ordinal regression with random effects

[Jannik Vindeløv]

Dear Group

I have strains (B) that are scored according to the inhibition (I) by a sample (S) on a four point ordinal scale (NO, LOW, MEDIUM, HIGH).

Individual strains (B) can be used in combination with other strains, and a specific combination of strains constitutes a product (F).

Furthermore, the samples (S) originate from different customers (C).

I have a large number of strains, products and customers and consider them to originate from a population of strain, products and customers.

To simplify, I start with a fairly simple hierarchical model (ordinal regression with customers(C) and strains (B) as random effects) on which I will later expand (multi membership hierarchical ordinal regression... ?):

model <- brm(formula = I ~ (1|C) + (1|B), data = D, family = "cumulative")

I would like to infer which strains (B) are the most inhibited, but I fail to understand the scale of the data returned by ranef(model)$B ?

• How should I interpret the numbers returned by ranef?
  
• How could I predict the ranef numbers on the ordinal scale?
  
• What is the implicit distribution of the random effects?

Thanks

Jannik

[Paul Buerkner]

1. The higher the ranefs, the higher the probabilities for higher categories.

You can think of the ranefs as being on the logit scale, although the situation in ordinal models in a bit more complicate than that.

2. You could use for instance

fitted(model, newdata = data.frame(B = unique(D$B)), re_formula = ~ (1|B))

to only include the random effects of B in the predictions (and not those of C).

3. brms assumes a normal distribution (normal prior) for the random effects, just as most other multilevel packages do.

Best,

Paul

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[Jannik Vindeløv]

Thanks Paul,

Just what I needed.

/Jannik

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