Parameter Estimates for Centered and Scaled Predictors

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Fitting Linear Models • Generalized Regression Models • Model Fit Reports • Parameter Estimates for Centered and Scaled Predictors

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Parameter Estimates for Centered and Scaled Predictors

The Parameter Estimates for Centered and Scaled Predictors report gives estimates and other results for all parameters in the model. The initial table includes the coefficients for the predictors in the model. An additional table includes other model parameters such as scale, dispersion, or zero inflation parameters. See Distribution. Both tables include the same columns of results.

Tip: You can click on terms in the Parameter Estimates for Centered and Scaled Predictors report to highlight the corresponding paths in the Solution Path Plot. The corresponding columns in the data table are also selected. This is useful in terms of running further analyses. Press Shift and click the terms to select multiple rows.

For all fits in the Generalized Regression personality, every predictor is centered to have mean zero and scaled to have sum of squares equal to one:

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The mean is subtracted from each observation.

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Each difference is then divided by the square root of the sum of the squared differences from the mean.

This puts all predictors on an equal footing relative to the penalties applied.

Note: When the No Intercept option is selected in the launch window, the predictors are not centered and scaled.

The Parameter Estimates for Centered and Scaled Predictors report gives parameter estimates for the model expressed in terms of the centered and scaled predictors. The estimates are determined by the Validation Method that you specified. The estimates are depicted in the Solution Path Plots by a vertical red line.

The report provides the following information:

A list of the model terms. “Forced in” appears next to any terms that were forced into the model using the Advanced Controls option.

The parameter estimate corresponding to the centered and scaled model term.

The standard error of the estimate. This is obtained using M-estimation and a sandwich formula (Zou 2006; Huber and Ronchetti 2009).

The ChiSquare value for a Wald test of whether the parameter is zero.

Prob > ChiSquare

The p-value for the Wald test.

The lower bound for a 95% confidence interval for the parameter. You can change the α level in the Fit Model window by selecting Set Alpha Level from the red triangle menu.

The upper bound for a 95% confidence interval for the parameter. You can change the α level in the Fit Model window by selecting Set Alpha Level from the red triangle menu.

Singularity Details

(Available only if there are linear dependencies among the model terms.) The linear function that the model term satisfies.

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Help created on 3/19/2020