Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 113
Restricted Maximum Likelihood (REML) Method
Table 3.13 Description of the LSMeans Student’s t and LSMeans Tukey’s HSD Options (Continued)
Ordered Differences
Report
Detailed Comparisons
Equivalence Test
Ranks the differences from lowest to highest. It also plots the differences on a
histogram that has overlaid confidence interval lines.
Compares each level of the effect with all other levels in a pairwise fashion.
Each section shows the difference between the levels, standard error and
confidence intervals, t-ratios, p-values, and degrees of freedom. A plot
illustrating the comparison appears on the right of each report.
Uses the TOST (Two One-Sided Tests) method to test for practical
equivalence. For details, see the Basic Analysis and Graphing book.
Test Slices
The Test Slices option, which is enabled for interaction effects, is a quick way to do many contrasts at the
same time. For each level of each classification column in the interaction, it makes comparisons among all
the levels of the other classification columns in the interaction. For example, if an interaction is A*B*C, then
there is a slice called A=1, which tests all the B*C levels when A=1. There is another slice called A=2, and so
on, for all the levels of B, and C. This is a way to detect the importance of levels inside an interaction.
Restricted Maximum Likelihood (REML) Method
Random effects are those where the effect levels are chosen randomly from a larger population of levels.
These random effects represent a sample from the larger population. In contrast, the levels of fixed effects
are of direct interest rather than representative. If you have both random and fixed (nonrandom) effects in a
model, it is called a mixed model.
Note: It is very important to declare random effects. Otherwise, the test statistics produced from the fitted
model are calculated with the wrong assumptions.
Typical random effects can be any of the following:
• Subjects in a repeated measures experiment, where the subject is measured at several times.
• Plots in a split plot experiment, where an experimental unit is subdivided and multiple measurements are
taken, usually with another treatment applied to the subunits.
• Measurement studies, where multiple measurements are taken in order to study measurement variation.
• Random coefficients models, where the random effect is built with a continuous term crossed with
categories.
The Fit Model platform in JMP fits mixed models using these modern methods, now generally regarded as
best practice:
• REML estimation method (Restricted Maximum Likelihood)
• Kenward-Roger tests