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theta_1
2012 May 29
0
mlogit package inquiry
...x{ U(i,j) | 1 <= j <= m_i }
? Therefore, each outcome was chosen among m_i items by finding the
index j such that U(i,j) = U*(i).
? For the utility function U(i,j), there are some independent
variables, V_ij(k), 1 <= k <= N
? i.e. ?U(i,j) = theta_1 * V_ij(1) + theta_2 * V_ij(2) + ... + theta_N V_ij(N)
? Further assume the?probability?of choosing H(i,j) in observations i is:
? P(i,j) = exp(U(i,j)) / sum_{j=1}^{m_i} ( exp(U(i,j))
? Then, I will estimate the parameters of the model theta_1, theta_2,
..., theta_N by maximizing the the log-likelihood function
? L = log { prod_{i=1}^{n} P*(...