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Could I have some advice which, if any, random-effects structure should be added to my model please.

My data includes multiple people (50) indicating whether they like/don't like a bunch of toys (15). Not every person gives a measure for each toy. The predictors are descriptions of each toy; colouful, fluffy, battery-operated, and such.

The aim is to get a prediction of whether a new toy will be liked given its feature set by a new individual. The data looks like:

Person Toy Like X1 X2 X3
     1   1    0  1  1  0
     1   2    0  0  1  0
     1   3    1  0  0  0
     1   4    1  0  1  0
     2   2    0  1  1  1
     2   3    1  0  0  0
     2   4    1  1  1  0
     2   5    1  0  0  1

I am using a logistic regression model. I have estimated a random-intercept model using 'Person' as the grouping variable.

Like = X1 + X2 + X3 + (1|Person)

Is this sensible. Should I, and if so how should I, include the 'Toy' indicator? Thanks.

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This looks like a case of partially crossed random effects.

There are repeated measures for Person and also for Toy. So, observations made by the same Person on different Toys are likely to be more similar to each other than for a different Person on different Toys. The same applies to Toy - observations made on the same Toy are likely to be more similar to each other than for a different Toy. So you would specify a model with random intercepts for both Person and Toy. There is apparently no nesting of random effects (that is, no particular toy "belongs" to a particular person or vice versa), so using the syntax in the OP, to specify crossed random effects for your data you can use:

Like ~ X1 + X2 + X3 + (1|Person) + (1|Toy)
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    $\begingroup$ That makes sense, thank you Robert. I appreciate the help. $\endgroup$ – user2957945 Dec 2 '19 at 13:07

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