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 for example by using proper scaling procedures. In order to compare, by simulation, scaling 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 questionnaire 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