Confidence intervals for fscores

[Tim]

Dear Phil,

first of all congratulations to this really great package! As being relatively inexperienced in IRT, your package definitely helps to advance my knowledge on the topic!

I just have a general question: is it possible to compute confidence intervals for every latent trait estimate in the fscores function? I saw that you can compute standards errors but I would be more interested in the confidence intervals for the latent traits of every single respondent.

Thanks for your help in advance and best wishes,

Tim

[Phil Chalmers]

Hi Tim,

If you apply the usual large sample symmetric interval then sure, you could obtain CIs. The reason that this isn't done by default is that many factor score computations include some Bayesian prior information (often borrowed from the model itself), so you don't really get CIs but rather the Bayesian analogue symmetric "credible regions", in which case the usual large-sample quantiles are not really kosher anymore. See below on how to compute CIs for ML estimates, in which this strategy is more in-line with theory.

#---------------------------

library(mirt)

mod <- mirt(Science, 1)

fs <- fscores(mod, full.scores.SE=TRUE, method = 'ML')

head(fs)

# 95% large-sample symmetric CIs: x +- q * SE

CIs <- t(apply(fs, 1, function(x) x['F1'] + qnorm(c(.025, .975)) * x['SE_F1']))

head(CIs)

#---------------------------

Phil

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[Tim]

Hi Phil,

thank you so much for your help! That was a very valuable advice for me.

Best,

Tim