What metrics can you use to evaluate your machine learning algorithms?
In this post you will discover how you can evaluate your machine learning algorithms in R using a number of standard evaluation metrics.
Let’s get started.
Model Evaluation Metrics in R
There are many different metrics that you can use to evaluate your machine learning algorithms in R.
When you use caret to evaluate your models, the default metrics used are accuracy for classification problems and RMSE for regression. But caret supports a range of other popular evaluation metrics.
In the next section you will step through each of the evaluation metrics provided by caret. Each example provides a complete case study that you can copyandpaste into your project and adapt to your problem.
Note that this post does assume you are already know how to interpret these other metrics. Don’t fret if they are new to you, I’ve provided some links for further reading where you can learn more.
Metrics To Evaluate Machine Learning Algorithms
In this section you will discover how you can evaluate machine learning algorithms using a number of different common evaluation metrics.
Specifically, this section will show you how to use the following evaluation metrics with the caret package in R:
 Accuracy and Kappa
 RMSE and R^2
 ROC (AUC, Sensitivity and Specificity)
 LogLoss
Accuracy and Kappa
These are the default metrics used to evaluate algorithms on binary and multiclass classification datasets in caret.
Accuracy is the percentage of correctly classifies instances out of all instances. It is more useful on a binary classification than multiclass classification problems because it can be less clear exactly how the accuracy breaks down across those classes (e.g. you need to go deeper with a confusion matrix). Learn more about Accuracy here.
Kappa or Cohen’s Kappa is like classification accuracy, except that it is normalized at the baseline of random chance on your dataset. It is a more useful measure to use on problems that have an imbalance in the classes (e.g. 7030 split for classes 0 and 1 and you can achieve 70% accuracy by predicting all instances are for class 0). Learn more about Kappa here.
In the example below the Pima Indians diabetes dataset is used. It has a class break down of 65% to 35% for negative and positive outcomes.

# load libraries library(caret) library(mlbench) # load the dataset data(PimaIndiansDiabetes) # prepare resampling method control <– trainControl(method=“cv”, number=5) set.seed(7) fit <– train(diabetes~., data=PimaIndiansDiabetes, method=“glm”, metric=“Accuracy”, trControl=control) # display results print(fit) 
Running this example, we can see tables of Accuracy and Kappa for each machine learning algorithm evaluated. This includes the mean values (left) and the standard deviations (marked as SD) for each metric, taken over the population of cross validation folds and trials.
You can see that the accuracy of the model is approximately 76% which is 11 percentage points above the baseline accuracy of 65% which is not really that impressive. The Kappa the other hand shows approximately 46% which is more interesting.

Generalized Linear Model
768 samples 8 predictor 2 classes: ‘neg’, ‘pos’
No preprocessing Resampling: CrossValidated (5 fold) Summary of sample sizes: 614, 614, 615, 615, 614 Resampling results
Accuracy Kappa Accuracy SD Kappa SD 0.7695442 0.4656824 0.02692468 0.0616666 
RMSE and R^2
These are the default metrics used to evaluate algorithms on regression datasets in caret.
RMSE or Root Mean Squared Error is the average deviation of the predictions from the observations. It is useful to get a gross idea of how well (or not) an algorithm is doing, in the units of the output variable. Learn more about RMSE here.
R^2 spoken as R Squared or also called the coefficient of determination provides a “goodness of fit” measure for the predictions to the observations. This is a value between 0 and 1 for nofit and perfect fit respectively. Learn more about R^2 here.
In this example the longly economic dataset is used. The output variable is a “number employed”. It is not clear whether this is an actual count (e.g. in millions) or a percentage.

# load libraries library(caret) # load data data(longley) # prepare resampling method control <– trainControl(method=“cv”, number=5) set.seed(7) fit <– train(Employed~., data=longley, method=“lm”, metric=“RMSE”, trControl=control) # display results print(fit) 
Running this example, we can see tables of RMSE and R Squared for each machine learning algorithm evaluated. Again, you can see the mean and standard deviations of both metrics are provided.
You can see that the RMSE was 0.38 in the units of Employed (whatever those units are). Whereas, the R Square value shows a good fit for the data with a value very close to 1 (0.988).

Linear Regression
16 samples 6 predictor
No preprocessing Resampling: CrossValidated (5 fold) Summary of sample sizes: 12, 12, 14, 13, 13 Resampling results
RMSE Rsquared RMSE SD Rsquared SD 0.3868618 0.9883114 0.1025042 0.01581824 
Area Under ROC Curve
ROC metrics are only suitable for binary classification problems (e.g. two classes).
To calculate ROC information, you must change the summaryFunction in your trainControl to be twoClassSummary. This will calculate the Area Under ROC Curve (AUROC) also called just Area Under curve (AUC), sensitivity and specificity.
ROC is actually the area under the ROC curve or AUC. The AUC represents a models ability to discriminate between positive and negative classes. An area of 1.0 represents a model that made all predicts perfectly. An area of 0.5 represents a model as good as random. Learn more about ROC here.
ROC can be broken down into sensitivity and specificity. A binary classification problem is really a tradeoff between sensitivity and specificity.
Sensitivity is the true positive rate also called the recall. It is the number instances from the positive (first) class that actually predicted correctly.
Specificity is also called the true negative rate. Is the number of instances from the negative class (second) class that were actually predicted correctly. Learn more about sensitivity and specificity here.

# load libraries library(caret) library(mlbench) # load the dataset data(PimaIndiansDiabetes) # prepare resampling method control <– trainControl(method=“cv”, number=5, classProbs=TRUE, summaryFunction=twoClassSummary) set.seed(7) fit <– train(diabetes~., data=PimaIndiansDiabetes, method=“glm”, metric=“ROC”, trControl=control) # display results print(fit) 
Here, you can see the “good” but not “excellent” AUC score of 0.833. The first level is taken as the positive class, in this case “neg” (no onset of diabetes).

Generalized Linear Model
768 samples 8 predictor 2 classes: ‘neg’, ‘pos’
No preprocessing Resampling: CrossValidated (5 fold) Summary of sample sizes: 614, 614, 615, 615, 614 Resampling results
ROC Sens Spec ROC SD Sens SD Spec SD 0.8336003 0.882 0.5600978 0.02111279 0.03563706 0.0560184 
Logarithmic Loss
Logarithmic Loss or LogLoss is used to evaluate binary classification but it is more common for multiclass classification algorithms. Specifically, it evaluates the probabilities estimated by the algorithms. Learn more about log loss here.
In this case we see logloss calculated for the iris flower multiclass classification problem.

# load libraries library(caret) # load the dataset data(iris) # prepare resampling method control <– trainControl(method=“cv”, number=5, classProbs=TRUE, summaryFunction=mnLogLoss) set.seed(7) fit <– train(Species~., data=iris, method=“rpart”, metric=“logLoss”, trControl=control) # display results print(fit) 
Logloss is minimized and we can see the optimal CART model had a cp of 0.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

CART
150 samples 4 predictor 3 classes: ‘setosa’, ‘versicolor’, ‘virginica’
No preprocessing Resampling: CrossValidated (5 fold) Summary of sample sizes: 120, 120, 120, 120, 120 Resampling results across tuning parameters:
cp logLoss logLoss SD 0.00 0.4105613 0.6491893 0.44 0.6840517 0.4963032 0.50 1.0986123 0.0000000
logLoss was used to select the optimal model using the smallest value. The final value used for the model was cp = 0. 
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Summary
In this post you discovered different metrics that you can use to evaluate the performance of your machine learning algorithms in R using caret. Specifically:
 Accuracy and Kappa
 RMSE and R^2
 ROC (AUC, Sensitivity and Specificity)
 LogLoss
You can use the recipes in this post you evaluate machine learning algorithms on your current or next machine learning project.
Next Step
Work through the example in this post.
 Open your R interactive environment.
 Type of copypaste the sample code above.
 Take your time and understand what is going on, use R help to readup on functions.
Do you have any questions? Leave a comment and I will do my best.