Item response theory: what it is and what it is for in psychometrics

Psychometry is a discipline framed within experimental psychology, which aims to study and determine how psychological tests are constructed. Within it, we find different models that have tried to facilitate this work (the construction of tests).

In this article we will talk about one of these models: item response theory. We tell you what it consists of, what limitations it overcame from its previous model (Classical Test Theory), what it is for and what its basic concepts and characteristics are.

• Related article: "Types of psychological tests: their functions and characteristics"

Tests in psychology

In the field of psychology, tests are procedures that allow us to collect large amounts of information (or very specific information) in relation to something that we want to find out or study in an individual or in a group of them (for example a personality trait, anxiety, motivation, etc.).

How are the tests constructed? They are made from a series of psychometric models that allow us to evaluate the quality of the measurement of these tests

, as well as obtaining certain guarantees of said measure.

In psychometrics (which we will see later on), there are different "Test Theories", which configure a frame of reference, both theoretical and methodological, to group the different models and theories that will allow us to construct and use the tests in a adequate. Next, we are going to learn about one of these models: Item Response Theory (IRT).

Item response theory (IRT)

The item response theory (TRI, or in English IRT), also called "Theory of the characteristic curve of the item", "Latent trait theory" (TRL) or "Reactive response theory" (TRR), is a theory that is framed within the psychometry. Said theory It is used in the field of psychology to construct different psychological tests and tests.

For its part, psychometry is a part of experimental psychology; It is a discipline, in charge of studying and developing all those methods and theories that are used to measure the psychological variables of people.

The Item Response Theory overcame the disadvantages or limitations of a previous theory: the Classical Test Theory (TCT). This last theory was developed by Charles spearman in 1904; This is the theory with which psychometry began (the first), and it was intended to explain how from a value in a test, obtained by a person, a true value can be extrapolated or concluded in relation to the manifestation of a characteristic or personality trait that is being studied.

• You may be interested: "Psychometrics: what is it and what is it responsible for?"

What is TRI for?

The objective of the item response theory is to specify what relationship exists between the empirical scores obtained by the of a subject (or several subjects) in a test, and an unobservable characteristic or trait that is being studied in that subject (or subjects). An example of a trait to measure can be impulsiveness, extraversion, introversion, etc.

Thus, the Item Response Theory serves so that we can build measurement instruments (tests) with properties that do not vary between populations; in this way, if two people have the same measured trait level, they will both have the same probability of giving the same answer, and this is independent of the population to which they belong.

Overcoming the limitations of TCT

As we have seen at the beginning, the Item Response Theory overcomes some of the limitations presented by the Classical Test Theory.

• The new theory is formulated at the level of the total test, and not at the level of the item.
• The scores of the subjects depend on the particular content of the test and its difficulty.
• Difficulties with measurement parallelism are overcome.
• The assumption of homoscedasticity of measurement errors is overcome (IRR allows obtaining an error term for different levels of aptitude)
• Now the tests are also suitable for subjects who are not of average aptitude and from majority populations.

Basics and features

In order to better understand Item Response Theory, let's see some of its basics and highlights:

1. Observed score

We must be clear that the score observed in a test is a random variable, with a certain distribution. This distribution depends on two variables: the level of aptitude or ability of the subject, and how the trait is evaluated by the item. (or test).

2. Dimensionality

This concept is also part of the Item Response Theory. Dimensionality is a part of the latent trait. Any individual can be described in a trait by determining the values ​​of said dimensions; in practice, we speak of one-dimensional models.

3. Local independence

Another characteristic of Item Response Theory is the local independence of the items and the subjects examined. Thus, when we speak of local independence, we mean that the probability p (x) that a subject responds correctly to one item is not influenced by the responses given to other items.

On the other hand, if the unidimensionality mentioned in the previous point is fulfilled, the local independence is also fulfilled in the test.

4. Test information function

Another concept or idea that is part of the Item Response Theory is the information function of the test. This function is actually a property that the test has, which is what allows us to calculate the amount of information that a test can provide us at any level of aptitude.

In this way, the higher value the information function of a test provides for a level of determined aptitude, the greater discrimination will have for that level and the smaller measurement error will exist in the test.

5. Characteristic curve of the item

This curve, also called the regression curve, represents the expected values ​​in an item on the variable "aptitude".

Parameters of the item characteristic curve

In relation to this curve, typical of the Item Response Theory, a series of parameters appear associated, the "item characteristic curve parameters", which are three and are represented by letters:

1. B: item difficulty

It consists of the subject's fitness level, which is located at the inflection point of the curve. The greater the shift to the right, the greater the difficulty of the item (the more difficult it is).

2. A: item discrimination

The item discrimination is the slope of the curve; the steeper, the more item discrimination.

3. C: pseudo-chance or divination

Finally, the parameter C is the pseudo-chance or the divination; It consists of the probability of hitting an item by chance, and is measured in the lower asymptote of the curve. For the item to be adequate, at most this parameter must be worth 0.35.

Bibliographic references:

• Agraresi, H.F., Lozzia, G.S., Abal, J.P., Galibert, M.S. and Aguerri, M.E. (2009). Item Response Theory. Basic concepts and applications for the measurement of psychological constructs. Argentine Journal of Psychological Clinic, 18 (2): 179-188.
• Martinez, R. (1995). Psychometrics: Theory of psychological and educational tests. Madrid: Synthesis.
• Muñiz, J. (1997). Introduction to item response theory. Madrid: Pyramid Editions.
• Santisteban, C. (1990). Psychometry: Theory and practice in test construction. Madrid: Norma Editions.