## Using the MATERN covariance structure in PROC MIXED

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Posts: 13

# Using the MATERN covariance structure in PROC MIXED

My long term question is how to duplicate a particular analysis in R but first I'm trying to understand the output from SAS.  Here is the analysis code:

``````* Blackcap example from the corrHLfit function in the R spaMM library;

* Input data;
data test;
input latitude longitude migStatus means pos;
cards;
36.1291   -5.3469       0.0 161.4000   1
15.0522  -23.6010       0.0 162.2857   2
43.5226    4.7189       1.0 162.6111   3
28.6742  -17.7859       0.5 163.4400   4
32.6743  -16.9105       0.5 162.6667   5
28.1600  -17.1980       0.5 163.6667   6
28.4772  -16.4479       0.5 163.4000   7
41.5335    2.2991       1.0 162.6818   8
40.6653   -4.0871       1.5 162.3667   9
48.2850   16.9086       2.0 162.8800  10
-0.1671   37.0154       2.5 163.5000  11
47.8160    8.9887       2.0 163.7049  12
41.7425   12.4035       2.0 163.1667  13
55.7559   37.6197       2.5 163.8333  14
run;

* Run analysis;
proc mixed data=test method=ml;
model migStatus = means / solution;
repeated / type=sp(matern)(latitude longitude);
run;

/* Output:

Covariance Parameter
Estimates

Cov Parm       Estimate

SP(MATERN)       1.0000
Smoothness       0.5000
Residual         0.5263

*/
``````

I don't understand the "Cov Parm" estimates.  Even when I change the data, I get the same estimates for SP(MATERN) and Smoothness.  And given that the values certainly don't look like typical estimates (1.0 and 0.5), I'm wondering if these are just set to a default value and not fitted using maximum likelihood.  Can someone explain this output to me?

Thanks,

Jim

Accepted Solutions
Solution
‎09-25-2015 06:23 AM
Posts: 2,655

## Re: Using the MATERN covariance structure in PROC MIXED

I would never have guessed this, but try

``````proc mixed data=test method=reml;

model migStatus = means / solution;
repeated /subject=intercept type=sp(matern)(latitude longitude);
run;``````

This seems to solve both problems of moving off the initial values and getting rid of the non-positive definite Hessian output warning.  A subject= option is definitely needed, it was just lucky that I looked at the anisotropic spherical example above the Matern examples in the documentation.

Steve Denham

All Replies
Posts: 2,655

## Re: Using the MATERN covariance structure in PROC MIXED

Some quick testing seems to indicate that since all of the observations are "lumped" into the same subject, there is no movement away from the initial values.  I tried the following:

``````data test;
input latitude longitude migStatus means pos;
id=mod(pos,7);
cards;
36.1291   -5.3469       0.0 61.4000   1
15.0522  -23.6010       0.0 162.2857   2
43.5226    4.7189       1.0 162.6111   3
28.6742  -17.7859       0.5 163.4400   4
32.6743  -16.9105       0.5 162.6667   5
28.1600  -17.1980       0.5 163.6667   6
28.4772  -16.4479       0.5 163.4000   7
41.5335    2.2991       1.0 162.6818   8
40.6653   -4.0871       1.5 162.3667   9
48.2850   16.9086       2.0 162.8800  10
-0.1671   37.0154       2.5 163.5000  11
47.8160    8.9887       2.0 163.7049  12
41.7425   12.4035       2.0 163.1667  13
55.7559   37.6197       2.5 163.8333  14
run;

* Run analysis;
proc mixed data=test method=reml;
class id;
model migStatus = means / solution;
repeated /subject=id type=sp(matern)(latitude longitude);
run;``````

This introduces subject to subject variability (note that it is all made up at this point).  The results from this were:

 Covariance Parameter Estimates Cov Parm Subject Estimate SP(MATERN) id 0.9001 Smoothness id 0.5211 Residual 0.7293
So it appears you need a subject= option in the REPEATED statement to move the estimates away from the initial values.

It still results in a non-positive Hessian warning in the output, as well.

And I have no idea why this is now centered, or how to get back to normal fomatting
Spoiler

Steve Denham
Solution
‎09-25-2015 06:23 AM
Posts: 2,655

## Re: Using the MATERN covariance structure in PROC MIXED

I would never have guessed this, but try

``````proc mixed data=test method=reml;

model migStatus = means / solution;
repeated /subject=intercept type=sp(matern)(latitude longitude);
run;``````

This seems to solve both problems of moving off the initial values and getting rid of the non-positive definite Hessian output warning.  A subject= option is definitely needed, it was just lucky that I looked at the anisotropic spherical example above the Matern examples in the documentation.

Steve Denham

Occasional Contributor
Posts: 13

## Re: Using the MATERN covariance structure in PROC MIXED

Excellent!  Thank you!  That makes everything match up between SAS and R.

For others who might have this issue I offer the following Rosetta Stone:

SAS parameter = corrHLfit parameter

SP(MATERN) = 1/rho

Smoothness = nu

Residual = lambda

SAS counts the fixed effects and the covariance terms as parameters in the construction of the AIC statistic whereas the corrHLfit function in R only considers the fixed effects (i.e., adding in twice the number of parameters).

Thanks again!

Jim

Valued Guide
Posts: 684

## Re: Using the MATERN covariance structure in PROC MIXED

With a repeated statement: If you do not specify a subject, then each observation is considered a subject. Thus, there could be no correlation structure. If you specify subject=intercept, the entire dataset is considered to be one large subject, so that every observation could be correlated (depending on the correlation structure parameters).

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