Item Response Theory - Information

Information

One of the major contributions of item response theory is the extension of the concept of reliability. Traditionally, reliability refers to the precision of measurement (i.e., the degree to which measurement is free of error). And traditionally, it is measured using a single index defined in various ways, such as the ratio of true and observed score variance. This index is helpful in characterizing a test's average reliability, for example in order to compare two tests. But IRT makes it clear that precision is not uniform across the entire range of test scores. Scores at the edges of the test's range, for example, generally have more error associated with them than scores closer to the middle of the range.

Item response theory advances the concept of item and test information to replace reliability. Information is also a function of the model parameters. For example, according to Fisher information theory, the item information supplied in the case of the 1PL for dichotomous response data is simply the probability of a correct response multiplied by the probability of an incorrect response, or,

I(\theta)=p_i(\theta) q_i(\theta).\,

The standard error of estimation (SE) is the reciprocal of the test information of at a given trait level, is the

\text{SE}(\theta) = \frac{1}{\sqrt{I(\theta)}}.

Thus more information implies less error of measurement.

For other models, such as the two and three parameters models, the discrimination parameter plays an important role in the function. The item information function for the two parameter model is

I(\theta)=a_i^2 p_i(\theta) q_i(\theta).\,

The item information function for the three parameter model is

I(\theta)=a_i^2 \frac{(p_i(\theta) - c_i)^2}{(1 - c_i)^2} \frac{q_i(\theta)}{p_i(\theta)}

In general, item information functions tend to look bell-shaped. Highly discriminating items have tall, narrow information functions; they contribute greatly but over a narrow range. Less discriminating items provide less information but over a wider range.

Plots of item information can be used to see how much information an item contributes and to what portion of the scale score range. Because of local independence, item information functions are additive. Thus, the test information function is simply the sum of the information functions of the items on the exam. Using this property with a large item bank, test information functions can be shaped to control measurement error very precisely.

Characterizing the accuracy of test scores is perhaps the central issue in psychometric theory and is a chief difference between IRT and CTT. IRT findings reveal that the CTT concept of reliability is a simplification. In the place of reliability, IRT offers the test information function which shows the degree of precision at different values of theta, θ.

These results allow psychometricians to (potentially) carefully shape the level of reliability for different ranges of ability by including carefully chosen items. For example, in a certification situation in which a test can only be passed or failed, where there is only a single "cutscore," and where the actually passing score is unimportant, a very efficient test can be developed by selecting only items that have high information near the cutscore. These items generally correspond to items whose difficulty is about the same as that of the cutscore.

Read more about this topic:  Item Response Theory

Famous quotes containing the word information:

    “Theories of child development and guidelines for parents are not cast in stone. They are constantly changing and adapting to new information and new pressures. There is no “right” way, just as there are no magic incantations that will always painlessly resolve a child’s problems.”
    —Lawrence Kutner (20th century)

    “Information networks straddle the world. Nothing remains concealed. But the sheer volume of information dissolves the information. We are unable to take it all in.”
    —Günther Grass (b. 1927)

    “Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it.”
    —Samuel Johnson (1709–1784)