```
postResample(pred, obs)
defaultSummary(data, lev = NULL, model = NULL)
```twoClassSummary(data, lev = NULL, model = NULL)

R2(pred, obs, formula = "corr", na.rm = FALSE)
RMSE(pred, obs, na.rm = FALSE)

pred

A vector of numeric data (could be a factor)

obs

A vector of numeric data (could be a factor)

data

a data frame or matrix with columns

`obs`

and `pred`

for the observed and predicted outcomes. For `twoClassSummary`

, columns should also
include predicted probabilities for each class. See the `classProbs`

lev

a character vector of factors levels for the response. In regression cases, this would be

`NULL`

.model

a character string for the model name (as taken form the

`method`

argument of `train`

.formula

which $R^2$ formula should be used? Either "corr" or "traditional". See Kvalseth (1985) for a summary of the different equations.

na.rm

a logical value indicating whether

`NA`

values should be stripped before the computation proceeds.- A vector of performance estimates.

`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. To use this function, the `classProbs`

argument of `trainControl`

should be `TRUE`

.

Other functions can be used via the `summaryFunction`

argument of `trainControl`

. Custom functions must have the same arguments as`defaultSummary`

.

`trainControl`

predicted <- matrix(rnorm(50), ncol = 5) observed <- rnorm(10) apply(predicted, 2, postResample, obs = observed)