Psychometrics is a branch of psychology that is responsible for measuring and evaluating psychological characteristics of people. One of the most used tools in psychometrics is item response theory (IRT), which aims to analyze the relationship between individuals' responses to the items of a test and the characteristic that is intended to be measured.
Origin and foundations of item response theory
Item response theory has its roots in statistics and psychometrics. It emerged as an alternative to classical test theory, which was based on the analysis of the internal consistency of a test through measures such as Cronbach's alpha coefficient or factor analysis. IRT focuses on the analysis of each item individually, considering the probability that an individual responds correctly to an item based on their level of the characteristic being evaluated.
Key concepts of the theory of response to the item
To understand IRT in depth, it is necessary to be clear about some key concepts:
- Item: It is each of the questions or statements that make up a psychometric test.
- Item parameters: These are the values that characterize the difficulty and discrimination of an item. Difficulty indicates the probability of getting an item correct for individuals with a medium level in the measured characteristic, while discrimination refers to the ability of the item to differentiate between individuals with a high and low level in said characteristic.
- Item characteristic curve (ICC): It is the relationship between the probability of a correct response to an item and the level of the measured characteristic. This curve is unique for each item and usually has a sigmoid shape.
- Test parameters: These are the values that characterize the difficulty and precision of a test as a whole. Precision is reflected in the consistency of the scores obtained in the test.
Applications of item response theory
IRT has various applications in psychometrics and in other related fields. Some of the most relevant are:
Evaluation of the reliability and validity of a test
IRT allows the quality of a test to be evaluated through the analysis of its items. By knowing the parameters of each item, it is possible to identify those that do not work properly, either because they are very easy or very difficult, or because they do not adequately discriminate between individuals with different levels of the measured characteristic. This facilitates the review and improvement of the tests, increasing their reliability and validity.
Adaptation of tests to different populations
IRT is very useful for adapting tests to different populations, since it allows you to compare the function of items in different groups and adjust item parameters to ensure fairness in measurement. For example, a test designed for adults may not work correctly in children, but through IRT analysis it is possible to identify and correct these problems.
Estimation of latent levels
The models IRT allows us to estimate the latent levels of a characteristic that cannot be measured directly, such as cognitive ability or personality. By analyzing individuals' responses to items, it is possible to infer their level in the measured characteristic, which is especially useful in fields such as education and clinical psychology.
Types of theory models response to item
There are several models in IRT, each with its own characteristics and assumptions. Some of the most used are:
Rasch model
The Rasch model is one of the simplest in IRT, since it assumes that the probability of responding correctly to an item It depends solely on the individual's level on the characteristic measured and the difficulty of the item. This model is useful for evaluating the unidimensionality of a test and for calibrating items on a common scale.
Two-parameter model (2PL)
The two-parameter model adds to the consideration of the difficulty of the item, its discrimination. It is assumed that the probability of a correct response is influenced by the level of the individual and the discrimination of the item. This model is useful for tests in which we want to know not only if the individual answers correctly, but also how well they can differentiate between individuals with different levels of the measured characteristic.
Three-parameter model (3PL)
The three-parameter model incorporates a third parameter that considers the probability of responding correctly at random. This parameter is added to the 2PL model to correct possible random responses of individuals, increasing the precision of the measurement. The 3PL model is useful in tests with more complex items that can induce random responses.
Considerations and limitations of item response theory
Despite its advantages, IRT also has some important limitations and considerations that should be taken into account:
Assumptions
IRT models are based on certain assumptions, such as the unidimensionality of the measured characteristic and the local independence of the items. If these assumptions are not met, the results obtained through IRT may not be valid. Therefore, it is essential to evaluate the validity of these assumptions before applying IRT.
Item calibration
The calibration of items in IRT is a complex process that requires a adequate number of responses to obtain reliable parameter estimates. Furthermore, it is necessary to have samples that are sufficiently representative of the population to which you wish to generalize the results. Otherwise, the precision and validity of the measurement may be compromised.
Interpretation of results
Interpretation of results in IRT may not always be intuitive, especially for people without statistical training. It is important to have professionals trained in psychometrics and statistics to adequately analyze the data and draw valid conclusions from the analysis of the items and tests.
Conclusions
In conclusion, the Item response theory is a powerful tool in psychometrics that allows a detailed analysis of the relationship between individuals' responses to the items of a test and the characteristic that is intended to be measured. Using IRT, it is possible to improve the quality of tests, adapt them to different populations, estimate latent levels and obtain more precise and valid measurements in various fields of psychology and education.
It is important to take into account the considerations and limitations of IRT to guarantee the validity and reliability of the measurements carried out. With proper test design and analysis, IRT can be an invaluable tool for psychological evaluation and data-based decision making in different contexts.