Alva's personality test is powered by the Expected A Posteriori (EAP) scoring method, which is an implementation of Bayes' Theorem.

Facet scores
First, the posterior probability distribution of the facet is calculated using a prior distribution and the likelihood function. Second, the expectation and variance of the posterior distribution are calculated using quadrature approximations. 

This is repeated for every administered question in the facet, and the posterior expectation and variance from the previous question are used to form the prior for the current question.

The methodology implemented is described by de Ayala (2008) in The Theory and Practice of Item Response Theory. It was adapted for the Graded Response Model (GRM) by modifying the likelihood function.

The results for each facet are then transformed to the Standard Ten scale, with a mean of 5.5 and a standard deviation of 2. 

Factor scores
Factor scores are calculated as linear combinations of the relevant facet scores, and are also transformed to the Standard Ten scale. 

Some facets are more broadly defined than others, and therefore cover a wider range of behaviors. For example, Assertiveness and Sociability are broader than Energy level within the Extraversion factor. As a consequence, the broad facets get a higher weight when calculating the factor scores than the narrow facets. 

Extraversion
Broad facets: Assertiveness and Sociability
Narrow facet: Energy level

Agreeableness
Broad facets: Compassion and Politeness
Narrow facet: Trust

Conscientiousness
Broad facets: Goal striving and Carefulness
Narrow facet: Orderliness

Openness
Broad facets: Curiosity and Aesthetic orientation
Narrow facet: Change orientation

Emotional stability
Broad facets: Optimism, Stability and Stress tolerance
No narrow facet

If you are interested in more detailed information, don't hesitate to get in touch!