A procedure simulating Likert scale item responses

Data collected during a survey by means of a questionnaire are, in general, expressed with reference to a Likert type scale, giving rise to non-metric data (ordinal categorical). However most of the statistical procedures used to analyze survey data (for example FA or SEM) require at least interval scale measures, that may be obtained by using proper scaling procedures. In order to compare, by simulation, the quantification techniques 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 questionnaires items. Accordingly, we propose a discretization procedure that, starting from a continuous random variable, describing all possible individual responses to a given stimulus, generates the corresponding categories, choosen among a finite set of integer values.