cvq2 (version 1.2.0)

q2: 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: $y \sim x_1 + x_2 + \ldots + x_n$ DEFAULT: NULL If NULL, a generic formula is derived from the data set, assuming that the last column contains observations whereas the others contain para

nFold

The data set modelData is randomly partitioned into nFold equal sized subsets (test sets) during each run, DEFAULT: N, $2

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

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. }

concept

• cross-validation
• Pearson correlation coefficient
• squared correlation coefficient

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: $$k = \left\lceil\frac{N}{nFold}\right\rceil$$ In case $\frac{N}{nFold}$ 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 ($\code{nRun} = \lbrace1, 2, \ldots, x\rbrace$) the test sets are compiled individually by random. Within one iteration, each observation is predicted once. If $\code{nFold} = N$, one iteration is necessary only. } looq2(){ Same procedure as cvq2() (see above), but implicit $\code{nFold} = N$ to perform a Leave-One-Out cross-validation. For Leave-One-Out cross-validation one iteration (nRun = 1) is necessary only. }

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