Alva’s tests are built on the latest test theory, called “Item Response Theory” (IRT), also called “Latent Trait Theory”. The theories behind psychometric testing have evolved over the years and while most psychometric tests still rely on “Classical Test Theory”, the most recent research clearly points towards the superiority of IRT when developing psychometric tests. In contrast to Classical Test Theory, which heavily relies on well-designed scales and norm groups, IRT calculates the statistical relationship between latent traits and item responses. In our case, the traits are the personality dimensions and facets we are interested in and the items are the questions that correspond to different facets.

Item Response Theory (IRT) has a lot of advantages when comparing it to Classical Test Theory (CTT):

- IRT supports adaptive testing, where the most informative questions are presented based on your previous responses
- IRT supports item banking, which means lower exposure for each question and better coverage of the latent trait being measured
- IRT scoring increases the accuracy of the results, by taking item characteristics into account. This means that fewer questions are needed to get accurate results.

While CTT deals with a fixed number of questions to form a test scale, IRT deals with each question, or item, separately. This makes the process of continuously improving a test simpler - replacing one question doesn't change the entire scale.

For Alva's personality test, a specific IRT model is used called the Graded Response Model (Samejima, 1969; Muraki, 1990). This model provides a mathematical formula for the likelihood of selecting a given response option, given a latent trait of the test taker and characteristics of the question. A modification of the model is specifically developed for Likert-type data, as described by Muraki (1990).

Read more about IRT in this Wikipedia article.

**References**

Muraki, E. (1990). Fitting a Polytomous Item Response Model to Likert-Type Data. Applied Psychological Measurement, 14(1), 59-71. doi:10.1177/014662169001400106

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement, 34(4), 100.