ANCOVA Class |
Namespace: Imsl.Stat
The ANCOVA type exposes the following members.
Name | Description | |
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Compute |
Performs one-way analysis of covariance assuming parallelism and
returns an array containing the parallelism tests for the one-way
analysis of covariance.
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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.) | |
GetAdjustedANOVA |
Returns the partial sum of squares for the one-way analysis of
covariance.
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GetANCOVA |
Returns an array containing the one-way analysis of covariance
assuming parallelism.
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GetANOVATables |
Returns a matrix of size ngroup by 15 containing the
analysis of variance tables for each linear regression model fitted
separately to each treatment group.
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GetCoefficientTable |
Returns a matrix of size ncov + 1 by 4 containing statistics
for a linear regression model fitted separately for each of the
ngroup treatment groups.
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GetCoefficientTables |
Returns an array containing statistics for a linear regression
model fitted separately for all ngroup treatments.
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GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetMeans |
Returns a matrix containing the unadjusted means for the covariates
and the response variate and the means for the response variate
adjusted for the covariates.
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GetModelCoefficients |
Returns a matrix containing statistics for the regression
coefficients for the model assuming parallelism.
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GetR |
Returns the R matrix from the QR decomposition.
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GetType | Gets the Type of the current instance. (Inherited from Object.) | |
GetVarCovAdjustedMeans |
Returns a matrix containing the estimated variances and covariances
for the adjusted means assuming parallelism.
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GetVarCovCoefficients |
Returns a matrix containing the estimated variances and covariances
for the coefficients returned using GetModelCoefficients.
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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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NumberOfMissing |
The number of cases with missing values in
covariates or responses.
Cases with any missing values are not used in the analysis.
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Class ANCOVA performs analyses for models that combine the features of a one-way analysis of variance model with that of a multiple linear regression model. The basic one-way analysis of covariance model is
where, ngroup is the number of treatment groups, the observed value of constitutes the j-th response in the i-th group, denotes the y intercept for the regression function for the i-th group, , , ..., are the regression coefficients for the covariates, and the 's are independently distributed normal errors with mean zero and variance . This model allows the regression function for each group to have different intercepts. However, the remaining m regression coefficients are the same for each group, i.e., the regression functions are parallel.In practice, sometimes the regression functions are not parallel. In addition to estimates for the model assuming parallelism (parallel regression planes), ANCOVA computes estimates and summary statistics for the separate regressions of each group. These estimates can be examined using the methods GetCoefficientTables and GetANOVATables.
Estimates for the 's and , , ..., in the model assuming parallelism are returned using the method GetModelCoefficients. Summary statistics are also computed for this model and returned by the Compute method.
The adjusted group means, stored in the last column of xymean, are computed using the formula:
where xymean is the matrix returned by GetMeans and ncov is the number of covariates.
The estimated covariance between the -th and -th adjusted group mean is given by
where is the entry in covb[p-1][q-1], where covb is returned by GetVarCovCoefficients and is the estimated covariance between the p-th and q-th estimated coefficients in the regression function.