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I am trying to create a model to determine the effects of Stations and Circuits (and any interaction) on students scores in an OSCE exam, using the lmer function in R.

I have 3 factors: circuit $\beta$ (fixed), station $\gamma$ (fixed) and studentID $\rho$ (random) related as follows:

  1. Students are assigned to one circuit
  2. Within each circuit, there are 14 stations
  3. Students performance are measured at each of the 14 stations

Based on this, I concluded that:

  1. Students are nested within circuit
  2. Circuit and Station are crossed
  3. Student and station are crossed

The model I have designed is: $y_{ijk} = \mu + \beta_j + \gamma_k + (\beta \gamma)_{jk} + \rho_{i(j)} + (\gamma \rho)_{i(j)k} + \epsilon_{ijk} $

where the effects of Circuit, Station are fixed, the effect of StudentID nested within Circuit is random and the effect of StudentID nested in Circuit crossed with Station is random.

The two models I came up with in r are :

m1 <- lmer(Percentage  ~ Circuit*Station + (1| Circuit:StudentID) + (1: Circuit:StudentID:Station), REML= FALSE, data=statper2024) 

m12024 <- lmer(Percentage ~ Circuit*Station + (1| Circuit:StudentID), REML= FALSE, data=statper2024)

Both of the models reported the same AIC statics. I understand that m2 does not include an interaction term for Station and StudentID. However, I am unsure of how to code this interaction.

My questions are:

  1. Can I really say StudentID is nested within Circuit? I read that there must be a certain number of high-level units and since Circuit does not satisfy that, it should just be treated as a normal fixed predictor?
  2. How do I model the Station and StudentID interaction?
  3. I suspect that the variation amongst station scores will differ within Circuits. Is this variation included in my model? Or do I need to add a term as follows (0+Station|Circuit) . However, will this clash with the fact that I already specified fixed effects for Station and Circuit?
  4. Should I include a term for students variation over station? (Station|Student)

I am extremely conflicted regarding the terms to include in my model to consider all the possible interactions, crossed and nested effects.

For some insight into how my data is structured, see below:

enter image description here

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  • $\begingroup$ Welcome to cv. To help answer this question its useful to have some more conext. Could you provide more info on what a circuit and station are? Are circuits like experimental treatments? How do they vary? Are all the stations identical across the stations? What is ocse? Also in general something either appears as a fixed or a random effect so it's not clear why stations appears in both. (It can happen in eg split plot designs) $\endgroup$
    – N Brouwer
    Commented Apr 28 at 15:07
  • $\begingroup$ The OSCE is a clinical exam where students rotate between stations, with each station assessing a different clinical skill. Students are divided into groups and groups take the exam on different days (I didn't consider these factors). Due to resource constraints, each station can assess only one student at a time. As such, in a given group, each student starts at a different station. A circuit is the order in which the student moves through the stations so yes, they are like experimental treatments. The stations are identical across circuits. $\endgroup$
    – D Ram
    Commented Apr 28 at 15:36
  • $\begingroup$ Thanks! First, (Station|Student) is probably not necessary. Unless you have large sample sizes I've found these variable treatment effects to be hard to model. Second, follow up question- how many circuits are there? Also, how interested are you in the station effects, or are the circuit effects most interesting? Finally, how familiar Re you with random effects models overall? With 14 stations and multiple circuits, this may be useful to be modeled using just random effects $\endgroup$
    – N Brouwer
    Commented Apr 28 at 20:03
  • $\begingroup$ Thank you for your interest. There are 14 circuits. I am interested in the effects of Stations, Circuits and their interaction. $\endgroup$
    – D Ram
    Commented Apr 28 at 21:30

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