Over recent years, the international literature has converged towards the selection of a set of most relevant red flags of corruption risk in public procurement. Despite careful consideration is deserved to propose single red flag indicators and, to some extent, to develop composite indicators of corruption risk based on these measures, not enough attention is currently devoted to study the dimensionality structure of such a set of elementary red flag indicators. In our view, this is the first necessary step towards the validation of such measures. In fact, the measurement of a latent and unobservable concept such as corruption, by concrete proxy means (e.g., red flags indicators), can only be valid if the proxies measured are strongly correlated with the concept they are supposed to measure. Specifically, when assessing the content validity of a set of indicators, researchers are interested in evaluating the extent to which the measures can capture the higher-level theoretical construct they are intended to detect, by at the same time excluding irrelevant elements. When the higher-level theoretical construct is a simple and unidimensional construct, it is reasonable to assess the indicator validity as a unique and unidimensional set of interconnected measures, which all refer to the same higher-order unidimensional construct. However, when the construct of interest is a complex latent concept/variable - such as corruption and corruption risk - it is reasonable to expect that a few dimensions (or sub-groups) of red flags i. measure, from different perspectives, different aspects of the same underlying phenomenon and ii. are highly correlated (and co-vary) within sub-groups and, conversely, are uncorrelated between sub-groups. Purposely then, the assessment of the validity degree of a set of elementary indicators of corruption risk should focus primarily on finding out their structure of dimensionality and shared variation among sub-groups of indicators, rather than their alignment with a one-off higher order concept. Several methodological issues arises once the latent complexity (or multidimensionality) of phenomena is acknowledged. A major issue concerns the identification and selection of the dimensions which should be accounted for. In the present study, we undergo an explorative dimensionality analysis of a set of red flags of corruption risk in public procurement, by relying on an extended Item Response Theory model. This model allows us to obtain a clustering of the red flag indicators, in such a way that red flags clustered in the same group are referred to the same sub-dimension of the latent phenomenon they refer to (corruption risk). In this regard, we consider data contained in the Italian open database of public procurement. A first exploratory dimensionality analysis, carried out on a set of red flag indicators computed on all the tenders published in Italy in 2017, reveals that multidimensional models have a better fit than the unidimensional counterpart, thus highlighting that corruption risk cannot be considered a unique construct, but, conversely, composed by several sub-dimensions, each expressing a specific meaningful dimension of corruption risk.
