Calculating weighted scores from a multiple correspondence analysis solution

Survey response data to address attitudes, satisfaction and other variables of interest to social scientists often rely on a set of statements for which respondents choose one category among all possible ordinal categorical answers. For each respondent, scores are often calculated as the summation of individual values obtained from each response. However, summation scores may be less accurate in representing latent traits, as different profiles may result in identical integer score values among all possible response patterns. We propose a method for the calculation of weighted scores from a set of ordinal categorical variables based on the factor coordinates along the oriented axes obtained from Multiple Correspondence Analysis. Our simulation results and the application of the proposed methodology to real data suggest that the proposed score has the potential of better representing latent variables than the simple summation of values of categorical variables over all sets of responses. Our worked example illustrates that respondents with different profiles might be misrepresented by the summation scores, as they could have, in some situations, the same score assigned to them whereas the proposed weighted scores discriminate every single profile.