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I am not sure, what model should I use for this data:

  • ID - participant ID
  • Trial - 60 for each participant
  • Memory - between subject binary factor
  • State - within subject binary factor
  • Rating -the judgment made by participant after each trial on four point Likert scale

  • TargetPosition - the angle of the target. It's random effect.

  • Difficulty - 6 point scale equal to the number of items simultaneously displayed on the screen. The difficulty rose, when participant performed well, and vice versa (Staircase).

I'm interested in: how Memory, State and Rating impact the Difficulty. The ID, Trial and TargetPosition are all out of interest.

What I was thinking about:

model = glmer(Difficulty ~ (1|ID) + (1|TargetPosition)
        + Memory * State * Rating, data, family=poisson)

I'm especially not sure whether poisson is the right choice and whether I add random effects correctly.

(this is a study I asked about previously, but different model)

kjetil b halvorsen
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Piotr Falkowski
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    poisson is for count variables with a skewed right distribution, what you're dealing with is a likert type scale. You're better off using an ordinal logistic regression model (or multinomial logistic if you don't meet the assumptions of the former). If you think the intervals between your ranks in your DV are equivalent you might get away with regular OLS even. – Cyrus Mohammadian Aug 25 '16 at 21:14
  • What if I realy realy need to include a random factor on ID? – Piotr Falkowski Sep 23 '16 at 18:50
  • Are you sure `Difficulty` should be the response here? From your description, it sounds like the `Rating` is the response & `Difficulty` is a factor in the design of the study. – gung - Reinstate Monica Sep 23 '16 at 19:29
  • Yes, I'm sure, difficulty is also response. It is just another hypothesis testing. – Piotr Falkowski Sep 23 '16 at 19:32
  • Look into ordinal regression see https://stats.stackexchange.com/questions/47113/ordinal-regression-vs-summated-score and https://stats.stackexchange.com/questions/104684/can-i-use-averages-of-a-likert-scale-as-a-dependent-variable-in-ordinal-regressi – kjetil b halvorsen Sep 29 '17 at 20:25

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