A procedure simulating Likert scale item responses

Abstract

Data collected during a survey by means of a questionnaires are, in general, expressed with references to a Likert type scale, giving rise to non-metric data (ordinal categorical). However most of the statistocal procedures used to analyze survey data (for example FA or SEM) required at list interval scale measures, that may be obtained by using proper scaling procedures. In order to compare by simulation, the quantification thecniques most commonly used in the literature we consider necessary to achieve in advance an appropriate algorithm that best reproduces the discretization process followed by the respondents to the Likert questionnaire items. Accordingly, we propose a discretization procedures that, starting from a continuous random variables, describing all possible individual responses to a given stimulus, generates the corresponding categories, chosen among finite sets of integer values.