| int __stdcall NDK_PCR_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 | ||
| ) |
Returns an array of cells for the i-th principal component (or residuals).
- 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 variables data matrix, such that each column represents one variable [in] nXSize is the number of observations (i.e. rows) in X [in] nXVars is the number of variables (i.e. columns) in X [in] mask is the boolean array to select a subset of the input variables in X. If missing (i.e. NULL), all variables in X are included. [in] nMaskLen is the number of elements in mask [in] Y is the response or the dependent variable data array (one dimensional array) [in] nYSize is the number of elements in Y [in] intercept is the constant or the intercept value to fix (e.g. zero). If missing (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 ). - R-square (coefficient of determination)
- Adjusted R-square
- Regression Error (RMSE)
- Log-likelihood (LLF)
- Akaike information criterion (AIC)
- Schwartz/Bayesian information criterion (SIC/BIC)
[out] retVal is the calculated goodness of fit measure
- Remarks
-
- The underlying model is described here.
- The coefficient of determination, denoted \(R^2\), provides a measure of how well observed outcomes are replicated by the model. \[R^2 = \frac{\mathrm{SSR}} {\mathrm{SST}} = 1 - \frac{\mathrm{SSE}} {\mathrm{SST}}\]
- 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.
- The regression error is defined as the square root for the mean square error (RMSE): \[\mathrm{RMSE} = \sqrt{\frac{SSE}{N-p-1}}\]
- 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: \[\mathrm{AIC}=-\frac{2\mathrm{LLF}}{N}+\frac{2(p+1)}{N}\] \[\mathrm{BIC} = \mathrm{SIC}=-\frac{2\mathrm{LLF}}{N}+\frac{(p+1)\times\ln(p+1)}{N}\]
- The sample data may include missing values.
- Each column in the input matrix corresponds to a separate variable.
- Each row in the input matrix corresponds to an observation.
- Observations (i.e. row) with missing values in X or Y are removed.
- The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variables (X).
- The MLR_GOF function is available starting with version 1.60 APACHE.
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.DLL
