Copyright 2012 Aileen M. Echiverri-Cohen - University of Washington

Likelihood index as it corrects the -2 Restricted Log Liklihood for small sample sizes like in the
present study (Fields, 2001). A random intercept, fixed slopes model specified a covariance
structure of variable components, as is often the result of small sample size and small number of
repeated measures per participant or small levels of variance (Gallop & Tasca, 2009). Restricted
maximum likelihood (REML) was used as it yields unbiased estimates of the random effects
variances (Twisk, 2006).
The best-fitting model for treatment modality, time, and AB was a random intercept
model. This was evaluated by fitting nested structures of the most complex covariance structure
for multilevel models, where the specified random effect, (i.e., random intercept and random
slope) using an unstructured covariance design with random intercept and random slope terms,
were allowed to be correlated. The correlated random terms accounts for a possible relationship
between where an individual starts and their rate of change. If the correlation is not significantly
different from zero, under parsimony, then the next less complex structure using a variance
components structure was fitted to the model where the correlation of the random intercept and
random slope term was set to 0. This structure allows for subject-to-subject variability in their
group average intercept and group average slope but assumes where a person starts is
independent of how they change. If there is not sufficient subject-to-subject variability in rate of
change, the parsimonious structure is the least complex structure corresponding to a random
intercept model. Under the random intercept model, the covariance structure between the
repeated measures is modeled as a compound symmetry structure which is analogous to the
simplistic repeated measures ANOVA model for clustered data. Guidelines in assessing the
parsimonious covariance structure for the random effects terms was based on Gallop and Tasca
(2009).
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