Item Response Theory

IRT Model Basics

Item Response Curves

IRT models describe for each item in a scale how the item performs for measuring different levels of the measured construct. For example, the item/don't seem to care what happens to me would have IRT properties reflecting it is informative for measuring people with severe levels of depression, and an item such as/am happy most of the time would have IRT properties reflecting it is informative for measuring people with low levels of depression.

The probabilistic relationship between a person's response to an item and the latent variable (9) is expressed by item response curves (also referred to as category response curves or item trace lines). For example, Figure 1 presents the IRT response curves for the item/am unhappy some of the time, which has two responses, “false” and “true,” and is part of a scale measuring depression.

Individuals with little depression are located on the left side of the θ continuum in Figure 1, and people with severe depression are located on the right side of the axis. The vertical axis in Figure 1 indicates the probability that a person will select one of the item's response categories. Thus, the two response curves in Figure 1 indicate that the probability of responding “false” or “true” to the item I am unhappy some of the time depends on the respondent's depression level.

Figure 1 Item response curves representing the probability of a “false” or “true” response to the item I am unhappy some of the time conditional on a person's depression level. the threshold (b = 0.25) indicates the level of depression g(0) needed for a person to have a 50% probability for responding “false” or “true.”

Note: Numbers on the θ-axis are expressed in standardized units and, for the illustrations in this discussion, the mean depression level of the study population is set at 0 and the standard deviation is set to 1. Thus, a depression score equal to ( = 2.0) indicates that a person is 2 standard deviations above the population mean and is highly depressed.

The response curves in Figure 1 are represented by logistic curves that model the probability ρ that a person will respond “true” to this item (i) as a function of a

respondent's depression level θ, the relationship (a) of the item to the measured construct, and the severity or threshold (b) of the item on the θ scale. In IRT, a and b are referred to as item discrimination and threshold parameters, respectively.

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