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I am analyzing a dataset using a multilevel model approach and have been recommended to look at using crossed random effects due to the structure of data. I've currently been treating my data as 2 levels and nested within each other and having a difficult time understanding if there is going to be a crossed effect.

The data is a set of 30 participants who completed three different training scenarios and had multiple measurements taken during each scenario including: Jump height (Pre and post - variable of interest being change), grip strength (pre and post- variable of interest being change), and average heart rate.

I'm now wondering if this data is actually three levels with:

Level 1 being the participant

Level 2 being the event and

Level 3 being the measures

To my understanding (and some of the previous answers I've read on this site) the crossed effect would come from the same measures (level 3) being involved in multiple events.

Therefore my model would look something like

model <- lmer(HeartRateAvg ~ event + (1|Participant) + (1|Event), data = dt)

For more context the original question was to see if these measures had significant differences across the three events which was completed by using a repeated measures ANOVA. It was then decided to account for covariate factors (such as the effect of initial jump height on the change in jump height) which led to the multilevel models

Any advice, guidance, or further resources would be much appreciated!

TibialCuriosity
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  • Have you read this great explanation by @RobertLong about nested vs crossed effects in mixed models? – dipetkov Jun 29 '22 at 22:30
  • @dipetkov apologies for the delayed response! I have read it, but am having difficulty applying it to my situation. It seems in that scenario each class and their variables are part of multiple schools. In my current data set, each participant completes each event, but their variables are unique to each event as well. For example heart rate average was measured three times across three events. Will the participant still be considered cross each event? – TibialCuriosity Jul 04 '22 at 02:59
  • @dipetkov I've been doing some more reading and I think this data set is consisting of a cross and nested data set where participants have crossed effects with the different events while also having measures nested within each participant (as each measure was conducted for each testing). Therefore modelling these effects would look something like lmer(HeartRateAvg ~ event + (1|Participant/HeartRateAvg) + (1|ID), data = dt I'm not sure if this set up is correct but I'm thinking the first random effects term would be the nested variable and the second would be crossed. Any tips would be great! – TibialCuriosity Jul 04 '22 at 04:05
  • You seem to want to make everything a random effect? Since your study seems complex, I would consider first developing a model for each measurement as it's not even clear whether you want to treat measurements as predictors or responses; in a pre-post design pre-treatment measurements are usually predictors and the post-treatment measurement is an outcome. Participants and events would be crossed effects (I think) and it would be easier to fit and diagnose the models. – dipetkov Jul 04 '22 at 07:21
  • If you decide to give the separate models a try, note that you can still use all baseline measurements (jump height, grip strength, heart rate) as covariates to predict, say, heart rate after training. – dipetkov Jul 04 '22 at 07:26

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