discriminative-modelsitem-response-theorylogisticregression coefficients
In item response theory (IRT), 1-PL models, which include a slope parameter in addition to the intercept parameter, are better able to discriminate test-taker talent. Higher slopes translate to steeper sigmoid curves.
But what does a highly discriminative test mean? Why would a steeper slope yield increased learnings about test-takers?
Yes, assuming your IRT model is estimated using marginal maximum likelihood (MML), which is typically when $\mu_\theta$ = 0 and $\sigma_\theta$ = 1 are used to identify the model, IRT $\theta$ estimates (i.e., $\hat\theta$) may be converted to percentiles.
I also do not believe I have encountered many IRT references mentioning converting $\hat\theta$ to percentiles. One possible reason for this may be that the practice of converting $\hat\theta$ to percentiles would most likely take place in operational scenarios (e.g., ACT and SAT type stuff), and most of this work is not published.
If you decide to convert $\hat\theta$ to percentiles, I would also suggest you report their uncertainty. For example, for each percentile you calculate, you could also report the percentile for $-2*SE(\hat\theta)$ and the percentile for $+2*SE(\hat\theta)$. By doing this, you could obtain each percentile's 95% confidence region. All tests have regions where $\theta$ is measured more reliably than others (Note, this can be inspected by looking at the test information curve). Calculating percentile confidence regions allows uncertainty due to measurement error to be incorporated when interpreting percentiles.
how they are graphically represented in an IRT ICC plot
I don't think intercepts would be, because the ICCurve plots the probability of a particular response category (y axis) by the latent trait (x axis). Intercepts are only relevant on the latent-response scale. So if you plot the expected latent response (y axis) by the latent trait (x axis) in the case of uniform DIF across 2 groups, you would have 2 parallel lines (equal loadings, different intercepts). You could perhaps call this a latent-response characteristic curve (LRCC), in contrast to an (observed) item characteristic curve.
I was wondering if someone could please explain which (or both/neither) of these explanations is true?
I think your interpretation (a) is correct: Controlling for the latent trait (i.e., even among people with the same latent-trait values), the average latent response differs across groups. That is uniform DIF: a constant shift in the expected values. But in the linear case (for latent responses), that implies the same distance in the y-axis direction at any point on the x axis. In the nonlinear case (for observed item responses), "parallel" sigmoidal curves have different y-axis distances along the x-axis, despite the lines never intersecting (until $\pm \infty$ on the latent trait).
I think your interpretation (b) is also correct in terms of interpreting differences in difficulty. However, the GRM's difficulty parameters ($C-1$ per item) are analogous to CFA's thresholds ($C-1$ per item), not CFA's intercepts (1 per item). This is where it gets hairy because the GRM is generally only interpreted in terms of the observed (not latent) response scale. CFA was augmented with a threshold model as an ad-hoc way to have our continuous cake and discretely (sic) eat it too. So the thresholds are additional measurement parameters, on top of the intercepts and variances already included for continuous indicators (which latent responses are assumed to be).
Answering the question in your post's title will take some background, so please forgive me for covering a lot of concepts that I think you already understand. I just want to organize the concepts so we are on the same page.
Suppose we have 2 groups (it doesn't matter whether latent-trait means differ or not). Suppose that indicators are measured with a 5-point Likert scale, and the first 9 items have equal measurement parameters, but the 10th item has DIF in 1 of the 4 thresholds. (For simplicity, let's assume its loadings and intercepts are equal across groups.) Thus, for the first 9 items, group differences on the latent trait fully explain group differences in the probability of responding (e.g.) "strongly agree" rather than "somewhat agree". That is, there is a point on the latent-trait scale (a threshold, certain level of "difficulty") beyond which subjects stop responding "somewhat" and start responding "strongly".
Now, for the 10th item, suppose that last threshold is higher in group 2. That implies the people in group 2 need to be higher on the latent trait before they pass that threshold, to switch from "somewhat" to "strongly". That is a "more difficult" transition in group 2 than in group 1, so their 4th difficulty parameter is higher in the GRM, just like their 4th threshold is higher in CFA.
Okay, now suppose ALL thresholds are higher in group 2, shifted by the same amount (i.e., group 2's thresholds = group 1's thresholds + a constant). There is no way to statistically distinguish this situation from a situation in which the thresholds are the same in both groups, but group 2's latent-response intercept is shifted lower than group 1, by the same constant. This is exactly the situation we have with binary items (i.e., only 1 threshold): We can estimate the intercept with the threshold fixed to 0 for identification (standard in probit regression), or we can estimate the threshold with the intercept fixed to 0 (standard in CFA). We will get the same estimated absolute value either way, but with opposite signs.
It would be quite a coincidence for each of an item's thresholds to differ across groups by the exact same shift, so let's take for granted that the thresholds are in fact equal, and allow for group differences in the 10th item's intercept. Now, I can finally answer the question in your post's title :-)
This difference in intercepts reflects that the 2 groups agree more/less (on average) with the 10th item, even among members with the same level of the latent trait. That "average agreement" is on the latent response scale, and members of the group with higher average agreement have a greater probability of responding "strongly" rather than "somewhat". The item is just as "difficult", but more people pass that shared threshold in the group with the greater expected value. So DIF in intercepts simply pushes more people past the threshold in one group than another. It is the threshold that is analogous to a difficulty parameter, not the intercept. In case you have not already read it, this paper provides a formula to transform CFA to IRT parameters (or vice versa), at least in the simple binary case, but the same principle generalizes to more thresholds.
https://doi.org/10.1080/10705510701758406
Another hypothetical might make it even more concrete: Suppose there are differences both in the 4th threshold and in the intercept. Specifically, the 4th threshold is 0.5 higher in group 1 than 2, so it is that much more "difficult" to respond "strongly" than "somewhat". But the intercept is also 0.5 higher in group 1 than 2. In that case, group 2's latent-response distribution is shifted to the right, just enough to compensate for the greater difficulty. Thus, the probability of responding "strongly" would be the same in both groups, holding the latent trait constant, because just as much of the latent-response distribution exceeds the 4th threshold. However, group 2's latent-response distribution is shifted just as far to the right relative to all other thresholds, so response probabilities for lower categories would still differ between groups (holding the latent trait constant).
Best Answer
A steeper slope means a stronger relationship between ability and the question. It means that the item (and therefore the test) is more reliable - and reliability is the inverse of measurement error. Less error = better discrimination.
You can get higher reliability / discrimination / less measurement error by having more questions or having questions with larger slope parameters.