Item Response Theory (IRT)

The most important assumption of the IRT informs us that any measuring instrument must conform to an idea.
Item Response Theory (IRT)

One of the most important parts of psychological intervention is assessment. This is often strongly conditioned by the results of the tests administered. Thus, item response theory (IRT) is one of the test measurement theories that appears to complement classical test theory.

As mentioned earlier, classical test theory (TCT) and TRI can assess the same test. Each could establish a relevance or a score for each of the elements. So, it might give a different result for each person.

It should be noted that the TRI would give us a much better calibrated instrument. However, this paradigm is associated with a much higher cost and the intervention of specialized professionals.

The aim of these two test theories is the same. It’s about generating instruments that measure what we want them to measure with as few errors as possible. Thus, psychometrics requires a certain reliability and validity of all tests.

Remember that a test will be all the more reliable (will have greater reliability) if it reproduces the results well when it is measured by two subjects – or the same subject on different occasions – who have the same level of measurement. On the other hand, validity refers to the degree to which empirical evidence and theory supports the interpretation of test results.

A man taking a test.

The limits of TST leading to the emergence of IRT

Without depreciating the services rendered, which have been numerous and useful, the classical approach to test theory has certain limitations. Gaps that demand that we take a step forward in terms of test construction and evaluation.

In TCT, the measurements are not invariant with respect to the instrument used. So, imagine that a psychologist evaluates the intelligence of three people with a different test for each of them. In this case, the results could not be compared. But why ?

Indeed, each test has its own scale. So, to compare, for example, the intelligence of a group of people who have been assessed using different intelligence tests, it would be necessary to transform the scores obtained into other scaled scores.

In this sense , IRR allows us to compare the results obtained using different instruments on the same scale. In addition, another limitation of the classical approach is the lack of invariance of the properties of the tests with respect to the people used to estimate them. The IRR approach is also responsible for improving this fact.

Assumptions of item response theory (IRT)

In order to overcome these limitations, the TRI must formulate stronger and more restrictive assumptions than the TCT. They are three in number.

First hypothesis

Thus, the most important hypothesis of IRR informs us that any measuring instrument must conform to an idea. This means that there is a functional relationship between the values ​​of the variable measured by the items and the probability of obtaining the correct items.

This function is called the characteristic curve of the item (CCI). It seems that item response theory offers a new idea for TST.

It is based on the idea that, for example, the most complex questions on an intelligence test would only be answered by the most intelligent people. On the other hand, a question to which all the people evaluated answer in the same way would not have the power to discriminate between more or less intelligence in a subject.

Second hypothesis

Another assumption of IRR is that most of its models assume that the items constitute a single dimension. That is, they are one-dimensional.

Thus, before using the IRT models, it is necessary to ensure that the data respect this one-dimensionality. This is an important restriction for their use: many instruments used by psychologists do not collect data on only one dimension.

A woman taking a test.

Third hypothesis

A third assumption of the item response theory models is local independence. This means that in order to use these models, the elements must be independent of each other. In other words, the response to one item cannot be conditioned by the response to other items.

However, if the unidimensionality is satisfied, so is local independence (there is no interdependence between items or a shared variance that is unrelated to the measured dimension). Thus, the two hypotheses are sometimes treated together.

Muñiz (2010) underlines the importance of advances in the field of psychometrics and the interpretation of tests. So it makes sense that we are starting to take one more step in that direction, since the tests analyzed under the TRI paradigm are, to say the least, giving worrying results about how they are currently measured.

Statistical inference in psychology
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Can we deduce the behavior of the whole population by studying only a sample? This is the role of statistical inference.

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