Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 119
Restricted Maximum Likelihood (REML) Method
This was refined by Kenward and Roger (1997) to correct further and obtain the degrees of freedom that
gave the closest match of an F-distribution to the distribution of the test statistic. These are not easy
calculations. Consequently, they can take some time to perform for larger models.
If you have a simple balanced model, the results from REML-Kenward-Roger agree with the results from
the traditional approach, provided that the estimates are not bounded at zero.
• These results do not depend on analyzing the syntactic structure of the model. There are no rules about
finding containing effects. The method does not care if your whole plot fixed effects are purely nested in
whole plot random effects. It gets the right answer regardless.
• These results do not depend on having categorical factors. It handles continuous (random coefficient)
models just as easily.
• These methods produce different (and better) results than older versions of JMP (that is, earlier than
JMP 6) that implemented older, less precise, technology to do these tests.
• These methods do not depend on having positive variance components. Negative variance components
are not only supported, but need to be allowed in order for the tests to be unbiased.
Our goal in implementing these methods was not just to handle general cases, but to handle cases without
the user needing to know very much about the details. Just declare which effects are random, and everything
else is automatic. It is particularly important that engineers learn to declare random effects, because they
have a history of performing inadvertent split-plot experiments where the structure is not identified.
Specifying Random Effects
Split Plot
Models with Random Effects use the same Fit Model dialog as other models. To specify a random effect,
highlight it in the Construct Model Effects list and select Attributes > Random Effect. This appends
&Random to the effect name in the model effect list.
The most common type of layered design is a balanced split plot, often in the form of repeated measures
across time. One experimental unit for some of the effects is subdivided (sometimes by time period) and
other effects are applied to these subunits.
Example of a Split Plot
Consider the data in the Animals.jmp sample data table (the data are fictional). The study collected
information about differences in the seasonal hunting habits of foxes and coyotes. Each season for one year,
three foxes and three coyotes were marked and observed periodically. The average number of miles that they
wandered from their dens during different seasons of the year was recorded (rounded to the nearest mile).
The model is defined by the following aspects:
• The continuous response variable called miles
• The species effect with values fox or coyote
• The season effect with values fall, winter, spring, and summer
• An animal identification code called subject, with nominal values 1, 2, and 3 for both foxes and coyotes