  A coordinate system free definition of complex structure multidimensional
item response theory (MIRT) for dichotomously scored items is presented. The
point of view taken emphasizes the possibilities and subtleties of
understanding MIRT as a multidimensional extension of the ``classical''
unidimensional item response theory models. The main theorem of the paper is
that every monotonic MIRT model looks the same; they are all trivial extensions
of univariate item response theory.
