NDK_CHOWTEST

Returns the p-value of the regression stability test (i.e. whether the coefficients in two linear regressions on different data sets are equal).

Returns

status code of the operation

Return values

NDK_SUCCESS	Operation successful
NDK_FAILED	Operation unsuccessful. See Macros for full list.

Parameters

[in]	XX1	is the independent variables data matrix of the first data set (two dimensional).
[in]	M	is the number of variables (columns) in XX1 and XX2.
[in]	Y1	is the response or the dependent variable data array for the first data set (one dimensional array).
[in]	N1	is the number of observations (rows) in the first data set.
[in]	XX2	is the independent variables data matrix of the second data set, such that each column represents one variable.
[in]	Y2	is the response or the dependent variable data array of the second data set (one dimensional array).
[in]	N2	is the number of observations (rows) in the second data set.
[in]	mask	is the boolean array to select a subset of the input variables in X. If NULL, all variables in X are included.
[in]	nMaskLen	is the number of elements in the mask, which must be zero or equal to M.
[in]	intercept	is the regression constant or the intercept value (e.g. zero). If missing, an intercept is not fixed and will be computed from the data set.
[in]	retType	is a switch to select the return output Method Value Description TEST_PVALUE 1 P-Value TEST_SCORE 2 Test statistics (aka score) TEST_CRITICALVALUE 3 Critical value.
[in]	retVal	is the calculated Chow test statistics.

Remarks

• The data sets may include missing values.
• Each column in the explanatory (predictor) matrix corresponds to a separate variable.
• Each row in the explanatory matrix and corresponding dependent vector correspond to one observation.
• Observations (i.e. row) with missing values in X or Y are removed.
• Number of observation of each data set must be larger than the number of explanatory variables.
• In principle, the Chow test constructs the following regression models:
  • Model 1 (Data set 1): \[y_t = \alpha_1 + \beta_{1,1}\times X_1 + \beta_{2,1}\times X_2 + \cdots + \epsilon\]
  • Model 2 (Data set 2): \[y_t = \alpha_2 + \beta_{1,2}\times X_1 + \beta_{2,2}\times X_2+ \cdots + \epsilon\]
  • Model 3 (Data sets 1 + 2): \[y_t = \alpha + \beta_1\times X_1 + \beta_2 \times X_2 + \cdots + \epsilon\]
• The Chow test hypothesis:
  
  \[ H_{o}= \left\{\begin{matrix} \alpha_1 = \alpha_2 = \alpha \\ \beta_{1,1} = \beta_{1,2} = \beta_1 \\ \beta_{2,1} = \beta_{2,2} = \beta_2 \end{matrix}\right. \] \(H_{1}: \exists \alpha_i \neq \alpha, \exists \beta_{i,j} \neq \beta_i\)
  Where:
  • \(H_{o}\) is the null hypothesis.
  • \(H_{1}\) is the alternate hypothesis.
  • \(\beta_{i,j}\) is the i-th coefficient in the j-th regression model (j=1,2,3).
• The Chow statistics are defined as follows: \[\frac{(\mathrm{SSE}_C -(\mathrm{SSE}_1+\mathrm{SSE}_2))/(k)}{(\mathrm{SSE}_1+\mathrm{SSE}_2)/(N_1+N_2-2k)}\] Where:
  • \(\mathrm{SSE}\) is the sum of the squared residuals.
  • \(K\) is the number of explanatory variables.
  • \(N_1\) is the number of non-missing observations in the first data set.
  • \(N_2\) is the number of non-missing observations in the second data set.
• The Chow test statistics follow an F-distribution with \(k\), and \(N_1+N_2-2\times K\) degrees of freedom.

Exceptions

Exception Type	Condition
None	N/A

Requirements

Namespace	NumXLAPI
Class	SFSDK
Scope	Public
Lifetime	Static
Package	NumXLAPI.DLL

Examples