I have undertaken an RCT and, given multiple irregular time-point measures of the DV, have used linear mixed models to analyse the results and include moderator/predictor variables.
CONSORT is quite emphatic about the reporting of effect sizes. However, SPSS does not produce these for linear mixed models, as far as I am aware.
Also, I have not seen many papers report them either. The one that I have references this paper as to how they calculated them:
Article Power Analysis and Effect Size in Mixed Effects Models: A Tutorial
But looking at the equation, I am not sure which bits correspond to which parts of my SPSS output.
Can anyone simplify this method?
Provide me with another way of calculating effect sizes from LMM?
Or provide me with evidence and rationale as to why effect sizes are not needed when reporting LMMs?
Many many thanks!
I always thought, that the merit and add-on value of effect sizes, as compared to simply reporting significance is that the audience has a clearer understanding of how big the difference between conditions or factor levels are.
With that being said, there are some that promote the idea that (z)standardized model parameters are suitable to judge the amount of these differences.
On the other hands it might be more appealing to some audiences to read 'classic' effect sizes such as d for group comparisons. An approach to calculate these is provided by Westfall et al. The idea is to report the ratio of systematic variance (fixed effects) to unsystematic variance (random effects, -slopes and intercepts). The formula is given in the paper and an example for SPSS output too.
Thank you for your answer Sven Greving. The paper I cited mentions the Westfall et al. method. However, the explanation is beyond my level understanding for how it maps onto my LMM output in SPSS. Mainly because it talks about difference of means. I am only looking at one group, one continuous outcome DV, and the model has 3 predictor variables (2 continuous one binary) - and I do not understand where I get 2 means from from each variable to use in their equation, let alone the other terms in the equation for calculating a cohen's d.
If anyone has any resource or link to breakdown their equation, that would be amazing!
John Butler Let's back up a bit. Which predictor are you treating as a random factor in the model?
Which of the two continuous IVs is taken as of random effect? What is the group sample size, and are there nested variable? The truth is that you CANNOT treat a continuous variable as a random effect, not even time constant IVs. There is possibility of same factor being fixed and random, if it can account for the group individual differences. Perhaps I can join the backup
The reason I ask the question above is that random effects are only used with categorical variables. Continuous variables cannot serve as grouping factors for random effects. It's also not recommended that binary predictors be treated as random effects. Unless you are treating 'subjects' as a random factor, for instance, a LMM is not appropriate because there are no random factors. In this case, you should use multiple regression instead.
Blaine Tomkins I am only using time as a random effect in the model. The other moderators are just being added as fixed effects into the model, with their time-interaction terms too.
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