Beta Likelihood for Likert Scale Averages

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Beta Likelihood for Likert Scale Averages

Hi John,

I was able to execute my idea about using betas to model the data where scores are averages of sets of Likert scale ratings. Instead of using BEST, I modified your BernTwoJags to scale my data originally [1,5] to [0,1] and to apply the following model.

model {
    # Likelihood. Each observation is described as coming from a beta distribution.
    for ( i in 1 : N1 ) { y1[i] ~ dbeta( a1, b1 ) }
    for ( i in 1 : N2 ) { y2[i] ~ dbeta( a2, b2 ) }
    # Prior. Broad uniform distributions on shape parameters. (Critiques? Suggestions?)
    a1 ~ dunif( 0 , 1000 )
    b1 ~ dunif( 0 , 1000 )
    a2 ~ dunif( 0 , 1000 )
    b2 ~ dunif( 0 , 1000 )


From the estimated shape parameters I was able to derive the unrescaled credible means, standard deviations, differences in means and standard deviations, and effect sizes.

You may recall that the post predictive graphs didn't indicate a good fit when I used t-distributions with your BEST software. I made up some small data sets to try out the new model on skewed (both directions), symmetric, and bimodal distributions. The images below show the post predictive checks. I'm anxious to hear what you think about this approach and any suggestions you may have about improving the model.