q2 {cvq2} R Documentation

## Model prediction power calculation.

### Description

Determines the prediction power of model M. Therefore M is applied to an external data set and its observations are compared to the model predictions. If an external data set is not available, the prediction power is calculated while performing a cross-validation to the model data set.

### Usage

```  looq2( modelData, formula = NULL, nu = 1, round = 4,
extOut = FALSE, extOutFile = NULL )

cvq2( modelData, formula = NULL, nFold = N, nRun = 1, nu = 1,
round = 4, extOut = FALSE, extOutFile = NULL )

q2( modelData, predictData, formula = NULL, nu = 0, round = 4,
extOut = FALSE, extOutFile = NULL )
```

### Arguments

 `modelData` The model data set consists of parameters x_1, x_2, ..., x_n and an observation y `predictData` The prediction data set consists of parameters x_1, x_2, ..., x_n and an observation y `formula` The formula used to predict the observation: y ~ x_1 + x_2 + … + x_n DEFAULT: NULL If NULL, a generic formula is derived from the data set, assuming that the last column contains observations whereas the others contain parameters x_1, x_2, …, x_n `nFold` The data set `modelData` is randomly partitioned into nFold equal sized subsets (test sets) during each run, DEFAULT: N, 2 <= nFold <= N `nRun` Number of iterations, the cross-validation is repeated for this data set. This corresponds to the number of individual predictions per observation, 1 <= nRun, DEFAULT: 1 Must be 1, if nFold = N. `nu` The degrees of freedom used in rmse calculation in relation to the prediction power, DEFAULT: 1 (`looq2(),cvq2()`), 0 (else) `round` The rounding value used in the output, DEFAULT: 4 `extOut` Extended output, DEFAULT: FALSE If `extOutFile` is not specified, write to stdout() `extOutFile` Write extended output into file (implies `extOut = TRUE`), DEFAULT: NULL

### Details

The calibration of model M with `modelData` is done with a linear regression.

#### `q2()`

Alias: `qsq()`, `qsquare()`

The model described by `modelData` is used to predict the observations of `predictData`. These predictions are used to calculate the predictive squared correlation coefficient, q^2.

#### `cvq2()`

Alias: `cvqsq()`, `cvqsquare()`

A cross-validation is performed for `modelData`, whereas `modelData` (N elements) is split into `nFold` disjunct and equal sized test sets. Each test set consists of k elements:

k=ceil(N/nFold)

In case k=N/nFold is a decimal number, some test sets consist of k-1 elements. The remaining N-k elements are merged together as training set for this test set and describe the model M'. This model is used to predict the observations in the test set. Note, that M' is slighlty different to model M, which is a result of the missing k values.
Each observation from `modelData` is predicted once. The difference between the prediction and the observation within the test sets is used to calculate the PREdictive residual Sum of Squares (PRESS). Furthermore for any training set the mean of the observed values in this training set, y_mean^N-k,i, is calculated. PRESS and y_mean^N-k,i are required to calculate the predictive squared correlation coefficient, q^2_cv.
In case k>1 one can repeat the cross-validation to overcome biasing. Therefore in each iteration (nRun = 1,2 …, x) the test sets are compiled individually by random. Within one iteration, each observation is predicted once. If nFold = N, one iteration is necessary only.

#### `looq2()`

Same procedure as `cvq2()` (see above), but implicit nFold = N to perform a Leave-One-Out cross-validation. For Leave-One-Out cross-validation one iteration (`nRun = 1`) is necessary only.

### Value

#### `q2()`

The method `q2` returns an object of class `"q2"`. It contains information about the model calibration and its prediction performance on the external data set, `predictData`.

#### `cvq2(), looq2()`

The methods `cvq2` and `looq2` return an object of class `"cvq2"`. It contains information about the model calibration and its prediction performance as well as data about the cross-validation applied to `modelData`.

### Author(s)

Torsten Thalheim <torstenthalheim@gmx.de>

### Examples

```  require(methods)
require(stats)
library(cvq2)

data(cvq2.sample.A)
result <- cvq2( cvq2.sample.A )
result

data(cvq2.sample.B)
result <- cvq2( cvq2.sample.B, y ~ x, nFold = 3 )
result

data(cvq2.sample.B)
result <- cvq2( cvq2.sample.B, y ~ x, nFold = 3, nRun = 5 )
result

data(cvq2.sample.A)
result <- looq2( cvq2.sample.A, y ~ x1 + x2 )
result

data(cvq2.sample.A)
data(cvq2.sample.A_pred)
result <- q2( cvq2.sample.A, cvq2.sample.A, y ~ x1 + x2 )
result
```

[Package cvq2 version 1.2.0 Index]