Question: With three outcome categories and a single explanatory variable, suppose ????ij = exp(????j0 + ????jxi)[1 + exp(????10 + ????1xi ) + exp(????20 + ????2xi)], j

With three outcome categories and a single explanatory variable, suppose

????ij = exp(????j0 + ????jxi)∕[1 + exp(????10 + ????1xi

) + exp(????20 + ????2xi)], j = 1, 2. Show that ????i3 is

(a) decreasing in xi if ????1 > 0 and ????2 > 0,

(b) increasing in xi if ????1 < 0 and ????2 < 0, and

(c) nonmonotone when ????1 and ????2 have opposite signs.

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