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Multidimensionality is a core concept in the measurement and analysis of psychological data. In personality assessment, for example, constructs are mostly theoretically defined as unidimensional, yet responses collected from the real world are almost always determined by multiple factors. Significant research efforts have concentrated on the use of simulated studies to evaluate the robustness of unidimensional item response models when applied to multidimensional data with a dominant dimension. In contrast, in the present paper, I report the result from a theoretical investigation that a multidimensional item response model is empirically indistinguishable from a locally dependent unidimensional model, of which the single dimension represents the actual construct of interest. A practical implication of this result is that multidimensional response data do not automatically require the use of multidimensional models. Circumstances under which the alternative approach of locally dependent unidimensional models may be useful are discussed.