Kernel Function

Specify the kernel function used to compute the covariance matrix of the observations while performing ridge regression in PROC MIXED.

Available options are described in the table below:

Kernel Function	Description
Dot	Corresponds to the same structure induced by random effects, which is the outer dot product of the Z matrix. This option is typically used when the covariance is approximately constant.
Linear	This option is chosen when the covariance declines linearly.
Spherical	This option is chosen when the covariance declines quadratically.
Exponential	This option is chosen when the covariance declines exponentially.
Gaussian	This option is chosen when the covariance declines squared exponentially.
Matern	Represent covariance structures in a class defined by Matérn1. It is more general than the other structures and can include exponential or Gaussian functions.   Note: The Matern kernel can take a long time to run due to its complex nature.

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1

Matérn, B. (1986), Spatial Variation, Second Edition, Lecture Notes in Statistics, New York: Springer-Verlag.

The Linear, Spherical, Exponential, Gausian, and Matern kernels correspond to spatial structures.

Note: For the spatial kernels you may need to add a PARMS statement in the PROC MIXED Additional Statements field to specify good starting values since the likelihood function can be multimodal. You also might need to relax the convergence tolerance, e.g. specify convg=1e-6 in the PROC MIXED Statement Options field. Refer to the REPEATED statement portion of the SAS PROC MIXED documentation for details

You can select a a specific structure if you know roughly how the covariance changes. Otherwise you can determine the appropriate option by fitting several different structures and comparing the model fit statistics.

To Specify the Kernel Function:

Select the desired function by clicking within the appropriate radio button.