Weighted log ratio analysis by means of Poisson factor models: a case study to evaluate the quality of the public services offered to the citizens

In this paper we analyse the degree of dissatisfaction expressed by citizens regarding the quality of public services offered by municipalities in an average size city in the south of Italy. A previous study, carried out by multiple correspondence analysis, showed that the degree of dissatisfaction was closely linked to the age and education level of interviewed subjects, and the urban area (neighbourhood) in which they lived. On the basis of this result, we created two contingency tables. The first contingency, NN , represents a cross classification of n dissatisfied individuals based upon three variables: Urban area (residential neighbourhood), age, and education. Taking population distribution (based on Age and Education) within each neighbourhood into account, we considered another table, SS , which intersects the same variable and represents the target population. We started with a Goodman RC(M) association model, and obtained a weighted log ratio analysis. In particular, we propose a weighted log ratio analysis using Poisson factor models that explicitly considers count nature and automatically incorporates an offset. Moreover, we have compared the results of the log ratio analysis with and without offset by means of the RV coefficient.