| int __stdcall NDK_PCR_PRFTest | ( | double ** | X, |
| size_t | nXSize, | ||
| size_t | nXVars, | ||
| double * | Y, | ||
| size_t | nYSize, | ||
| double | intercept, | ||
| LPBYTE | mask1, | ||
| size_t | nMaskLen1, | ||
| LPBYTE | mask2, | ||
| size_t | nMaskLen2, | ||
| double | alpha, | ||
| 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] 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] mask1 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] nMaskLen1 is the number of elements in mask1 [in] mask2 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] nMaskLen2 is the number of elements in mask2 [in] alpha is the statistical significance of the test (i.e. alpha) [in] nRetType is a switch to select the return output (1 = P-Value (default), 2 = Test Stats, 3 = Critical Value.) [out] retVal is the calculated test statistics/
- Remarks
-
- The underlying model is described here.
- Model 1 must be a sub-model of Model 2. In other words, all variables included in Model 1 must be included in Model 2.
- The coefficient of determination (i.e. \(R^2\)) increases in value as we add variables to the regression model, but we often wish to test whether the improvement in R square by adding those variables is statistically significant.
- To do so, we developed an inclusion/exclusion test for those variables. First, let's start with a regression model with \(K_1\) variables: \[Y_t = \alpha + \beta_1 \times X_1 + \cdots + \beta_{K_1} \times X_{K_1}\] Now, let's add few more variables \(\left(X_{K_1+1} \cdots X_{K_2}\right):\) \[Y_t = \alpha + \beta_1 \times X_1 + \cdots + \beta_{K_1} \times X_{K_1} + \cdots + \beta_{K_1+1} \times X_{K_1+1} + \cdots + \beta_{K_2} \times X_{K_2}\]
- The test of hypothesis is as follows: \[H_o : \beta_{K_1+1} = \beta_{K_1+2} = \cdots = beta_{K_2} = 0\] \[H_1 : \exists \beta_{i} \neq 0, i \in \left[K_1+1 \cdots K_2\right]\]
- Using the change in the coefficient of determination (i.e. \(R^2\)) as we added new variables, we can calculate the test statistics: \[\mathrm{f}=\frac{(R^2_{f}-R^2_{r})/(K_2-K_1)}{(1-R^2_f)/(N-K_2-1)}\sim \mathrm{F}_{K_2-K_1,N-K2-1}\] Where:
- \(R^2_f\) is the \(R^2\) of the full model (with added variables).
- \(R^2_r\) is the \(R^2\) of the reduced model (without the added variables).
- \(K_1\) is the number of variables in the reduced model.
- \(K_2\) is the number of variables in the full model.
- \(N\) is the number of observations in the sample data.
- 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_ANOVA function is available starting with version 1.60 APACHE.
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.DLL
