aic.c File Reference

Functions for using Akaike's information criteria. More...

#include "tpcclibConfig.h"
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>
#include "tpcextensions.h"
#include "tpcmodels.h"

Go to the source code of this file.

Functions
double	aicSS (double ss, const unsigned int n, const unsigned int k)
	Calculate corrected AIC.
unsigned int	parFreeNr (const unsigned int n, double *pLower, double *pUpper)
	Calculate the number of free parameters.

Detailed Description

Functions for using Akaike's information criteria.

Definition in file aic.c.

Function Documentation

aicSS()

double aicSS	(	double	ss,
		const unsigned int	n,
		const unsigned int	k )

Calculate corrected AIC.

Calculate AICc in the special case of sum-of-squares optimization from the SS, number of fitted samples, and number of fitted parameters.

If variance is different between the data points, weighted SS must be given.

See also

parFreeNr, tacWSampleNr

Returns

Returns the AIC value, or NaN in case of invalid input values.

Parameters

ss	Sum-of-Squares of the fit (weighted, if necessary).
n	Sample size, i.e. number of fitted samples; do not include samples with zero weight.
k	Number of fitted model parameters; do not include fixed parameters; AICc calculation is valid only when (n-k)>1.

Definition at line 29 of file aic.c.

  {
  if(!(ss>=0.0) || n<1 || (n-k)<2) return(nan(""));
 
  int dr=n-k-1; 
  int dv=2*k*(k+1);
  double aic=0.0, bias_adj=0.0, css;
  if(dr>0) bias_adj=((double)dv)/((double)dr); else bias_adj=0.0;
  if(ss<1.0e-50) css=1.0e-50; else css=ss; /* Because log(0) is an error */
  aic= n*log(css/(double)n) + 2.0*(double)k + bias_adj;
  return(aic);
}

parFreeNr()

unsigned int parFreeNr	(	const unsigned int	n,
		double *	pLower,
		double *	pUpper )

Calculate the number of free parameters.

Model parameters can be fixed by setting lower and upper limit to equal values. This function simply checks the limits for each parameter.

Returns

Returns the number of free parameters.

Author

Vesa Oikonen

See also

aicSS, tacWSampleNr

Parameters

n	Nr of parameters
pLower	Lower limits (array of length n)
pUpper	Upper limits (array of length n)

Definition at line 60 of file aic.c.

  {
  if(n==0 || pLower==NULL || pUpper==NULL) return(0);
  unsigned int nf=0;
  for(unsigned int i=0; i<n; i++) {
    double range=pUpper[i]-pLower[i];
    if(range>1.0E-10) nf++;
  }
  return(nf);
}