# Item information in IRT

According to item information curves, item information for a 2PL IRT model is

$I(\theta)=a^2_i p_i(\theta) q_i(\theta)$

1. To determine $p_i(\theta)$ and $q_i(\theta)$, do you just use the observed response pattern for the item, e.g., 1110 implies $p_i(\theta)=0.75$? Do you use the responses of all individuals or just one?

2. Why doesn't item difficulty affect item information?

3. (Perhaps this is the same as 2.) Using this definition of item information, how can you plot item information as a function of individual proficiency $\theta_p$?

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2. Item difficulty appears in the expressions for $p_i(\theta)$. In fact, the product $p_i(\theta)q_i(\theta)$ is maximized when $\theta=$ difficulty, as then both $p_i(\theta)=q_i(\theta)=1/2$.
3. Uhm... you just plot $I(\theta)$ as a function of $\theta$?
I must be missing something obvious. Could you give the formula for $p_i(\theta)$? –  Jack Tanner Nov 12 '12 at 18:24
Ah, figured it out. $p_i(\theta) = \frac{1}{1 + exp(a_i(b_i - \theta_p))}$. –  Jack Tanner Nov 12 '12 at 20:05