Credit risk modeling with logistic regression
Leandro Kellermann de Oliveira
3/29/2020
Credit risk analysis with logistic regression
Just to practice.
Loading packages:
Loading packages to calculate skewness (moments), data manipulation (dplyr), create a logistic regression model (caret),string manipulation (stringr), ROC and auxiliary plots to evaluate logistic regression models (ROCit and prerec) and correlation matrix plot (corrplot).
##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Loading required package: lattice## Loading required package: ggplot2## corrplot 0.84 loadedLoading dataset:
df = read.csv("credit_dataset.csv")
View(df)Selecting numerical and categorical variables names:
numVariables = c('credit.duration.months', 'credit.amount', 'age')
catVariables =names(df[,!names(df) %in% numVariables]) Central tendencies measurements:
summary(df[numVariables])## credit.duration.months credit.amount age
## Min. : 4.0 Min. : 250 Min. :19.00
## 1st Qu.:12.0 1st Qu.: 1366 1st Qu.:27.00
## Median :18.0 Median : 2320 Median :33.00
## Mean :20.9 Mean : 3271 Mean :35.54
## 3rd Qu.:24.0 3rd Qu.: 3972 3rd Qu.:42.00
## Max. :72.0 Max. :18424 Max. :75.00Frequency distribution of numerical variables
Ploting frequency distribution of all numerical variables:
for(i in 1:length(numVariables)){
hist(df[,numVariables[i]], main = paste('Frequency of',numVariables[i]), freq = TRUE,xlab=numVariables[i],ylab = paste('Frequency of',numVariables[i]) )
}
Measuring skewness to all numerical variables:
for(i in 1:length(numVariables)){
cat(sprintf('Skewness %s: %.3f.\n',numVariables[i],skewness(df[,numVariables[i]])))
}## Skewness credit.duration.months: 1.093.
## Skewness credit.amount: 1.947.
## Skewness age: 1.023.Transforming numerical variables:
Data must have similar scale and normal-shaped.
for(i in 1:length(numVariables)){
hist(log(df[,numVariables[i]],base=exp(1)), main = paste('Frequency of',numVariables[i]),freq = TRUE ,xlab=numVariables[i],ylab = paste('Frequency of',numVariables[i]) )
}
Trying to transform data:
for(i in 1:length(numVariables)){
cat(sprintf('Skewness %s: %.3f.\n',numVariables[i],skewness(sqrt(log(df[,numVariables[i]],base=exp(1))))))
}## Skewness credit.duration.months: -0.367.
## Skewness credit.amount: 0.003.
## Skewness age: 0.334.Defining new column credit.amount.transformed:
df$credit.amount.transformed = sqrt(log(df$credit.amount, base = exp(1)))Ln transformations:
for(i in 1:length(numVariables)){
cat(sprintf('Skewness %s: %.3f.\n',numVariables[i],skewness(log(df[,numVariables[i]],base=exp(1)))))
}## Skewness credit.duration.months: -0.127.
## Skewness credit.amount: 0.129.
## Skewness age: 0.414.Another try:
for(i in 1:length(numVariables)){
cat(sprintf('Skewness %s: %.3f.\n',numVariables[i],skewness(log1p(df[,numVariables[i]])^1/3)))
}## Skewness credit.duration.months: -0.051.
## Skewness credit.amount: 0.130.
## Skewness age: 0.429.So we have:
df$credit.duration.months.transformed =log1p(df$credit.duration.months)^1/3 … Another try:
for(i in 1:length(numVariables)){
cat(sprintf('Skewness %s: %.3f.\n',numVariables[i],skewness((df[,numVariables[i]])^1/3)))
}## Skewness credit.duration.months: 1.093.
## Skewness credit.amount: 1.947.
## Skewness age: 1.023.Let’s keep the first age transformation:
df$age.transformed = sqrt(log(df$age, base = exp(1)))Redefying numerical and categorical variables:
numTransformed = c('credit.duration.months.transformed','credit.amount.transformed','age.transformed')
for(i in 1:length(numTransformed)){
hist(df[,numTransformed[i]], main = paste('Hist. of',numTransformed[i]),freq = TRUE ,xlab=numTransformed[i],ylab = paste('Frequency of',numTransformed[i]) )
}
for(i in 1:length(numTransformed)){
cat(sprintf('Skewness %s: %.3f.\n',numTransformed[i],skewness(df[,numTransformed[i]])))
}## Skewness credit.duration.months.transformed: -0.051.
## Skewness credit.amount.transformed: 0.003.
## Skewness age.transformed: 0.334.Statistical measurements for the new variables :
summary(df[numTransformed])## credit.duration.months.transformed credit.amount.transformed age.transformed
## Min. :0.5365 Min. :2.350 Min. :1.716
## 1st Qu.:0.8550 1st Qu.:2.687 1st Qu.:1.815
## Median :0.9815 Median :2.784 Median :1.870
## Mean :0.9803 Mean :2.787 Mean :1.876
## 3rd Qu.:1.0730 3rd Qu.:2.879 3rd Qu.:1.933
## Max. :1.4302 Max. :3.134 Max. :2.078Boxplots:
for(i in 1:length(numTransformed)){
boxplot(df[,numTransformed[i]], main = paste('Boxplot for',numTransformed[i]),ylab = numTransformed[i])
}
summary(df[numTransformed])## credit.duration.months.transformed credit.amount.transformed age.transformed
## Min. :0.5365 Min. :2.350 Min. :1.716
## 1st Qu.:0.8550 1st Qu.:2.687 1st Qu.:1.815
## Median :0.9815 Median :2.784 Median :1.870
## Mean :0.9803 Mean :2.787 Mean :1.876
## 3rd Qu.:1.0730 3rd Qu.:2.879 3rd Qu.:1.933
## Max. :1.4302 Max. :3.134 Max. :2.078Redefining categorical variables and numerical variables:
numVariables = c('credit.duration.months','credit.duration.months.transformed', 'credit.amount','credit.amount.transformed', 'age','age.transformed')
catVariables =names(df[,!names(df) %in% numVariables]) Correlation matrix:
numData = df[,names(df) %in% numTransformed]
corrplot(cor(numData),method = 'pie')
corrplot(cor(numData),method = 'number')
Frequency distribution of categorical variables:
for(i in 1:length(catVariables)){
hist(df[,catVariables[i]], main = paste('Hist. of',catVariables[i]),freq = TRUE ,xlab=catVariables[i],ylab = paste('Frequency of',catVariables[i]) )
}
Checking classes of categorical variables:
sapply(catVariables,class)## credit.rating account.balance
## "character" "character"
## previous.credit.payment.status credit.purpose
## "character" "character"
## savings employment.duration
## "character" "character"
## installment.rate marital.status
## "character" "character"
## guarantor residence.duration
## "character" "character"
## current.assets other.credits
## "character" "character"
## apartment.type bank.credits
## "character" "character"
## occupation dependents
## "character" "character"
## telephone foreign.worker
## "character" "character"Transforming categorical variables into factors:
df[(names(df)%in%catVariables)] = lapply(df[(names(df)%in%catVariables)],as.factor)
# Just checking if the above line works:
for(i in 1:length(catVariables)){
a = class(df[1,catVariables[i]])
cat(sprintf('Type of %s: %s.\n',catVariables[i],a))
}## Type of credit.rating: factor.
## Type of account.balance: factor.
## Type of previous.credit.payment.status: factor.
## Type of credit.purpose: factor.
## Type of savings: factor.
## Type of employment.duration: factor.
## Type of installment.rate: factor.
## Type of marital.status: factor.
## Type of guarantor: factor.
## Type of residence.duration: factor.
## Type of current.assets: factor.
## Type of other.credits: factor.
## Type of apartment.type: factor.
## Type of bank.credits: factor.
## Type of occupation: factor.
## Type of dependents: factor.
## Type of telephone: factor.
## Type of foreign.worker: factor.rm(a)Feature selection
Selecting variable names that will be used and defining feature selection function.
features = c(numTransformed, catVariables)
featureSelection <- function(numIters = 100, featureVars, classVars){
set.seed(3659)
variableSizes <- 1:30
control <- rfeControl(functions = rfFuncs,
method = 'cv',
verbose = FALSE,
returnResamp = 'all',
number = numIters)
resultsRFE <- rfe(x = featureVars,
y = classVars,
sizes = variableSizes,
rfeControl = control)
return(resultsRFE)
}Creating train and test partitions for feature selection:
featureDF = df[,(names(df) %in% features)]
index = sample(1:nrow(featureDF),size = .75*nrow(featureDF))
trainFeature = featureDF[index,]
testFeature = featureDF[-index,]Applying user-defined function featureSelection and showing its result:
resultsRFE = featureSelection(featureVars = featureDF[,-1],classVars = featureDF[,1])
varImp(resultsRFE)## Overall
## account.balance 26.246856
## credit.duration.months.transformed 13.277859
## previous.credit.payment.status 10.913693
## credit.amount.transformed 8.708697
## savings 7.452023
## current.assets 5.269912
## guarantor 5.060788
## age.transformed 4.161562
## employment.duration 4.093572
## apartment.type 3.849470
## credit.purpose 3.839569
## occupation 3.757153
## marital.status 3.615173
## foreign.worker 3.587833
## bank.credits 3.563263
## installment.rate 3.530525
## dependents 3.100130
## telephone 3.034385Getting the variables with overall score greater than 2:
varImpOutput = t(varImp(resultsRFE))
mostValuable = varImpOutput[,varImpOutput>2]
mostValuableNames = names(mostValuable)Generating test and train subsets for a first model:
firstModelDF = featureDF
set.seed(6521)
index = sample(1:nrow(firstModelDF),size = 0.75*nrow(firstModelDF))
trainFM = firstModelDF[index,]
testFM = firstModelDF[-index,]Creating first logistic regression model:
firstModel = glm('credit.rating ~.', data=trainFM, family = 'binomial')
summary(firstModel)##
## Call:
## glm(formula = "credit.rating ~.", family = "binomial", data = trainFM)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6484 -0.7296 0.3898 0.7169 1.8190
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.5930 4.0552 0.393 0.694440
## account.balance2 0.4178 0.2474 1.689 0.091213 .
## account.balance3 1.5285 0.2473 6.182 6.33e-10 ***
## previous.credit.payment.status2 0.7080 0.3438 2.059 0.039451 *
## previous.credit.payment.status3 1.2643 0.3762 3.361 0.000777 ***
## credit.purpose2 -0.9148 0.4278 -2.138 0.032489 *
## credit.purpose3 -0.9181 0.4170 -2.202 0.027681 *
## credit.purpose4 -1.4528 0.4037 -3.599 0.000319 ***
## savings2 0.4385 0.3179 1.379 0.167753
## savings3 0.8493 0.3767 2.254 0.024172 *
## savings4 0.9894 0.3114 3.177 0.001487 **
## employment.duration2 0.4395 0.2675 1.643 0.100436
## employment.duration3 1.1045 0.3308 3.339 0.000840 ***
## employment.duration4 0.4651 0.3090 1.505 0.132298
## installment.rate2 -0.3640 0.3596 -1.012 0.311482
## installment.rate3 -0.3662 0.3970 -0.922 0.356302
## installment.rate4 -0.6166 0.3619 -1.704 0.088373 .
## marital.status3 0.5279 0.2281 2.314 0.020650 *
## marital.status4 0.4954 0.3722 1.331 0.183164
## guarantor2 0.4426 0.3351 1.321 0.186618
## residence.duration2 -0.9230 0.3444 -2.680 0.007359 **
## residence.duration3 -0.6445 0.3981 -1.619 0.105455
## residence.duration4 -0.5174 0.3424 -1.511 0.130713
## current.assets2 -0.3245 0.2872 -1.130 0.258403
## current.assets3 -0.2409 0.2658 -0.906 0.364844
## current.assets4 -0.9523 0.4734 -2.012 0.044265 *
## other.credits2 0.2215 0.2513 0.881 0.378116
## apartment.type2 0.6046 0.2698 2.241 0.025052 *
## apartment.type3 0.5583 0.5360 1.042 0.297614
## bank.credits2 -0.1977 0.2709 -0.730 0.465480
## occupation2 -0.4640 0.6880 -0.674 0.500066
## occupation3 -0.5524 0.6665 -0.829 0.407225
## occupation4 -0.3684 0.7087 -0.520 0.603179
## dependents2 -0.2672 0.2909 -0.918 0.358368
## telephone2 0.3757 0.2212 1.698 0.089446 .
## foreign.worker2 1.4841 0.7149 2.076 0.037896 *
## credit.amount.transformed -0.5659 1.1565 -0.489 0.624590
## credit.duration.months.transformed -2.6853 0.8033 -3.343 0.000829 ***
## age.transformed 1.6210 1.5008 1.080 0.280098
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 931.04 on 749 degrees of freedom
## Residual deviance: 692.07 on 711 degrees of freedom
## AIC: 770.07
##
## Number of Fisher Scoring iterations: 5Predict:
predictFirstModel = predict(firstModel, testFM, type="response")
predictFirstModel = round(predictFirstModel)Evaluating:
confusionMatrix(
table(
data=predictFirstModel,
reference = testFM[,1]),
positive = '1')## Confusion Matrix and Statistics
##
## reference
## data 0 1
## 0 24 17
## 1 42 167
##
## Accuracy : 0.764
## 95% CI : (0.7064, 0.8152)
## No Information Rate : 0.736
## P-Value [Acc > NIR] : 0.175868
##
## Kappa : 0.3087
##
## Mcnemar's Test P-Value : 0.001781
##
## Sensitivity : 0.9076
## Specificity : 0.3636
## Pos Pred Value : 0.7990
## Neg Pred Value : 0.5854
## Prevalence : 0.7360
## Detection Rate : 0.6680
## Detection Prevalence : 0.8360
## Balanced Accuracy : 0.6356
##
## 'Positive' Class : 1
## Generating our second model:
if(('credit.rating' %in% mostValuableNames)==FALSE){
mostValuableNames = append(mostValuableNames, 'credit.rating')
}
secondModelDF = featureDF[,names(featureDF) %in% mostValuableNames]
set.seed(9721)
index = sample(1:nrow(secondModelDF),size = 0.75*nrow(secondModelDF))
trainSM = secondModelDF[index,]
testSM = secondModelDF[-index,]
if('credit.rating' %in% mostValuableNames){
t = mostValuableNames[mostValuableNames!= 'credit.rating']
formula <- paste('credit.rating ~',
str_c(t,
collapse = ' + '))
rm(t)
}else{
formula <- paste('credit.rating ~',
str_c(mostValuableNames,
collapse = ' + '))}
secondModel = glm(formula, data= trainSM, family = 'binomial')
summary(secondModel)##
## Call:
## glm(formula = formula, family = "binomial", data = trainSM)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6100 -0.6940 0.4161 0.7305 1.8367
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.1505216 3.8881548 1.325 0.185281
## account.balance2 0.2826920 0.2470994 1.144 0.252606
## account.balance3 1.4431639 0.2488900 5.798 6.70e-09 ***
## credit.duration.months.transformed -2.3281888 0.7714989 -3.018 0.002547 **
## previous.credit.payment.status2 0.7485760 0.3246103 2.306 0.021106 *
## previous.credit.payment.status3 1.5094700 0.3594319 4.200 2.67e-05 ***
## credit.amount.transformed -1.2086643 1.1189143 -1.080 0.280048
## savings2 0.0982942 0.3067908 0.320 0.748669
## savings3 0.6331030 0.3573445 1.772 0.076446 .
## savings4 1.1509229 0.3124389 3.684 0.000230 ***
## current.assets2 -0.2625445 0.2876063 -0.913 0.361316
## current.assets3 -0.3264492 0.2708186 -1.205 0.228043
## current.assets4 -1.0903610 0.4514891 -2.415 0.015734 *
## guarantor2 0.5263160 0.3352922 1.570 0.116479
## age.transformed 0.3942900 1.4344286 0.275 0.783412
## employment.duration2 -0.0008643 0.2598853 -0.003 0.997346
## employment.duration3 0.4461284 0.3224981 1.383 0.166557
## employment.duration4 0.1738148 0.2966347 0.586 0.557905
## apartment.type2 0.3312077 0.2558216 1.295 0.195430
## apartment.type3 0.4727864 0.5156360 0.917 0.359195
## credit.purpose2 -0.7279055 0.4326804 -1.682 0.092507 .
## credit.purpose3 -0.8335840 0.4098668 -2.034 0.041973 *
## credit.purpose4 -1.4766748 0.3961894 -3.727 0.000194 ***
## occupation2 -0.0211708 0.7040273 -0.030 0.976010
## occupation3 -0.1161336 0.6774614 -0.171 0.863890
## occupation4 -0.2003285 0.7174270 -0.279 0.780067
## marital.status3 0.4674848 0.2306714 2.027 0.042701 *
## marital.status4 0.1606438 0.3437541 0.467 0.640270
## foreign.worker2 0.7744927 0.6493793 1.193 0.233000
## bank.credits2 -0.3391546 0.2559429 -1.325 0.185132
## installment.rate2 0.0079589 0.3609444 0.022 0.982408
## installment.rate3 -0.1662233 0.3918120 -0.424 0.671389
## installment.rate4 -0.5891871 0.3609464 -1.632 0.102608
## dependents2 -0.3841625 0.2793579 -1.375 0.169081
## telephone2 0.3525408 0.2289247 1.540 0.123564
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 900.53 on 749 degrees of freedom
## Residual deviance: 690.66 on 715 degrees of freedom
## AIC: 760.66
##
## Number of Fisher Scoring iterations: 5Predicting and evaluating our second model:
predictSecondModel = predict(secondModel, testSM, type="response")
predictSecondModel = round(predictSecondModel)confusionMatrix(
table(
data=predictSecondModel,
reference = testSM[,1]),
positive = '1')## Confusion Matrix and Statistics
##
## reference
## data 0 1
## 0 35 18
## 1 49 148
##
## Accuracy : 0.732
## 95% CI : (0.6725, 0.7859)
## No Information Rate : 0.664
## P-Value [Acc > NIR] : 0.0124691
##
## Kappa : 0.3391
##
## Mcnemar's Test P-Value : 0.0002473
##
## Sensitivity : 0.8916
## Specificity : 0.4167
## Pos Pred Value : 0.7513
## Neg Pred Value : 0.6604
## Prevalence : 0.6640
## Detection Rate : 0.5920
## Detection Prevalence : 0.7880
## Balanced Accuracy : 0.6541
##
## 'Positive' Class : 1
## Creating a third model
Adapting our data:
if(('credit.rating' %in% mostValuableNames)==FALSE){
mostValuableNames = append(mostValuableNames, 'credit.rating')
}
thirdModelDF = featureDF[,names(featureDF) %in% mostValuableNames]
thirdModelDF$credit.amount.transformed = NULL
featureTMNames = mostValuableNames[mostValuableNames!='credit.amount.transformed']Train and test data:
set.seed(3217)
index = sample(1:nrow(thirdModelDF),size = 0.75*nrow(thirdModelDF))
trainTM = thirdModelDF[index,]
testTM = thirdModelDF[-index,]Generating our third model:
if('credit.rating' %in% featureTMNames){
t = featureTMNames[featureTMNames!= 'credit.rating']
formula <- paste('credit.rating ~',
str_c(t,
collapse = ' + '))
rm(t)
}else{
formula <- paste('credit.rating ~',
str_c(featureTMNames,
collapse = ' + '))}
thirdModel = glm(formula, data= trainTM, family = 'binomial')
summary(thirdModel)##
## Call:
## glm(formula = formula, family = "binomial", data = trainTM)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5992 -0.7256 0.4109 0.7220 2.0543
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.2001 2.9402 0.068 0.945748
## account.balance2 0.2765 0.2428 1.139 0.254625
## account.balance3 1.4079 0.2415 5.830 5.53e-09 ***
## credit.duration.months.transformed -2.8805 0.5981 -4.817 1.46e-06 ***
## previous.credit.payment.status2 1.1446 0.3315 3.453 0.000554 ***
## previous.credit.payment.status3 1.6068 0.3488 4.607 4.08e-06 ***
## savings2 0.4195 0.3294 1.274 0.202822
## savings3 0.5828 0.3597 1.620 0.105194
## savings4 0.8522 0.3003 2.838 0.004543 **
## current.assets2 -0.3942 0.2912 -1.354 0.175817
## current.assets3 -0.5048 0.2674 -1.888 0.059065 .
## current.assets4 -1.2258 0.4292 -2.856 0.004287 **
## guarantor2 0.1508 0.3457 0.436 0.662750
## age.transformed 1.6366 1.4588 1.122 0.261886
## employment.duration2 0.1555 0.2541 0.612 0.540463
## employment.duration3 0.8065 0.3223 2.502 0.012335 *
## employment.duration4 0.4793 0.3032 1.581 0.113947
## apartment.type2 0.5662 0.2610 2.170 0.030044 *
## apartment.type3 0.7482 0.5030 1.487 0.136893
## credit.purpose2 -0.9603 0.4133 -2.323 0.020166 *
## credit.purpose3 -0.9952 0.3810 -2.612 0.008997 **
## credit.purpose4 -1.2939 0.3736 -3.463 0.000534 ***
## occupation2 -0.5420 0.7384 -0.734 0.462932
## occupation3 -0.6206 0.7126 -0.871 0.383819
## occupation4 -0.8325 0.7450 -1.117 0.263809
## marital.status3 0.3903 0.2279 1.712 0.086846 .
## marital.status4 0.2392 0.3477 0.688 0.491514
## foreign.worker2 1.1916 0.7139 1.669 0.095097 .
## bank.credits2 -0.2238 0.2522 -0.888 0.374806
## installment.rate2 -0.2265 0.3469 -0.653 0.513847
## installment.rate3 -0.5413 0.3763 -1.438 0.150334
## installment.rate4 -0.7102 0.3171 -2.239 0.025135 *
## dependents2 -0.3775 0.2860 -1.320 0.186942
## telephone2 0.2574 0.2230 1.155 0.248257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 924.61 on 749 degrees of freedom
## Residual deviance: 699.29 on 716 degrees of freedom
## AIC: 767.29
##
## Number of Fisher Scoring iterations: 5Predicting values with our third model:
predictThirdModel = predict(thirdModel, testTM, type="response")
predictThirdModel = round(predictThirdModel)Evaluating our third model:
confusionMatrix(
table(
data=predictThirdModel,
reference = testTM[,1]),
positive = '1')## Confusion Matrix and Statistics
##
## reference
## data 0 1
## 0 34 16
## 1 36 164
##
## Accuracy : 0.792
## 95% CI : (0.7364, 0.8406)
## No Information Rate : 0.72
## P-Value [Acc > NIR] : 0.005759
##
## Kappa : 0.4348
##
## Mcnemar's Test P-Value : 0.008418
##
## Sensitivity : 0.9111
## Specificity : 0.4857
## Pos Pred Value : 0.8200
## Neg Pred Value : 0.6800
## Prevalence : 0.7200
## Detection Rate : 0.6560
## Detection Prevalence : 0.8000
## Balanced Accuracy : 0.6984
##
## 'Positive' Class : 1
## ROC Curves to all models above:
rocitObjFM = rocit(score=predictFirstModel, class=testFM[,1])
rocitObjSM = rocit(score=predictSecondModel,class=testSM[,1])
rocitObjTM = rocit(score=predictThirdModel,class=testTM[,1])
plot(rocitObjFM, title = 'First Model')
plot(rocitObjSM, title = 'Second Model')
plot(rocitObjTM, title = 'Second Model')
Other curves:
precrecObjFM = evalmod(scores=predictFirstModel,labels=testFM[,1],mode = 'basic')
precrecObjSM = evalmod(scores=predictSecondModel,labels=testSM[,1],mode='basic')
precrecObjTM = evalmod(scores=predictThirdModel,labels=testTM[,1],mode='basic')
autoplot(precrecObjFM) 
autoplot(precrecObjSM)
autoplot(precrecObjTM)