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

Item response theory allows the development of useful psychological measurement tools.

Psychometrics is a discipline 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 task (the construction of tests).

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

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 we want to find out or study in an individual or a group of individuals (e.g. a personality trait, anxiety, motivation, etc.).

How are the tests constructed? They are elaborated on the basis of a series of psychometric models that allow us to evaluate the quality of the measurement of these tests, as well as to obtain certain guarantees of this quality.and to obtain certain guarantees of such measurement.

In psychometrics (which we will see later what it is), there are different "Theories of Tests", which form a framework of reference, both theoretical and methodological, to group the different models and theories that allow us to build and use the tests properly. In the following we are going to know one of these models: the Item Response Theory (IRT).

Item Response Theory (IRT)

Item response theory (IRT), also called "Item characteristic curve theory", "Latent trait theory" (LFT) or "Item response theory" (IRT), is a theory within psychometrics. This theory is used in the field of psychology to construct different tests and psychological tests..

Psychometry is a part of experimental psychology; it is a discipline in charge of studying and developing all those methods and theories used to measure psychological variables in people.

The Item Response Theory overcame the disadvantages or limitations of a previous theory: the Classical Test Theory (CTT). The latter theory was developed by Charles Spearman in 1904; it is the theory with which psychometrics began (the first), and it sought to explain how from a value in a test, obtained by a person, one can extrapolate or conclude a true value in relation to the manifestation of a characteristic or personality trait being studied. in relation to the manifestation of a characteristic or personality trait being studied.

What is IRT for?

The purpose of item response theory is to specify what relationship exists between the empirical scores obtained by a subject (or several subjects) on a test, and an unobservable characteristic or trait that is being studied in that subject (or subjects). An example of a trait to be measured might be impulsivity, extroversion, introversion, etc.

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

Overcoming the limitations of TCT

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

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

Basic concepts and characteristics

In order to better understand Item Response Theory, let's take a look at some of its basic concepts and its some of its basic concepts and its most outstanding characteristics:

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). (or test).

2. Dimensionality

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

3. Local independence

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

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

4. Information function of the test

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 of the test, which allows us to calculate the amount of information that a test can provide us with at any proficiency level.

Thus, the greater the value provided by the information function of a test for a given proficiency level, the greater the discrimination for that level and the lower the measurement error in the test.

5. Item characteristic curve

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

Parameters of the item characteristic curve

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

1. B: item difficulty

Consists of the subject's level of aptitude, which is located at the inflection point of the item. 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

Item discrimination is the slope of the curve; the steeper the slope, the greater the item discrimination.

3. C: pseudo-azar or guessing

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

Bibliographical references:

• Attorresi, 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. Revista Argentina de Clínica Psicológica, 18(2): 179-188.
• Martínez, R. (1995). Psicometría: Teoría de los tests psicológicos y educativos. Madrid: Síntesis.
• Muñiz, J. (1997). Introduction to item response theory. Madrid: Ediciones Pirámide.
• Santisteban, C. (1990). Psicometría: Teoría y práctica en la construcción de tests. Madrid: Ediciones Norma.