How to interpret values of an IRT latent variable?

[Hunter Andrew]

I want to use an IRT graded response model to measure levels of a latent trait. I'm a little confused with how to interpret the values I create. My understanding is that the latent variable is standardised like a Z-score. Neverthless if I run the following example code in Stata:

webuse charity, clear
irt grm ta*
predict x, latent
summ x

The descriptive statistics don't look like that of a standardised variable - i.e. the standard deviation should be 1. Am I running the right code? Is there something I'm missing?

[Weiwen Ng]

You're definitely right that the latent variable should be standardized like a Z-score, so the respondents with average inclinations towards charity (or whatever you're measuring) should have a predicted score of 0. However, I think that the charity dataset only has 5 items. I don't recall the distribution, but I bet they're also skewed. The issue is likely to be the resolution of the instrument, like in the resolution of a telescope or a pair of measuring calipers or whatever. The actual distribution of IRT scores is probably chunky, basically. And that's causing the predicted values to not quite have SD = 1 (in my experience, the mean is usually 0 to within floating point precision, though)