The caret package (short for Classification And REgression Training) contains functions to streamline the model training process for complex regression and classification problems. The package utilizes a number of R packages but tries not to load them all at package start-up (by removing formal package dependencies, the package startup time can be greatly decreased). The package “suggests” field includes 32 packages. caret loads packages as needed and assumes that they are installed. If a modeling package is missing, there is a prompt to install it.
Install caret using
install.packages("caret", dependencies = c("Depends", "Suggests"))to ensure that all the needed packages are installed.
The main help pages for the package are at https://topepo.github.io/caret/ Here, there are extended examples and a large amount of information that previously found in the package vignettes.
caret has several functions that attempt to streamline the model building and evaluation process, as well as feature selection and other techniques.
One of the primary tools in the package is the train
function which can be used to
A formal algorithm description can be found in Section 5.1 of the caret manual.
There are options for customizing almost every step of this process (e.g. resampling technique, choosing the optimal parameters etc). To demonstrate this function, the Sonar data from the mlbench package will be used.
The Sonar data consist of 208 data points collected on 60 predictors.
The goal is to predict the two classes M for metal cylinder
or R for rock).
First, we split the data into two groups: a training set and a test
set. To do this, the createDataPartition function is
used:
library(caret)
library(mlbench)
data(Sonar)
set.seed(107)
inTrain <- createDataPartition(
y = Sonar$Class,
## the outcome data are needed
p = .75,
## The percentage of data in the
## training set
list = FALSE
)
## The format of the results
## The output is a set of integers for the rows of Sonar
## that belong in the training set.
str(inTrain)
#> int [1:157, 1] 1 2 3 4 5 7 10 11 12 13 ...
#> - attr(*, "dimnames")=List of 2
#> ..$ : NULL
#> ..$ : chr "Resample1"By default, createDataPartition does a stratified random
split of the data. To partition the data:
training <- Sonar[ inTrain,]
testing <- Sonar[-inTrain,]
nrow(training)
#> [1] 157
nrow(testing)
#> [1] 51To tune a model using the algorithm above, the train
function can be used. More details on this function can be found at https://topepo.github.io/caret/model-training-and-tuning.html.
Here, a partial least squares discriminant analysis (PLSDA) model will
be tuned over the number of PLS components that should be retained. The
most basic syntax to do this is:
plsFit <- train(
Class ~ .,
data = training,
method = "pls",
## Center and scale the predictors for the training
## set and all future samples.
preProc = c("center", "scale")
)However, we would probably like to customize it in a few ways:
To change the candidate values of the tuning parameter, either of the
tuneLength or tuneGrid arguments can be used.
The train function can generate a candidate set of
parameter values and the tuneLength argument controls how
many are evaluated. In the case of PLS, the function uses a sequence of
integers from 1 to tuneLength. If we want to evaluate all
integers between 1 and 15, setting tuneLength = 15 would
achieve this. The tuneGrid argument is used when specific
values are desired. A data frame is used where each row is a tuning
parameter setting and each column is a tuning parameter. An example is
used below to illustrate this.
plsFit <- train(
Class ~ .,
data = training,
method = "pls",
preProc = c("center", "scale"),
## added:
tuneLength = 15
)To modify the resampling method, a trainControl function
is used. The option method controls the type of resampling
and defaults to "boot". Another method,
"repeatedcv", is used to specify repeated K-fold
cross-validation (and the argument repeats controls the
number of repetitions). K is controlled by the
number argument and defaults to 10. The new syntax is
then:
ctrl <- trainControl(method = "repeatedcv", repeats = 3)
plsFit <- train(
Class ~ .,
data = training,
method = "pls",
preProc = c("center", "scale"),
tuneLength = 15,
## added:
trControl = ctrl
)Finally, to choose different measures of performance, additional
arguments are given to trainControl. The
summaryFunction argument is used to pass in a function that
takes the observed and predicted values and estimate some measure of
performance. Two such functions are already included in the package:
defaultSummary and twoClassSummary. The latter
will compute measures specific to two-class problems, such as the area
under the ROC curve, the sensitivity and specificity. Since the ROC
curve is based on the predicted class probabilities (which are not
computed automatically), another option is required. The
classProbs = TRUE option is used to include these
calculations.
Lastly, the function will pick the tuning parameters associated with
the best results. Since we are using custom performance measures, the
criterion that should be optimized must also be specified. In the call
to train, we can use metric = "ROC" to do
this.
ctrl <- trainControl(
method = "repeatedcv",
repeats = 3,
classProbs = TRUE,
summaryFunction = twoClassSummary
)
set.seed(123)
plsFit <- train(
Class ~ .,
data = training,
method = "pls",
preProc = c("center", "scale"),
tuneLength = 15,
trControl = ctrl,
metric = "ROC"
)
plsFit
#> Partial Least Squares
#>
#> 157 samples
#> 60 predictor
#> 2 classes: 'M', 'R'
#>
#> Pre-processing: centered (60), scaled (60)
#> Resampling: Cross-Validated (10 fold, repeated 3 times)
#> Summary of sample sizes: 141, 141, 142, 142, 141, 142, ...
#> Resampling results across tuning parameters:
#>
#> ncomp ROC Sens Spec
#> 1 0.805 0.726 0.690
#> 2 0.848 0.750 0.801
#> 3 0.849 0.764 0.748
#> 4 0.836 0.765 0.736
#> 5 0.812 0.748 0.755
#> 6 0.789 0.724 0.699
#> 7 0.794 0.744 0.689
#> 8 0.801 0.739 0.698
#> 9 0.793 0.758 0.677
#> 10 0.790 0.741 0.690
#> 11 0.787 0.742 0.710
#> 12 0.777 0.737 0.715
#> 13 0.772 0.738 0.700
#> 14 0.768 0.718 0.690
#> 15 0.768 0.715 0.690
#>
#> ROC was used to select the optimal model using
#> the largest value.
#> The final value used for the model was ncomp = 3.In this output the grid of results are the average resampled estimates of performance. The note at the bottom tells the user that 3 PLS components were found to be optimal. Based on this value, a final PLS model is fit to the whole data set using this specification and this is the model that is used to predict future samples.
The package has several functions for visualizing the results. One
method for doing this is the ggplot function for
train objects. The command ggplot(plsFit)
produced the results seen in Figure \(\ref{F:pls}\) and shows the relationship
between the resampled performance values and the number of PLS
components.
ggplot(plsFit)
To predict new samples, predict.train can be used. For
classification models, the default behavior is to calculate the
predicted class. The option type = "prob" can be used to
compute class probabilities from the model. For example:
plsClasses <- predict(plsFit, newdata = testing)
str(plsClasses)
#> Factor w/ 2 levels "M","R": 2 1 1 1 2 2 1 2 2 2 ...
plsProbs <- predict(plsFit, newdata = testing, type = "prob")
head(plsProbs)
#> M R
#> 6 0.288 0.712
#> 8 0.648 0.352
#> 9 0.659 0.341
#> 15 0.529 0.471
#> 26 0.430 0.570
#> 27 0.492 0.508caret contains a function to compute the confusion matrix and associated statistics for the model fit:
confusionMatrix(data = plsClasses, testing$Class)
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction M R
#> M 21 7
#> R 6 17
#>
#> Accuracy : 0.745
#> 95% CI : (0.604, 0.857)
#> No Information Rate : 0.529
#> P-Value [Acc > NIR] : 0.00131
#>
#> Kappa : 0.487
#>
#> Mcnemar's Test P-Value : 1.00000
#>
#> Sensitivity : 0.778
#> Specificity : 0.708
#> Pos Pred Value : 0.750
#> Neg Pred Value : 0.739
#> Prevalence : 0.529
#> Detection Rate : 0.412
#> Detection Prevalence : 0.549
#> Balanced Accuracy : 0.743
#>
#> 'Positive' Class : M
#> To fit an another model to the data, train can be
invoked with minimal changes. Lists of models available can be found at
https://topepo.github.io/caret/available-models.html
or https://topepo.github.io/caret/train-models-by-tag.html.
For example, to fit a regularized discriminant model to these data, the
following syntax can be used:
## To illustrate, a custom grid is used
rdaGrid = data.frame(gamma = (0:4)/4, lambda = 3/4)
set.seed(123)
rdaFit <- train(
Class ~ .,
data = training,
method = "rda",
tuneGrid = rdaGrid,
trControl = ctrl,
metric = "ROC"
)
rdaFit
#> Regularized Discriminant Analysis
#>
#> 157 samples
#> 60 predictor
#> 2 classes: 'M', 'R'
#>
#> No pre-processing
#> Resampling: Cross-Validated (10 fold, repeated 3 times)
#> Summary of sample sizes: 141, 141, 142, 142, 141, 142, ...
#> Resampling results across tuning parameters:
#>
#> gamma ROC Sens Spec
#> 0.00 0.778 0.723 0.682
#> 0.25 0.887 0.864 0.786
#> 0.50 0.876 0.851 0.730
#> 0.75 0.863 0.830 0.710
#> 1.00 0.734 0.680 0.636
#>
#> Tuning parameter 'lambda' was held constant at a
#> value of 0.75
#> ROC was used to select the optimal model using
#> the largest value.
#> The final values used for the model were gamma =
#> 0.25 and lambda = 0.75.
rdaClasses <- predict(rdaFit, newdata = testing)
confusionMatrix(rdaClasses, testing$Class)
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction M R
#> M 25 5
#> R 2 19
#>
#> Accuracy : 0.863
#> 95% CI : (0.737, 0.943)
#> No Information Rate : 0.529
#> P-Value [Acc > NIR] : 5.01e-07
#>
#> Kappa : 0.723
#>
#> Mcnemar's Test P-Value : 0.45
#>
#> Sensitivity : 0.926
#> Specificity : 0.792
#> Pos Pred Value : 0.833
#> Neg Pred Value : 0.905
#> Prevalence : 0.529
#> Detection Rate : 0.490
#> Detection Prevalence : 0.588
#> Balanced Accuracy : 0.859
#>
#> 'Positive' Class : M
#> How do these models compare in terms of their resampling results? The
resamples function can be used to collect, summarize and
contrast the resampling results. Since the random number seeds were
initialized to the same value prior to calling `train}, the same folds
were used for each model. To assemble them:
resamps <- resamples(list(pls = plsFit, rda = rdaFit))
summary(resamps)
#>
#> Call:
#> summary.resamples(object = resamps)
#>
#> Models: pls, rda
#> Number of resamples: 30
#>
#> ROC
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> pls 0.679 0.787 0.823 0.849 0.938 0.984 0
#> rda 0.750 0.847 0.889 0.887 0.940 1.000 0
#>
#> Sens
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> pls 0.556 0.625 0.750 0.764 0.875 1 0
#> rda 0.625 0.757 0.875 0.864 1.000 1 0
#>
#> Spec
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> pls 0.429 0.714 0.714 0.748 0.857 1 0
#> rda 0.500 0.714 0.750 0.786 0.875 1 0There are several functions to visualize these results. For example, a Bland-Altman type plot can be created using
xyplot(resamps, what = "BlandAltman")
The results look similar. Since, for each resample, there are paired
results a paired t-test can be used to assess whether there is
a difference in the average resampled area under the ROC curve. The
diff.resamples function can be used to compute this:
diffs <- diff(resamps)
summary(diffs)
#>
#> Call:
#> summary.diff.resamples(object = diffs)
#>
#> p-value adjustment: bonferroni
#> Upper diagonal: estimates of the difference
#> Lower diagonal: p-value for H0: difference = 0
#>
#> ROC
#> pls rda
#> pls -0.0378
#> rda 0.000544
#>
#> Sens
#> pls rda
#> pls -0.1
#> rda 0.000172
#>
#> Spec
#> pls rda
#> pls -0.0387
#> rda 0.136Based on this analysis, the difference between the models is -0.038 ROC units (the RDA model is slightly higher) and the two-sided p-value for this difference is 5e-04.