NDK_MLR_GOF

Last Modified on 07/15/2016 10:36 am CDT
int __stdcall NDK_MLR_GOF ( double **  X,
size_t  nXSize,
size_t  nXVars,
LPBYTE  mask,
size_t  nMaskLen,
double *  Y,
size_t  nYSize,
double  intercept,
WORD  nRetType,
double *  retVal 
)

Calculates a measure for the goodness of fit (e.g. \(R^2\)).

Returns
status code of the operation
Return values
NDK_SUCCESS  Operation successful
NDK_FAILED  Operation unsuccessful. See Macros for full list.
Parameters
[in] X is the independent (explanatory) variables data matrix, such that each column represents one variable.
[in] nXSize is the number of observations (rows) in X.
[in] nXVars is the number of independent (explanatory) variables (columns) in X.
[in] mask is the boolean array to choose the explanatory variables in the model. If missing, all variables in X are included.
[in] nMaskLen is the number of elements in the "mask."
[in] Y is the response or dependent variable data array (one dimensional array of cells).
[in] nYSize is the number of observations in Y.
[in] intercept is the constant or intercept value to fix (e.g. zero). If missing (i.e. NaN), an intercept will not be fixed and is computed normally.
[in] nRetType is a switch to select a fitness measure (1=R-square (default), 2=adjusted R-square, 3=RMSE, 4=LLF, 5=AIC, 6=BIC/SIC):
  1. R-square (coefficient of determination)
  2. Adjusted R-square
  3. Regression Error (RMSE)
  4. Log-likelihood (LLF)
  5. Akaike information criterion (AIC)
  6. Schwartz/Bayesian information criterion (SIC/BIC)
[out] retVal is the calculated goodness-of-fit statistics.
Remarks
  1. The underlying model is described here.
  2. The coefficient of determination, denoted \(R^2\) provides a measure of how well observed outcomes are replicated by the model. \[R^2 = \frac{\mathrm{SSR}} {\mathrm{SST}} = 1 - \frac{\mathrm{SSE}} {\mathrm{SST}}\]
  3. The adjusted R-square (denoted \(\bar R^2\)) is an attempt to take account of the phenomenon of the \(R^2\) automatically and spuriously increasing when extra explanatory variables are added to the model. The \(\bar R^2\) adjusts for the number of explanatory terms in a model relative to the number of data points. \[\bar R^2 = {1-(1-R^{2}){N-1 \over N-p-1}} = {R^{2}-(1-R^{2}){p \over N-p-1}} = 1 - \frac{\mathrm{SSE}/(N-p-1)}{\mathrm{SST}/(N-1)}\] Where:
    • \(p\) is the number of explanatory variables in the model.
    • \(N\) is the number of observations in the sample.
  4. The regression error is defined as the square root for the mean square error (RMSE): \[\mathrm{RMSE} = \sqrt{\frac{SSE}{N-p-1}}\]
  5. The log likelihood of the regression is given as: \[\mathrm{LLF}=-\frac{N}{2}\left(1+\ln(2\pi)+\ln\left(\frac{\mathrm{SSR}}{N} \right ) \right )\] The Akaike and Schwarz/Bayesian information criterion are given as: \[\mathrm{AIC}=-\frac{2\mathrm{LLF}}{N}+\frac{2(p+1)}{N}\] \[\mathrm{BIC} = \mathrm{SIC}=-\frac{2\mathrm{LLF}}{N}+\frac{(p+1)\times\ln(p+1)}{N}\]
  6. The sample data may include missing values.
  7. Each column in the input matrix corresponds to a separate variable.
  8. Each row in the input matrix corresponds to an observation.
  9. Observations (i.e. row) with missing values in X or Y are removed.
  10. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
  11. The MLR_GOF function is available starting with version 1.60 APACHE.
Requirements
Header SFSDK.H
Library SFSDK.LIB
DLL SFSDK.DLL
Namespace:  NumXLAPI
Class:  SFSDK
Scope:  Public
Lifetime:  Static
int NDK_MLR_GOF ( double  pXData,
UIntPtr  nXSize,
UIntPtr  nXVars,
byte[]  mask,
UIntPtr  nMaskLen,
double[]  pYData,
UIntPtr  nYSize,
double  intercept,
short  nRetType,
ref double  retVal 
)

Calculates a measure for the goodness of fit (e.g. \(R^2\)).

Return Value

a value from NDK_RETCODE enumeration for the status of the call. 

NDK_SUCCESS  operation successful
Error  Error Code
Parameters
[in] pXData is the independent (explanatory) variables data matrix, such that each column represents one variable.
[in] nXSize is the number of observations (rows) in pXData.
[in] nXVars is the number of independent (explanatory) variables (columns) in pXData.
[in] mask is the boolean array to choose the explanatory variables in the model. If missing, all variables in X are included.
[in] nMaskLen is the number of elements in the "mask."
[in] Y is the response or dependent variable data array (one dimensional array of cells).
[in] nYSize is the number of observations in Y.
[in] intercept is the constant or intercept value to fix (e.g. zero). If missing (i.e. NaN), an intercept will not be fixed and is computed normally.
[in] nRetType is a switch to select a fitness measure (1=R-square (default), 2=adjusted R-square, 3=RMSE, 4=LLF, 5=AIC, 6=BIC/SIC):
  1. R-square (coefficient of determination)
  2. Adjusted R-square
  3. Regression Error (RMSE)
  4. Log-likelihood (LLF)
  5. Akaike information criterion (AIC)
  6. Schwartz/Bayesian information criterion (SIC/BIC)
[out] retVal is the calculated goodness-of-fit statistics.
Remarks
  1. The underlying model is described here.
  2. The coefficient of determination, denoted \(R^2\) provides a measure of how well observed outcomes are replicated by the model. \[R^2 = \frac{\mathrm{SSR}} {\mathrm{SST}} = 1 - \frac{\mathrm{SSE}} {\mathrm{SST}}\]
  3. The adjusted R-square (denoted \(\bar R^2\)) is an attempt to take account of the phenomenon of the \(R^2\) automatically and spuriously increasing when extra explanatory variables are added to the model. The \(\bar R^2\) adjusts for the number of explanatory terms in a model relative to the number of data points. \[\bar R^2 = {1-(1-R^{2}){N-1 \over N-p-1}} = {R^{2}-(1-R^{2}){p \over N-p-1}} = 1 - \frac{\mathrm{SSE}/(N-p-1)}{\mathrm{SST}/(N-1)}\] Where:
    • \(p\) is the number of explanatory variables in the model.
    • \(N\) is the number of observations in the sample.
  4. The regression error is defined as the square root for the mean square error (RMSE): \[\mathrm{RMSE} = \sqrt{\frac{SSE}{N-p-1}}\]
  5. The log likelihood of the regression is given as: \[\mathrm{LLF}=-\frac{N}{2}\left(1+\ln(2\pi)+\ln\left(\frac{\mathrm{SSR}}{N} \right ) \right )\] The Akaike and Schwarz/Bayesian information criterion are given as: \[\mathrm{AIC}=-\frac{2\mathrm{LLF}}{N}+\frac{2(p+1)}{N}\] \[\mathrm{BIC} = \mathrm{SIC}=-\frac{2\mathrm{LLF}}{N}+\frac{(p+1)\times\ln(p+1)}{N}\]
  6. The sample data may include missing values.
  7. Each column in the input matrix corresponds to a separate variable.
  8. Each row in the input matrix corresponds to an observation.
  9. Observations (i.e. row) with missing values in X or Y are removed.
  10. The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
  11. The MLR_GOF function is available starting with version 1.60 APACHE.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI
Class SFSDK
Scope Public
Lifetime Static
Package NumXLAPI.DLL
Examples
References
* Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
* Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848

See Also

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