A detection tool for longitudinal data specific errors applied to the case of European universities

The increasing availability of longitudinal data (repeated numerical observations of same units at different times) requires the development of flexible techniques to automatically detect common errors in such data. Besides obvious and easily identifiable cases, such as missing or out-of-range data, large longitudinal dataset often present problems not easily traceable by the techniques used for generic datasets. In particular, elusive and baffling problems are i) inversion of one or more values from one unit to another; ii) anomalous jumps in the series of values, iii) errors in the timing of the values due to a recalculation operated by the data providers to compensate previous errors. This work proposes a statistical-mathematical approach based on a system of indicators that is able to capture the complexity of the described problems by working at the formal level, regardless of the specific meaning of the data. The proposed approach identifies suspect erroneous data and is applicable in a variety of contexts. We implement this approach in a relevant database of European Higher Education institutions (ETER) by analyzing Total academic staff, that is one of the most important variables, used in empirical analysis as proxy of size and also considered by policy makers at European level.