: 6 NA's: 6
## 3rd Qu.:38.23 3rd Qu.: 7.207
## Max. :80.25 Max. :28.000
## NA's :12
## V6 V7 V8 V9 V10
## c :137 v :399 Min. : 0.000 f:329 f:395
## q : 78 h :138 1st Qu.: 0.165 t:361 t:295
## w : 64 bb : 59 Median : 1.000
## i : 59 ff : 57 Mean : 2.223
## aa : 54 j : 8 3rd Qu.: 2.625
## (Other):289 (Other): 20 Max. :28.500
## NA's : 9 NA's : 9
## V11 V12 V13 V14 V15 y
## Min. : 0.0 f:374 g:625 Min. : 0 Min. : 0.0 -:383
## 1st Qu.: 0.0 t:316 p: 8 1st Qu.: 75 1st Qu.: 0.0 +:307
## Median : 0.0 s: 57 Median : 160 Median : 5.0
## Mean : 2.4 Mean : 184 Mean : 1017.4
## 3rd Qu.: 3.0 3rd Qu.: 276 3rd Qu.: 395.5
## Max. :67.0 Max. :2000 Max. :100000.0
## NA's :13
# Visualiza a resposta contra as preditoras métricas.
n <- sapply(cre[, -16], is.numeric)
f <- sprintf("y ~ %s",
paste(names(cre)[1:15][n],
collapse = " + "))
xyplot(as.formula(f),
outer = TRUE,
data = cre,
as.table = TRUE,
jitter.y = TRUE,
amount = 0.025,
scales = list(x = list(relation = "free", log = FALSE))) +
latticeExtra::layer(panel.smoother(x, y, method = lm))
xyplot(as.formula(f),
outer = TRUE,
data = na.omit(cre),
as.table = TRUE,
jitter.y = TRUE,
amount = 0.025,
scales = list(x = list(relation = "free", log = FALSE))) +
latticeExtra::layer({
mod <- glm(y ~ x, family = binomial)
xp <- seq(min(x), max(x), length.out = 101)
yp <- predict(mod, newdata = list(x = xp), type = "response")
panel.lines(x = xp, y = yp + 1)
})
# Visualiza contra as preditoras categóricas.
v <- names(cre)[1:15][sapply(cre[, -16], is.factor)]
length(v)
## [1] 9
keep <- logical(length(v))
names(keep) <- v
par(mfrow = c(3, 3))
for (i in v) {
xt <- xtabs(as.formula(sprintf("~y + %s", i)), data = cre)
# print(min(prop.table(xt)) > 0.1)
if (min(prop.table(xt)) > 0.1) {
keep[i] <- TRUE
}
mosaicplot(xt, main = NULL)
}
layout(1)
# Mantém só variáveis sem separação.
cre <- subset(cre,
select = setdiff(names(cre),
names(which(!keep))))
# Casos completos.
cc <- complete.cases(cre)
table(cc)
## cc
## FALSE TRUE
## 36 654
# Elimina os casos perdidos.
cre <- cre[cc, ]
# # Ajusta o modelo.
# m0 <- glm(y ~ 1, data = cre, family = binomial)
# Ajusta o modelo.
m0 <- glm(y ~ ., data = cre, family = binomial)
summary(m0)
##
## Call:
## glm(formula = y ~ ., family = binomial, data = cre)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6989 -0.7016 -0.5552 0.7280 2.1010
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.6920085 0.3622721 -4.671 3.00e-06 ***
## V1b -0.0494728 0.2141518 -0.231 0.8173
## V2 0.0007079 0.0090987 0.078 0.9380
## V3 0.0302197 0.0213279 1.417 0.1565
## V8 0.2429321 0.0453001 5.363 8.20e-08 ***
## V10t 0.8537006 0.2654346 3.216 0.0013 **
## V11 0.2019482 0.0504121 4.006 6.18e-05 ***
## V12t -0.0052904 0.2034309 -0.026 0.9793
## V14 -0.0007156 0.0006189 -1.156 0.2476
## V15 0.0005069 0.0001186 4.273 1.93e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.75 on 653 degrees of freedom
## Residual deviance: 628.00 on 644 degrees of freedom
## AIC: 648
##
## Number of Fisher Scoring iterations: 7
# Realiza seleção de preditoras com stepwise via BIC.
m1 <- step(m0, k = log(nrow(cre)))
## Start: AIC=692.83
## y ~ V1 + V2 + V3 + V8 + V10 + V11 + V12 + V14 + V15
##
## Df Deviance AIC
## - V12 1 628.00 686.35
## - V2 1 628.01 686.35
## - V1 1 628.05 686.40
## - V14 1 629.41 687.76
## - V3 1 629.99 688.34
## <none> 628.00 692.83
## - V10 1 638.13 696.48
## - V11 1 650.31 708.65
## - V8 1 662.47 720.82
## - V15 1 667.49 725.84
##
## Step: AIC=686.35
## y ~ V1 + V2 + V3 + V8 + V10 + V11 + V14 + V15
##
## Df Deviance AIC
## - V2 1 628.01 679.87
## - V1 1 628.05 679.92
## - V14 1 629.44 681.30
## - V3 1 629.99 681.86
## <none> 628.00 686.35
## - V10 1 638.14 690.00
## - V11 1 650.34 702.20
## - V8 1 663.72 715.58
## - V15 1 667.50 719.36
##
## Step: AIC=679.87
## y ~ V1 + V3 + V8 + V10 + V11 + V14 + V15
##
## Df Deviance AIC
## - V1 1 628.06 673.44
## - V14 1 629.45 674.83
## - V3 1 630.03 675.41
## <none> 628.01 679.87
## - V10 1 638.17 683.55
## - V11 1 650.68 696.06
## - V15 1 667.53 712.91
## - V8 1 667.57 712.95
##
## Step: AIC=673.44
## y ~ V3 + V8 + V10 + V11 + V14 + V15
##
## Df Deviance AIC
## - V14 1 629.56 668.46
## - V3 1 630.09 668.99
## <none> 628.06 673.44
## - V10 1 638.35 677.25
## - V11 1 650.78 689.68
## - V15 1 667.53 706.43
## - V8 1 667.65 706.55
##
## Step: AIC=668.46
## y ~ V3 + V8 + V10 + V11 + V15
##
## Df Deviance AIC
## - V3 1 632.19 664.60
## <none> 629.56 668.46
## - V10 1 639.44 671.86
## - V11 1 653.33 685.75
## - V8 1 668.29 700.70
## - V15 1 668.35 700.77
##
## Step: AIC=664.6
## y ~ V8 + V10 + V11 + V15
##
## Df Deviance AIC
## <none> 632.19 664.60
## - V10 1 642.23 668.16
## - V11 1 657.78 683.71
## - V15 1 672.36 698.29
## - V8 1 673.97 699.91
##
## Call:
## glm(formula = y ~ V8 + V10 + V11 + V15, family = binomial, data = cre)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6244 -0.6798 -0.5783 0.7310 1.9389
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.7140069 0.1572213 -10.902 < 2e-16 ***
## V8 0.2441045 0.0423819 5.760 8.43e-09 ***
## V10t 0.8394000 0.2618671 3.205 0.00135 **
## V11 0.2108932 0.0497906 4.236 2.28e-05 ***
## V15 0.0005055 0.0001186 4.263 2.02e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.75 on 653 degrees of freedom
## Residual deviance: 632.19 on 649 degrees of freedom
## AIC: 642.19
##
## Number of Fisher Scoring iterations: 7
# Realiza predição.
yp <- predict(m1, type = "response")
# Erro de classificação.
tb <- table(round(yp), cre$y)
tb
##
## - +
## 0 310 102
## 1 48 194
# Percentual de acertos.
sum(diag(tb))/sum(tb)
## [1] 0.7706422
Usando o pacote caret
library(caret)
# Criando as partições de treino e validação.
set.seed(789)
intrain <- createDataPartition(y = cre$y,
p = 0.75,
list = FALSE)
cre_train <- cre[intrain, ]
cre_test <- cre[-intrain, ]
list(train = nrow(cre_train),
test = nrow(cre_test),
ratio = nrow(cre_train)/nrow(cre))
# Parametriza a valiação cruzada.
trctrl <- trainControl(method = "repeatedcv", number = 10, repeats = 3)
# Boosted Logistic Regression e outras opções.
set.seed(159)
fit <- train(y ~ .,
data = cre_train,
method = c("LogitBoost", "regLogistic", "plr")[1],
trControl = trctrl)
fit
fit$finalModel
# Predição e matriz de confusão.
yp <- predict(fit, newdata = cre_test)
confusionMatrix(yp, cre_test$y)
Resposta politômica
Usando o VGAM
# Carrega o pacote.
library(VGAM)
#-----------------------------------------------------------------------
# Usando um par de preditoras para visualizar a fronteira.
# Ajuste do modelo.
fit <- vglm(Species ~ Sepal.Length + Sepal.Width,
family = multinomial,
data = iris)
summary(fit)
##
## Call:
## vglm(formula = Species ~ Sepal.Length + Sepal.Width, family = multinomial,
## data = iris)
##
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## log(mu[,1]/mu[,3]) -1.662 3.817e-13 8.162e-13 2.549e-06 0.1236
## log(mu[,2]/mu[,3]) -3.589 -4.853e-01 -3.069e-05 5.168e-01 2.1874
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept):1 93.6092 80.4706 1.163 0.244719
## (Intercept):2 13.0459 3.0980 4.211 2.54e-05 ***
## Sepal.Length:1 -33.4706 28.0742 -1.192 0.233175
## Sepal.Length:2 -1.9024 0.5169 -3.680 0.000233 ***
## Sepal.Width:1 27.9328 25.9237 1.078 0.281257
## Sepal.Width:2 -0.4045 0.8626 -0.469 0.639117
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of linear predictors: 2
##
## Names of linear predictors: log(mu[,1]/mu[,3]), log(mu[,2]/mu[,3])
##
## Residual deviance: 110.4801 on 294 degrees of freedom
##
## Log-likelihood: -55.24 on 294 degrees of freedom
##
## Number of iterations: 17
##
## Reference group is level 3 of the response
grid <- with(iris,
expand.grid(
Sepal.Length = seq(min(Sepal.Length),
max(Sepal.Length),
length.out = 61),
Sepal.Width = seq(min(Sepal.Width),
max(Sepal.Width),
length.out = 61),
KEEP.OUT.ATTRS = FALSE))
prob <- predict(fit, newdata = grid, type = "response")
grid$pred <- apply(prob, MARGIN = 1, FUN = which.max)
grid$pred <- factor(grid$pred, labels = levels(iris$Species))
# Gráfico com pontos, classficações, fronteira e vetores de suporte.
plot(Sepal.Width ~ Sepal.Length,
data = grid,
col = as.integer(grid$pred),
pch = 3)
points(Sepal.Width ~ Sepal.Length,
data = iris,
col = as.integer(iris$Species),
pch = 19)
#-----------------------------------------------------------------------
# Usando todas as preditoras.
# Ajusta o modelo.
fit <- vglm(Species ~ ., family = multinomial, data = iris)
# Exibe o resumo do ajuste.
summary(fit)
##
## Call:
## vglm(formula = Species ~ ., family = multinomial, data = iris)
##
##
## Pearson residuals:
## Min 1Q Median 3Q Max
## log(mu[,1]/mu[,3]) -0.0003362 7.294e-10 2.102e-09 9.960e-07 0.0003164
## log(mu[,2]/mu[,3]) -1.9700374 -3.420e-04 -4.358e-06 4.635e-04 2.5601905
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept):1 35.361 25704.949 0.001 0.9989
## (Intercept):2 42.638 25.708 1.659 0.0972 .
## Sepal.Length:1 9.637 7631.535 0.001 0.9990
## Sepal.Length:2 2.465 2.394 1.030 0.3032
## Sepal.Width:1 12.359 3557.648 0.003 0.9972
## Sepal.Width:2 6.681 4.480 1.491 0.1359
## Petal.Length:1 -23.214 5435.364 -0.004 0.9966
## Petal.Length:2 -9.429 4.737 -1.990 0.0465 *
## Petal.Width:1 -34.102 8576.875 -0.004 0.9968
## Petal.Width:2 -18.286 9.743 -1.877 0.0605 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Number of linear predictors: 2
##
## Names of linear predictors: log(mu[,1]/mu[,3]), log(mu[,2]/mu[,3])
##
## Residual deviance: 11.8985 on 290 degrees of freedom
##
## Log-likelihood: -5.9493 on 290 degrees of freedom
##
## Number of iterations: 20
##
## Reference group is level 3 of the response
# Obtém as predições.
prob <- predict(fit, newdata = iris, type = "response")
pred <- apply(prob, MARGIN = 1, FUN = which.max)
pred <- factor(pred, labels = levels(iris$Species))
# Acurácia.
caret::confusionMatrix(pred, iris$Species)
## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 49 1
## virginica 0 1 49
##
## Overall Statistics
##
## Accuracy : 0.9867
## 95% CI : (0.9527, 0.9984)
## No Information Rate : 0.3333
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.98
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: setosa Class: versicolor Class: virginica
## Sensitivity 1.0000 0.9800 0.9800
## Specificity 1.0000 0.9900 0.9900
## Pos Pred Value 1.0000 0.9800 0.9800
## Neg Pred Value 1.0000 0.9900 0.9900
## Prevalence 0.3333 0.3333 0.3333
## Detection Rate 0.3333 0.3267 0.3267
## Detection Prevalence 0.3333 0.3333 0.3333
## Balanced Accuracy 1.0000 0.9850 0.9850
Usando o caret
library(caret)
# Criando as partições de treino e validação.
set.seed(987)
intrain <- createDataPartition(y = iris$Species,
p = 0.75,
list = FALSE)
data_train <- iris[intrain, ]
data_test <- iris[-intrain, ]
# Parametriza a valiação cruzada.
trctrl <- trainControl(method = "repeatedcv",
number = 10,
repeats = 3)
# Penalized Multinomial Regression, usa a nnet::multinom().
set.seed(159)
fit <- train(Species ~ .,
data = data_train,
method = "multinom",
trControl = trctrl)
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 10.058950
## iter 20 value 3.313919
## iter 30 value 2.753694
## iter 40 value 2.344815
## iter 50 value 2.059893
## iter 60 value 1.078211
## iter 70 value 0.085099
## iter 80 value 0.052390
## iter 90 value 0.047081
## iter 100 value 0.044963
## final value 0.044963
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 22.120228
## iter 20 value 20.421492
## iter 30 value 20.413323
## final value 20.413322
## converged
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 10.087207
## iter 20 value 3.469245
## iter 30 value 3.008806
## iter 40 value 2.668432
## iter 50 value 2.547171
## iter 60 value 2.462195
## iter 70 value 2.396726
## iter 80 value 2.215847
## iter 90 value 2.170056
## iter 100 value 2.138382
## final value 2.138382
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.608284
## iter 20 value 3.365568
## iter 30 value 2.725861
## iter 40 value 2.621696
## iter 50 value 2.497843
## iter 60 value 2.458804
## iter 70 value 2.334704
## iter 80 value 2.318875
## iter 90 value 2.299643
## iter 100 value 2.290231
## final value 2.290231
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 21.694604
## iter 20 value 20.249971
## iter 30 value 20.245199
## final value 20.245198
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.629290
## iter 20 value 3.558949
## iter 30 value 3.097638
## iter 40 value 2.994255
## iter 50 value 2.896003
## iter 60 value 2.871370
## iter 70 value 2.840173
## iter 80 value 2.835462
## iter 90 value 2.835159
## iter 100 value 2.833610
## final value 2.833610
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.853687
## iter 20 value 2.721020
## iter 30 value 1.879755
## iter 40 value 1.707002
## iter 50 value 1.508190
## iter 60 value 1.436305
## iter 70 value 1.310874
## iter 80 value 1.208203
## iter 90 value 1.043079
## iter 100 value 0.991956
## final value 0.991956
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 21.585455
## iter 20 value 19.933990
## iter 30 value 19.927415
## final value 19.927413
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.874822
## iter 20 value 2.927391
## iter 30 value 2.311199
## iter 40 value 2.173429
## iter 50 value 2.046601
## iter 60 value 2.008326
## iter 70 value 1.975748
## iter 80 value 1.941134
## iter 90 value 1.937714
## iter 100 value 1.926236
## final value 1.926236
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.337024
## iter 20 value 3.311259
## iter 30 value 2.684744
## iter 40 value 2.564240
## iter 50 value 2.355098
## iter 60 value 2.333758
## iter 70 value 2.295767
## iter 80 value 2.283864
## iter 90 value 2.233473
## iter 100 value 2.228374
## final value 2.228374
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.178806
## iter 20 value 20.282813
## iter 30 value 20.276957
## final value 20.276956
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.358893
## iter 20 value 3.461489
## iter 30 value 2.971587
## iter 40 value 2.832324
## iter 50 value 2.788085
## iter 60 value 2.770211
## iter 70 value 2.758005
## iter 80 value 2.748028
## iter 90 value 2.745491
## iter 100 value 2.743057
## final value 2.743057
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.526752
## iter 20 value 2.986642
## iter 30 value 2.550081
## iter 40 value 2.470967
## iter 50 value 2.419740
## iter 60 value 2.342808
## iter 70 value 2.237692
## iter 80 value 2.226777
## iter 90 value 2.208501
## iter 100 value 2.198917
## final value 2.198917
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.476981
## iter 20 value 20.728722
## iter 30 value 20.722042
## final value 20.722041
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.548090
## iter 20 value 3.224451
## iter 30 value 2.947099
## iter 40 value 2.884974
## iter 50 value 2.830558
## iter 60 value 2.798373
## iter 70 value 2.772901
## iter 80 value 2.767892
## iter 90 value 2.765677
## iter 100 value 2.763441
## final value 2.763441
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.687019
## iter 20 value 0.464187
## iter 30 value 0.106958
## iter 40 value 0.083360
## iter 50 value 0.063492
## iter 60 value 0.032194
## iter 70 value 0.024215
## iter 80 value 0.019023
## iter 90 value 0.016613
## iter 100 value 0.015365
## final value 0.015365
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 21.366701
## iter 20 value 19.431403
## iter 30 value 19.422954
## final value 19.422953
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.707722
## iter 20 value 0.897126
## iter 30 value 0.749946
## iter 40 value 0.637899
## iter 50 value 0.590167
## iter 60 value 0.572858
## iter 70 value 0.566472
## iter 80 value 0.556389
## iter 90 value 0.550718
## iter 100 value 0.549579
## final value 0.549579
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 16.896707
## iter 20 value 2.733832
## iter 30 value 2.236462
## iter 40 value 2.213469
## iter 50 value 2.173935
## iter 60 value 2.153011
## iter 70 value 2.144302
## iter 80 value 2.139756
## iter 90 value 2.129501
## iter 100 value 2.125471
## final value 2.125471
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 23.736852
## iter 20 value 20.471540
## iter 30 value 20.465845
## final value 20.465844
## converged
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 16.910517
## iter 20 value 3.087470
## iter 30 value 2.906916
## iter 40 value 2.856550
## iter 50 value 2.844116
## iter 60 value 2.841072
## iter 70 value 2.838936
## iter 80 value 2.837493
## iter 90 value 2.837154
## iter 100 value 2.836331
## final value 2.836331
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 9.614492
## iter 20 value 2.139567
## iter 30 value 2.025601
## iter 40 value 1.894867
## iter 50 value 1.780075
## iter 60 value 1.727265
## iter 70 value 1.708027
## iter 80 value 1.664606
## iter 90 value 1.462858
## iter 100 value 1.415363
## final value 1.415363
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 21.150066
## iter 20 value 19.624107
## iter 30 value 19.619922
## final value 19.619921
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 9.640077
## iter 20 value 2.371402
## iter 30 value 2.309160
## iter 40 value 2.240246
## iter 50 value 2.218971
## iter 60 value 2.201167
## iter 70 value 2.179289
## iter 80 value 2.175295
## iter 90 value 2.171724
## iter 100 value 2.170403
## final value 2.170403
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.368773
## iter 20 value 3.428562
## iter 30 value 2.768394
## iter 40 value 2.581730
## iter 50 value 2.419817
## iter 60 value 2.375082
## iter 70 value 2.355333
## iter 80 value 2.287915
## iter 90 value 2.249191
## iter 100 value 2.231214
## final value 2.231214
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.135801
## iter 20 value 20.286577
## iter 30 value 20.279960
## final value 20.279959
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.389904
## iter 20 value 3.557514
## iter 30 value 3.068576
## iter 40 value 2.914015
## iter 50 value 2.878056
## iter 60 value 2.862775
## iter 70 value 2.828644
## iter 80 value 2.815578
## iter 90 value 2.814121
## iter 100 value 2.813286
## final value 2.813286
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 11.886832
## iter 20 value 3.711261
## iter 30 value 2.947521
## iter 40 value 2.746559
## iter 50 value 2.474241
## iter 60 value 2.428065
## iter 70 value 2.349470
## iter 80 value 2.328919
## iter 90 value 2.249387
## iter 100 value 2.242101
## final value 2.242101
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 22.103776
## iter 20 value 20.074399
## iter 30 value 20.068171
## final value 20.068170
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 11.906517
## iter 20 value 3.832631
## iter 30 value 3.208825
## iter 40 value 3.025699
## iter 50 value 2.933498
## iter 60 value 2.900151
## iter 70 value 2.869737
## iter 80 value 2.835172
## iter 90 value 2.833778
## iter 100 value 2.831347
## final value 2.831347
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.521549
## iter 20 value 2.382716
## iter 30 value 1.475890
## iter 40 value 1.256580
## iter 50 value 1.101588
## iter 60 value 1.029033
## iter 70 value 0.910071
## iter 80 value 0.863022
## iter 90 value 0.829202
## iter 100 value 0.796240
## final value 0.796240
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.087535
## iter 20 value 20.202474
## iter 30 value 20.195091
## final value 20.195089
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.542806
## iter 20 value 2.674549
## iter 30 value 2.088542
## iter 40 value 1.979874
## iter 50 value 1.858244
## iter 60 value 1.819887
## iter 70 value 1.770612
## iter 80 value 1.762224
## iter 90 value 1.747811
## iter 100 value 1.743595
## final value 1.743595
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 11.164916
## iter 20 value 3.642719
## iter 30 value 2.998992
## iter 40 value 2.740063
## iter 50 value 2.553786
## iter 60 value 2.495677
## iter 70 value 2.363403
## iter 80 value 2.345552
## iter 90 value 2.318312
## iter 100 value 2.303538
## final value 2.303538
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 21.498559
## iter 20 value 19.426595
## iter 30 value 19.419110
## final value 19.419109
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 11.184895
## iter 20 value 3.739934
## iter 30 value 3.206687
## iter 40 value 2.990811
## iter 50 value 2.922457
## iter 60 value 2.894806
## iter 70 value 2.855592
## iter 80 value 2.842779
## iter 90 value 2.830631
## iter 100 value 2.825832
## final value 2.825832
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 10.653084
## iter 20 value 3.459082
## iter 30 value 2.886125
## iter 40 value 2.666738
## iter 50 value 2.457834
## iter 60 value 2.384016
## iter 70 value 2.339957
## iter 80 value 2.325396
## iter 90 value 2.127211
## iter 100 value 2.110871
## final value 2.110871
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 21.906128
## iter 20 value 20.480904
## iter 30 value 20.476064
## final value 20.476063
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 10.676310
## iter 20 value 3.609304
## iter 30 value 3.160464
## iter 40 value 2.951682
## iter 50 value 2.903116
## iter 60 value 2.884291
## iter 70 value 2.859536
## iter 80 value 2.847768
## iter 90 value 2.840694
## iter 100 value 2.836514
## final value 2.836514
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.150188
## iter 20 value 0.170193
## iter 30 value 0.040198
## iter 40 value 0.021669
## iter 50 value 0.019203
## iter 60 value 0.014318
## iter 70 value 0.013841
## iter 80 value 0.011215
## iter 90 value 0.010691
## iter 100 value 0.009751
## final value 0.009751
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 20.952140
## iter 20 value 18.688561
## iter 30 value 18.680147
## final value 18.680146
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.172148
## iter 20 value 0.566791
## iter 30 value 0.521028
## iter 40 value 0.482339
## iter 50 value 0.466406
## iter 60 value 0.458861
## iter 70 value 0.452270
## iter 80 value 0.444979
## iter 90 value 0.441979
## iter 100 value 0.438323
## final value 0.438323
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 10.533456
## iter 20 value 3.320200
## iter 30 value 2.740985
## iter 40 value 2.605528
## iter 50 value 2.479773
## iter 60 value 2.412366
## iter 70 value 2.341897
## iter 80 value 2.322930
## iter 90 value 2.300208
## iter 100 value 2.285191
## final value 2.285191
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 21.866147
## iter 20 value 20.879901
## iter 30 value 20.875694
## final value 20.875693
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 10.555694
## iter 20 value 3.500634
## iter 30 value 3.088693
## iter 40 value 2.962627
## iter 50 value 2.890929
## iter 60 value 2.873477
## iter 70 value 2.866132
## iter 80 value 2.851656
## iter 90 value 2.845177
## iter 100 value 2.841772
## final value 2.841772
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.853444
## iter 20 value 2.780161
## iter 30 value 2.445493
## iter 40 value 2.366060
## iter 50 value 2.313306
## iter 60 value 2.286798
## iter 70 value 2.219912
## iter 80 value 2.214296
## iter 90 value 2.183693
## iter 100 value 2.168964
## final value 2.168964
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 21.549300
## iter 20 value 19.835653
## iter 30 value 19.828405
## final value 19.828404
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.874976
## iter 20 value 2.956613
## iter 30 value 2.698845
## iter 40 value 2.618609
## iter 50 value 2.605802
## iter 60 value 2.594572
## iter 70 value 2.590589
## iter 80 value 2.586455
## iter 90 value 2.585758
## iter 100 value 2.584765
## final value 2.584765
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 14.923060
## iter 20 value 1.964673
## iter 30 value 1.636347
## iter 40 value 1.602874
## iter 50 value 1.577700
## iter 60 value 1.546491
## iter 70 value 1.397358
## iter 80 value 1.366959
## iter 90 value 1.357536
## iter 100 value 1.327677
## final value 1.327677
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 23.067727
## iter 20 value 19.972618
## iter 30 value 19.970337
## iter 30 value 19.970337
## iter 30 value 19.970337
## final value 19.970337
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 14.940953
## iter 20 value 2.371331
## iter 30 value 2.289167
## iter 40 value 2.279977
## iter 50 value 2.273071
## iter 60 value 2.271010
## iter 70 value 2.270465
## iter 80 value 2.269334
## iter 90 value 2.268255
## iter 100 value 2.267388
## final value 2.267388
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 12.583378
## iter 20 value 3.898478
## iter 30 value 2.759048
## iter 40 value 2.630367
## iter 50 value 2.477005
## iter 60 value 2.246793
## iter 70 value 1.953055
## iter 80 value 1.934780
## iter 90 value 1.930418
## iter 100 value 1.929158
## final value 1.929158
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 24.432169
## iter 20 value 20.813927
## final value 20.812337
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 12.604731
## iter 20 value 4.003439
## iter 30 value 3.076894
## iter 40 value 2.979778
## iter 50 value 2.909899
## iter 60 value 2.884447
## iter 70 value 2.847221
## iter 80 value 2.836751
## iter 90 value 2.835513
## iter 100 value 2.835434
## final value 2.835434
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 11.539835
## iter 20 value 3.228376
## iter 30 value 2.765767
## iter 40 value 2.547794
## iter 50 value 2.433012
## iter 60 value 2.350842
## iter 70 value 2.287578
## iter 80 value 2.274032
## iter 90 value 2.079071
## iter 100 value 2.074303
## final value 2.074303
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 22.324207
## iter 20 value 20.342682
## iter 30 value 20.334969
## final value 20.334967
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 11.561386
## iter 20 value 3.439069
## iter 30 value 3.107322
## iter 40 value 2.946091
## iter 50 value 2.904852
## iter 60 value 2.885528
## iter 70 value 2.853939
## iter 80 value 2.840727
## iter 90 value 2.835199
## iter 100 value 2.831364
## final value 2.831364
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.597095
## iter 20 value 3.506591
## iter 30 value 2.854329
## iter 40 value 2.725586
## iter 50 value 2.528168
## iter 60 value 2.440575
## iter 70 value 2.340382
## iter 80 value 2.322020
## iter 90 value 2.286262
## iter 100 value 2.276409
## final value 2.276409
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.502472
## iter 20 value 20.771672
## iter 30 value 20.764787
## final value 20.764785
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.618818
## iter 20 value 3.660464
## iter 30 value 3.150695
## iter 40 value 2.970631
## iter 50 value 2.914183
## iter 60 value 2.888638
## iter 70 value 2.874133
## iter 80 value 2.847959
## iter 90 value 2.844346
## iter 100 value 2.842027
## final value 2.842027
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 8.416104
## iter 20 value 0.375657
## iter 30 value 0.093820
## iter 40 value 0.021593
## iter 50 value 0.013219
## iter 60 value 0.012122
## iter 70 value 0.008820
## iter 80 value 0.005902
## iter 90 value 0.004538
## iter 100 value 0.004168
## final value 0.004168
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 19.616272
## iter 20 value 18.128422
## iter 30 value 18.121328
## final value 18.121327
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 8.437607
## iter 20 value 0.717124
## iter 30 value 0.568591
## iter 40 value 0.441653
## iter 50 value 0.432775
## iter 60 value 0.418673
## iter 70 value 0.414476
## iter 80 value 0.409278
## iter 90 value 0.405466
## iter 100 value 0.402052
## final value 0.402052
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.776361
## iter 20 value 3.387383
## iter 30 value 2.733112
## iter 40 value 2.541947
## iter 50 value 2.359174
## iter 60 value 2.323200
## iter 70 value 2.309241
## iter 80 value 2.255203
## iter 90 value 2.196342
## iter 100 value 2.188389
## final value 2.188389
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.545790
## iter 20 value 20.433209
## iter 30 value 20.426336
## final value 20.426335
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.798433
## iter 20 value 3.524797
## iter 30 value 3.000039
## iter 40 value 2.852180
## iter 50 value 2.800368
## iter 60 value 2.778511
## iter 70 value 2.764575
## iter 80 value 2.748001
## iter 90 value 2.744716
## iter 100 value 2.742835
## final value 2.742835
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 9.826426
## iter 20 value 2.975276
## iter 30 value 2.464157
## iter 40 value 2.019901
## iter 50 value 1.852295
## iter 60 value 1.147724
## iter 70 value 0.350121
## iter 80 value 0.151463
## iter 90 value 0.056127
## iter 100 value 0.003360
## final value 0.003360
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 21.940084
## iter 20 value 20.290368
## iter 30 value 20.282435
## final value 20.282433
## converged
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 9.853953
## iter 20 value 3.190129
## iter 30 value 2.827557
## iter 40 value 2.552238
## iter 50 value 2.442922
## iter 60 value 2.332185
## iter 70 value 2.196599
## iter 80 value 2.163835
## iter 90 value 2.131875
## iter 100 value 2.127668
## final value 2.127668
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.704293
## iter 20 value 3.738157
## iter 30 value 3.081312
## iter 40 value 2.811885
## iter 50 value 2.564089
## iter 60 value 2.508378
## iter 70 value 2.455351
## iter 80 value 2.395447
## iter 90 value 2.287156
## iter 100 value 2.276268
## final value 2.276268
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 21.434528
## iter 20 value 19.706090
## iter 30 value 19.699379
## final value 19.699378
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.726163
## iter 20 value 3.864694
## iter 30 value 3.318783
## iter 40 value 3.062209
## iter 50 value 2.973490
## iter 60 value 2.937337
## iter 70 value 2.898941
## iter 80 value 2.867438
## iter 90 value 2.843001
## iter 100 value 2.839720
## final value 2.839720
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 13.160938
## iter 20 value 2.461714
## iter 30 value 1.996681
## iter 40 value 1.983673
## iter 50 value 1.982675
## iter 60 value 1.967616
## iter 70 value 1.960090
## iter 80 value 1.954125
## iter 90 value 1.948286
## iter 100 value 1.944641
## final value 1.944641
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 22.295387
## iter 20 value 20.134450
## final value 20.133453
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 13.181480
## iter 20 value 2.989987
## iter 30 value 2.831725
## iter 40 value 2.805669
## iter 50 value 2.791145
## iter 60 value 2.756508
## iter 70 value 2.751284
## iter 80 value 2.748310
## iter 90 value 2.746018
## iter 100 value 2.743410
## final value 2.743410
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 12.781897
## iter 20 value 3.485193
## iter 30 value 2.866932
## iter 40 value 2.595311
## iter 50 value 2.455839
## iter 60 value 2.417514
## iter 70 value 2.309864
## iter 80 value 2.294372
## iter 90 value 2.244235
## iter 100 value 2.234667
## final value 2.234667
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 22.950130
## iter 20 value 20.960036
## iter 30 value 20.952764
## final value 20.952763
## converged
## # weights: 18 (10 variable)
## initial value 113.157066
## iter 10 value 12.800812
## iter 20 value 3.648241
## iter 30 value 3.159915
## iter 40 value 2.938728
## iter 50 value 2.904593
## iter 60 value 2.887298
## iter 70 value 2.861552
## iter 80 value 2.845514
## iter 90 value 2.840125
## iter 100 value 2.838223
## final value 2.838223
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.710947
## iter 20 value 3.497026
## iter 30 value 2.703753
## iter 40 value 2.618162
## iter 50 value 2.522601
## iter 60 value 2.354803
## iter 70 value 2.281699
## iter 80 value 2.261934
## iter 90 value 2.095505
## iter 100 value 2.092118
## final value 2.092118
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.411870
## iter 20 value 20.496966
## iter 30 value 20.490698
## final value 20.490697
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.732120
## iter 20 value 3.619062
## iter 30 value 3.023467
## iter 40 value 2.938373
## iter 50 value 2.875497
## iter 60 value 2.856747
## iter 70 value 2.842300
## iter 80 value 2.826151
## iter 90 value 2.823403
## iter 100 value 2.819824
## final value 2.819824
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.902014
## iter 20 value 2.094202
## iter 30 value 1.315588
## iter 40 value 1.190280
## iter 50 value 1.156381
## iter 60 value 0.962627
## iter 70 value 0.862794
## iter 80 value 0.825826
## iter 90 value 0.773550
## iter 100 value 0.634255
## final value 0.634255
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 21.926222
## iter 20 value 20.184752
## iter 30 value 20.178877
## final value 20.178876
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 10.924581
## iter 20 value 2.448728
## iter 30 value 2.043111
## iter 40 value 1.979604
## iter 50 value 1.884443
## iter 60 value 1.876729
## iter 70 value 1.841300
## iter 80 value 1.834826
## iter 90 value 1.833027
## iter 100 value 1.829532
## final value 1.829532
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 11.837199
## iter 20 value 3.441463
## iter 30 value 2.873366
## iter 40 value 2.658225
## iter 50 value 2.452165
## iter 60 value 2.400712
## iter 70 value 2.308646
## iter 80 value 2.293888
## iter 90 value 2.163452
## iter 100 value 2.150172
## final value 2.150172
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 22.285476
## iter 20 value 20.580793
## iter 30 value 20.573901
## final value 20.573900
## converged
## # weights: 18 (10 variable)
## initial value 114.255678
## iter 10 value 11.857175
## iter 20 value 3.603846
## iter 30 value 3.168904
## iter 40 value 2.957697
## iter 50 value 2.914638
## iter 60 value 2.892919
## iter 70 value 2.870918
## iter 80 value 2.857006
## iter 90 value 2.846988
## iter 100 value 2.844076
## final value 2.844076
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.825292
## iter 20 value 3.692065
## iter 30 value 2.930938
## iter 40 value 2.662292
## iter 50 value 2.447062
## iter 60 value 2.400162
## iter 70 value 2.196491
## iter 80 value 2.178661
## iter 90 value 2.115359
## iter 100 value 2.109406
## final value 2.109406
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 22.355794
## iter 20 value 20.675284
## iter 30 value 20.669042
## final value 20.669040
## converged
## # weights: 18 (10 variable)
## initial value 112.058453
## iter 10 value 11.846023
## iter 20 value 3.826636
## iter 30 value 3.200056
## iter 40 value 2.968267
## iter 50 value 2.913320
## iter 60 value 2.882034
## iter 70 value 2.835163
## iter 80 value 2.834883
## iter 90 value 2.834749
## iter 100 value 2.834688
## final value 2.834688
## stopped after 100 iterations
## # weights: 18 (10 variable)
## initial value 125.241801
## iter 10 value 23.853936
## iter 20 value 21.517212
## iter 30 value 21.505461
## final value 21.505458
## converged
## Penalized Multinomial Regression
##
## 114 samples
## 4 predictors
## 3 classes: 'setosa', 'versicolor', 'virginica'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 3 times)
## Summary of sample sizes: 104, 102, 102, 102, 102, 102, ...
## Resampling results across tuning parameters:
##
## decay Accuracy Kappa
## 0e+00 0.9678283 0.9517730
## 1e-04 0.9622727 0.9434397
## 1e-01 0.9717172 0.9576132
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was decay = 0.1.
## Call:
## nnet::multinom(formula = .outcome ~ ., data = dat, decay = param$decay)
##
## Coefficients:
## (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width
## versicolor 1.32149 -0.2153398 -2.236748 2.530654 -0.3423041
## virginica -2.62065 -2.5074644 -3.600806 5.503678 4.2504433
##
## Residual Deviance: 43.01092
## AIC: 63.01092
# Predição e matriz de confusão.
yp <- predict(fit, newdata = data_test)
confusionMatrix(yp, data_test$Species)
## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor virginica
## setosa 12 0 0
## versicolor 0 11 1
## virginica 0 1 11
##
## Overall Statistics
##
## Accuracy : 0.9444
## 95% CI : (0.8134, 0.9932)
## No Information Rate : 0.3333
## P-Value [Acc > NIR] : 1.728e-14
##
## Kappa : 0.9167
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: setosa Class: versicolor Class: virginica
## Sensitivity 1.0000 0.9167 0.9167
## Specificity 1.0000 0.9583 0.9583
## Pos Pred Value 1.0000 0.9167 0.9167
## Neg Pred Value 1.0000 0.9583 0.9583
## Prevalence 0.3333 0.3333 0.3333
## Detection Rate 0.3333 0.3056 0.3056
## Detection Prevalence 0.3333 0.3333 0.3333
## Balanced Accuracy 1.0000 0.9375 0.9375
