Two ways to analyze repeated measures data

Prism can analyze repeated measures data in two ways:

•Repeated measures ANOVA

•Fitting a mixed effects model. This analysis works fine even when there are some missing values. The results will only be meaningful, of course, if the values are missing for random reasons. For example, those results won't be helpful or meaningful if the values are missing because those participants were very sick, or those values were too high to measure (or too low to measure). Fitting a mixed model with missing values only makes sense when there is zero association between the treatments or time-points and the reason why some values are missing.

In general, fitting a mixed effects model is a much more versatile method. As implemented in Prism 8, the two are completely equivalent when there are no missing values. But the mixed effects model method can also fit data with missing values.

Analyze using which method

The repeated measures tab of the ANOVA dialog (same for one-, two- and three-way data) gives you three choices:

•Use repeated measures ANOVA always. If there are missing values, no results will be reported. This matches what Prism 7 and earlier did. Prism is not "smart enough" to remove all data for a participant with missing values, but you could exclude all those values and rerun the ANOVA.

• Fit a mixed effects model always. This will make all analyses be consistent, whether or not there are missing values. If there are no missing values, the key results will be the same as repeated measures ANOVA but the results will be presented in an format unfamiliar to those used to repeated measures ANOVA.

•Report the fit to a mixed effects model only when there are missing values, when repeated measures ANOVA is impossible. When there are no missing values, report the familiar repeated measures ANOVA results.

How to fit the mixed effects model any random factor is zero or negative

The whole point of repeated measures or mixed model analyses is that you have multiple response measurements on the same subject or when individuals are matched (twins or litters), so need to account for any correlation among multiple responses from the same subject. Mixed model analysis does this by estimating variances between subjects. In a simple mixed model, where only one variable is repeated, it’s possible that this correlation for the particular data in your study is zero or even negative  (of course it is impossible for a variance to be negative, but it can happen with mixed effects models). You are given two choices for what Prism should do when this happens:

•Analyze as usual. If there are no missing values, this will match repeated measures ANOVA.

•Remove the subject factor from the model and refit. This approach will have one more degree of freedom and thus have a bit more power. This approach is better but means the mixed model results may not match repeated measures ANOVA results.

In more complicated models, where there is more than one repeated measures variable, there are even more possible variance estimates (generally interactions with subject), and any of those could turn out to be zero or negative. It’s best to take these out as leaving them in can make the results unstable.

Defaults for future analyses

Check an option at the bottom of the Repeated Measures tab to make your choices the default for future analyses. Your default will apply to one-, two- and three-way ANOVA.