Update to Restricted Maximum Likelihood (REML) Calculations in Prism 9.2.0

The big picture

The release of Prism 9.2.0 included an update to the way that Restricted Maximum Likelihood (REML) calculations were performed for mixed model analysis. In some (rare) cases, this change may cause differences in calculated results for analysis of models containing more than one random factor. Examples of analyses that may have been affected include two-way ANOVA with missing data and repeated measures in both factors, or three-way ANOVA with missing data and repeated measures in two or more factors. In most cases, the results generated in Prism 9.2.0 for these analyses will be identical to the results generated in previous versions. Note that tests that have only one random factor were reporting accurate results prior to this change, and are unaffected by the update (the results are correct in Prism 9.2.0 and in earlier versions). These tests include:

• Nested t test
• Nested one-way ANOVA
• One-way ANOVA with repeated measures
• Two- and three-way ANOVA with repeated measures in only one factor

The details

The process of performing restricted maximum likelihood (REML) calculations is an iterative process that requires initial values to be defined. When performing REML calculations for mixed models, Prism employs two methods for specification of these initial values for the parameter estimates of the specified model. The first set of initial values is obtained directly from the GLM fit of the input data, while the second set of initial values is specified as close to zero (specifically, 0.1) for all parameters.

In previous versions of Prism, this second set of initial values was used only when the fit using the initial values from the GLM estimates did not converge, or if the GLM estimates produced invalid results (such as negative values for variance which - by definition - must be positive). Starting in Prism 9.2.0, Prism now performs REML calculations using both sets of initial values regardless of whether or not the fit using the GLM estimates converges. After performing REML with both sets of initial values, Prism selects the best fit between these two. As mentioned previously, if the initial values from the GLM estimates cause the model to not converge or produce invalid results, Prism will only use the second set of initial values, and will not perform any comparison between fits.

The effect of this change is that Prism will always report results from the best fit, regardless if the fit using the GLM estimates as the initial values converges. In some (but not all) cases, this means that the results for models with more than one random factor may different (more accurate) in Prism 9.2.0 than in previous versions. Models with a single random factor will not be affected by this change.