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What do complexity measures measure? Correlating and validating corpus-based measures of morphological complexity

We present an analysis of eight measures used for quantifying morphological complexity of natural languages. The measures we study are corpus-based measures of morphological complexity with varying requirements for corpus annotation. We present similarities and differences between these measures visually and through correlation analyses, as well as their relation to the relevant typological variables. Our analysis focuses on whether these `measures' are measures of the same underlying variable, or whether they measure more than one dimension of morphological complexity. The principal component analysis indicates that the first principal component explains 92.62 % of the variation in eight measures, indicating a strong linear dependence between the complexity measures studied.