1

I am analysing data from a questionnaire with different subscores. The subscores are calculated like this, for example:

Subscore 1 = $(Item_1 + Item_2+ ....+ Item_n)/ n*2$.

Each Item can have a score of 0, 1 or 2, which is why the sum is divided by the number of items multiplied by two.

I would like to calculate a GLMM using the r package lme4. Because the subscores are proportional data, I figured a binomial distribution with $n*2$ as weights could be appropriate:

# adding an extra column for divisor
data$subscore1_weight <- rep(2*n, dim(data)[2])

setting up the model


m1<- glmer(Subscore1~ PredictorA + 
                      PredictorB +
                      PredictorA:PredictorB+ 
                      (1|participant),

                      weights = subscore1_weight,
                      family = binomial,
                      data = data)

... I read that a binomial model for proportional data should only be applied for 1s in n trials.. which is not exactly the case because we are looking at items.

Am I on the right path or completely wrong?

a.henrietty
  • 375

1 Answers1

1

I think you are on the right track. A similar discussion can be found here: How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?.

Alternatively you could use something like a fractional logit model, where the dependent variable is a fraction. A reference for that can be found here: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/%28SICI%291099-1255%28199611%2911%3A6%3C619%3A%3AAID-JAE418%3E3.0.CO%3B2-1. For the glm model type this can be implemented by changing the family to quasibinomial. However, I am not sure whether this also works in mixed effects models.

gregorsteiner
  • 41
  • Dear @gregorsteiner, thanks for your answer. Yes, subscore 1 is a fraction in [0, 1]. In GLM and GLMM fractions can be modelled by binomial distributions, see f.e. [here] (https://stats.stackexchange.com/questions/233366/how-to-fit-a-mixed-model-with-response-variable-between-0-and-1) or here. .... Is this what you mean? – a.henrietty Jul 30 '21 at 13:23
  • 1
    Hey, I just edited my answer. After doing some research, I think your initial approach does also work. I think the second reference in your comment explains it quite well. – gregorsteiner Jul 30 '21 at 13:25
  • Excellent, thanks for this reference, @gregorsteiner. – a.henrietty Jul 30 '21 at 13:30