PartialCovariances Class |
Namespace: Imsl.Stat
The PartialCovariances type exposes the following members.
Name | Description | |
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PartialCovariances(Int32, Double, Int32) |
Creates a PartialCovariances object from a covariance or correleation matrix
with a the independent variables in the initial columns and the dependent
variables in the final columns.
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PartialCovariances(Int32, Double, Int32) |
Creates a PartialCovariances object from a covariance or correleation matrix
with a mix of dependent and independent variables.
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Name | Description | |
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetPartialCorrelationMatrix |
Returns the partial correlation matrix.
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GetPartialCovarianceMatrix |
Returns the partial covariance matrix.
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GetPValues |
Calculates the p-values for testing the null hypothesis that the
associated partial covariance/correlation is zero.
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GetType | Gets the Type of the current instance. (Inherited from Object.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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NumberOfProcessors |
Perform the parallel calculations with the maximum possible number of
processors set to NumberOfProcessors.
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PartialDegreesOfFreedom |
The degrees of freedom in the test that the
partial correlation (covariance) is zero.
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If the "independent" variables (the linear "effect" of the independent variables is removed in computing the partial covariances/correlations) are linearly related to one another, PartialCovariances detects the linearity and eliminates one or more of the independent variables from the list of independent variables. The number of variables eliminated, if any, can be determined from the property PartialDegreesOfFreedom.
Given a covariance or correlation matrix partitioned as
class PartialCovariances computes the partial covariances (of the standardized variables if is a correlation matrix) as A positive semidefinite solver is used to compute .If partial correlations are desired, these are computed as
where denotes the matrix containing the diagonal of its argument along its diagonal with zeros off the diagonal. If is singular, then as many variables as required are deleted from (and ) in order to eliminate the linear dependencies. The computations then proceed as above.The p-value for a partial covariance tests the null hypothesis , where is the (i, j) element in matrix . The p-value for a partial correlation tests the null hypothesis , where is the (i, j) element in matrix . The p-values are returned by GetPValues. If the degrees of freedom for sigma, df, is not known, the resulting p-values may be useful for comparison, but they should not by used as an approximation to the actual probabilities.