Note: When you enter more than 500 covariates, a JMP Alert recommends that you switch to the Wide Linear method. This is because computation time can be considerable when you use the other methods with a large number of columns. Click Wide Linear, Many Columns to switch to the Wide Linear method. Click Continue to use the method you originally selected.
The Linear, Quadratic, and Regularized methods are illustrated in Figure 4.7. The methods are described here briefly. For technical details, see Saved Formulas.
Performs linear discriminant analysis. This method assumes that the within-group covariance matrices are equal. See Linear Discriminant Method.
Performs quadratic discriminant analysis. This method assumes that the within-group covariance matrices differ. This method requires estimating more parameters than the Linear method requires. If group sample sizes are small, you risk obtaining unstable estimates. See Quadratic Discriminant Method.
Provides two ways to impose stability on estimates when the within-group covariance matrices differ. This is a useful option when group sample sizes are small. See Regularized, Compromise Method and Regularized Discriminant Method.
Useful in fitting models based on a large number of covariates, where other methods can have computational difficulties. This method assumes that all within-group covariance matrices are equal. This method uses a singular value decomposition approach to compute the inverse of the pooled within-group covariance matrix. See Description of the Wide Linear Algorithm.
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The first parameter (Lambda, Shrinkage to Common Covariance) specifies how to mix the individual and group covariance matrices. For this parameter, 1 corresponds to Linear Discriminant Analysis and 0 corresponds to Quadratic Discriminant Analysis.
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The second parameter (Gamma, Shrinkage to Diagonal) is a multiplier that specifies how much deflation to apply to the non-diagonal elements (the covariances across variables). If you choose 1, then the covariance matrix is forced to be diagonal.
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Assigning 0 to each of these two parameters is identical to requesting quadratic discriminant analysis. Similarly, assigning 1 to Lambda and 0 to Gamma requests linear discriminant analysis. Use Table 4.1 to help you decide on the regularization. See Figure 4.7 for examples of linear, quadratic, and regularized discriminant analysis.