Survey Statistics: relevant alternatives ?

Three weeks ago we modeled vote choice with candidates C = {Left, Right, Other} as a multinomial logit: P[voter i chooses candidate c from C] = exp(f(X_ic)) / sum_c’ exp(f(X_ic’)) We saw this model implies independence from irrelevant alternatives (IIA): gec commented about accounting for non-IIA, suggesting expanding the model above to include choice set C within the logits: f(X_ic,C). So in gec’s model: P[i chooses Left from C]/ P[i chooses Right from C] = exp(f(X_iLeft) + K[Left,Right] + K[Left,Other])/exp(f(X_iLeft) + K[Right,Left] + K[Right,Other]) compare this to: P[i chooses Left from {Left,Right}] / P[i chooses Right from {Left,Right}] = exp(f(X_iLeft) + K[Left,Right])/exp(f(X_iLeft) + K[Right,Left]) These are equal (i.e. IIA holds) if K[Left,Other] = K[Right,Other]. Train (2009) proposes this as a test of IIA in Chapter 3. This requires some survey questions where folks are given the full choice set and some where they are only given two parties {Left, Right}, though Train…