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I conducted an experiment where I want to predict response times in a picture classification task from person characteristics (age, prior experience) and item characteristics (similarity; color, shape, background). All participants saw all items and the "similarity" characteristic comprises all combinations of color, shape and backgroup.

   subject     age    prior_exp tria        rt   sim color  shape backg
   <fct>     <dbl>        <dbl> <chr>    <dbl> <dbl>  <dbl> <dbl> <dbl>
 1 930179102    22            5 trial1   1647     0      0     0     0
 2 930179102    22            5 trial2   1949     1      1     0     0
 3 930179102    22            5 trial3   2198     1      0     1     0
 4 930179102    22            5 trial4   2051     1      0     0     1
 5 930179102    22            5 trial5   1475     2      1     1     0
 6 930179102    22            5 trial6   2402     2      0     1     1
 7 930179102    22            5 trial7   1399     2      1     0     1

I'm just getting started with mixed models. As I understand it, age and prior_exp are fixed effects and similarity is a random effect, and color/shape/backg are crossed factors. Is that correct? I fitted this model but am not sure, how to incorporate the crossed factors.

lmm <- lmer(rt ~ age + prior_exp + sim + (sim|subject), data = df)

Is my reasoning so far correct and can anybody please help me with the crossed factors or point me in the right direction?

Robert Long
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achmed
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  • Can you explain more about the factors similarity, color, shape, background. How many are there of each and how are they related ? – Robert Long Sep 16 '20 at 06:27
  • The task is similar to the game "Set". Particpants are presented with 4 cards and must decide whether the color, shape and backgroud displayed on those cards are all identical or all different across all cards. Color = 1 indicates that for this specific item, the color was equal in all cards. Similarity is the sum of all attributes (color, shape, background) that are equal across all cards. – achmed Sep 16 '20 at 06:38

1 Answers1

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Here, items are crossed with subjects because all subjects saw all items.

So subject and item should be the random effects, and the characteristic of them should be fixed effects. So according to your data, you will need an identifier for each item and the model will look something like this:

rt ~ age + prior_exp + color + shape + backg + (1|subject) + (1|item)

Note that, since similarity is the sum of the other item attributes, then it isn't identified as a unique parameter, so you can't include it as a fixed effect along with the others (you could include it but exclude at least one of the other three though I don't see much point in that).

Robert Long
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