postResample is meant to be used with apply across a matrix.
For numeric data the code checks to see if the standard deviation of either
vector is zero. If so, the correlation between those samples is assigned a
value of zero. NA values are ignored everywhere.
Note that many models have more predictors (or parameters) than data points,
so the typical mean squared error denominator (n - p) does not apply. Root
mean squared error is calculated using sqrt(mean((pred - obs)^2.
Also, \(R^2\) is calculated wither using as the square of the correlation
between the observed and predicted outcomes when form = "corr". when
form = "traditional", $$ R^2 = 1-\frac{\sum (y_i -
\hat{y}_i)^2}{\sum (y_i - \bar{y}_i)^2} $$
For defaultSummary is the default function to compute performance
metrics in train. It is a wrapper around postResample.
twoClassSummary computes sensitivity, specificity and the area under
the ROC curve. mnLogLoss computes the minus log-likelihood of the
multinomial distribution (without the constant term): $$ -logLoss =
\frac{-1}{n}\sum_{i=1}^n \sum_{j=1}^C y_{ij} \log(p_{ij}) $$ where the
y values are binary indicators for the classes and p are the
predicted class probabilities.
prSummary (for precision and recall) computes values for the default
0.50 probability cutoff as well as the area under the precision-recall curve
across all cutoffs and is labelled as "AUC" in the output. If assumes
that the first level of the factor variables corresponds to a relevant
result but the lev argument can be used to change this.
multiClassSummary computes some overall measures of for performance
(e.g. overall accuracy and the Kappa statistic) and several averages of
statistics calculated from "one-versus-all" configurations. For example, if
there are three classes, three sets of sensitivity values are determined and
the average is reported with the name ("Mean_Sensitivity"). The same is true
for a number of statistics generated by confusionMatrix. With
two classes, the basic sensitivity is reported with the name "Sensitivity"
To use twoClassSummary and/or mnLogLoss, the classProbs
argument of trainControl should be TRUE.
multiClassSummary can be used without class probabilities but some
statistics (e.g. overall log loss and the average of per-class area under
the ROC curves) will not be in the result set.
Other functions can be used via the summaryFunction argument of
trainControl. Custom functions must have the same arguments
asdefaultSummary.
The function getTrainPerf returns a one row data frame with the
resampling results for the chosen model. The statistics will have the prefix
"Train" (i.e. "TrainROC"). There is also a column called
"method" that echoes the argument of the call to
trainControl of the same name.