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I've been reading about item response model guides for R and my model is :

mod <- glmer(response ~ 0 + item + (1|house_id), 
              family = binomial, nAGQ = 0)

and I want to investigate the random effects (which will be used as indices to compare the houses in the model above) using:

ranef(mod)["(Intercept)"]

I used bootstrap = 1000 for my model and obtained the CIs. However, without nAGQ = 0, it'll take 2 hours for my computer to process this. When nAGQ = 0 was activated, it took me 2 minutes. Some guides/opinion out there been saying that n = 0 only integrates over theta, while nAGQ = 1 integrate over theta and beta. Also, nAGQ = 0 claimed to be less accurate, but I think the bootstrapping process re-increase the power of the statistical inference of this model relates to its random effects.

I'm suspecting that this relates to coefficient like Y = B0 + B1X but I might be wrong. Does this referring to random and fixed effects and if I'm only interested for the random effects, does using nAGQ = 0 affect it?

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Estimation of mixed-effects logistic regression requires numerically integrating the random effects to calculate the likelihood of the model. There are several approaches to do this and you can find more information in this post.

In general, and even though setting nAGQ much greater than 1 takes more time, it is to be preferred. This will ensure that the error in the approximation of the likelihood function is minimized.

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  • $\begingroup$ If I incoporate nAGQ = 0 with bootstrap to estimate the random effect coefficients, I think it'll produce a "conservative" estimate as the error in the approximation is bigger. However, I haven't seen (from online sources and the link) anything that says nAGQ = 0 makes our estimates biased, therefore a model with nAGQ = 0 is still valid, isn't it? Do you think comparing bootsrapped coefficients of two nAGQ = 0 model is valid as well given that they operates in the same premise (all same variables but different data)? $\endgroup$
    – user282983
    May 14, 2020 at 0:30
  • $\begingroup$ @user282983 nAGQ = 0 is less accurate than nAGQ >= 1, and using the Bootstrap will not alleviate the problem. I.e., the estimates are expected to be more biased with this option. $\endgroup$ May 14, 2020 at 5:35
  • $\begingroup$ Final follow up question: If I'm comparing two models with both nAGQ = 0 (i.e model1 : response ~ var1, var2, var3, and model2: response ~ var4, var5, var6 and then compare their random effects, will it be valid? Since the two models are both biased, and the only difference between them is the set of predictors $\endgroup$
    – user282983
    May 15, 2020 at 4:46
  • $\begingroup$ @user282983 The comparison will not be trustworthy. $\endgroup$ May 15, 2020 at 6:28

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