A Genetic Algorithm and an Exact Algorithm for Classifying the Items of a Questionnaire Into Different Competences

Abstract

A Likert scale is a psychometric response scale primarily used in questionnaires to obtain participant's preferences or degree of agreement with a statement or set of statements. Respondents are asked to indicate their level of agreement with a given statement by way of an ordinal scale. The most commonly used is a 5-point scale ranging from ``Strongly Disagree'' on one end to ``Strongly Agree'' on the other with ``Neither Agree nor Disagree'' in the middle.

Normally, when a company wants to check the capabilities and skills of their employees (or when looking for new employees), a huge Likert scale questionnaire is asked to be filled up. With such a questionnaire, different competences are evaluated and therefore, the result of a questionnaire will provide important information about capabilities and skills of the respondents for each competence.

As an example, we will describe, for a real questionnaire of 170 Likert items (questions) and 23 competences, how to classify each question with the corresponding competence. That is, to find out, for each Likert item, which competence is evaluated. We will present how to face and solve the problem using two different techniques:

1.- A genetic algorithm}, adapting characteristics of genetic algorithms such as selection, genetic engineering, crossover, mutation and cloning to our classification problem. One of the main advantages of this method is that it can even be used when there are less equations (filled questionnaires) than unknowns (items) and this technique can leads to find the required solution. 2.- An exact method}, by solving a quadratic system of n equations and n unknowns, converting it to a linear system which provides the solution in a easy way. This technique required the use of a Computer Algebra System (specifically, we used {\sc Derive}) for exact computations. One of the main advantages of this technique is that if there are enough equations, this exact method will lead to the solution faster than the numerical approach.

After this example, we will set the basics to solve this competence-assignment problem for a generalized version of similar questionnaires with $n$ Likert items for evaluating $m$ competences using both techniques.

Finally, we will describe also other advantages and disadvantages of both techniques in addition of the ones described above.