Dear all,
? I am implementing a stochastic utility model that will eventually
make use of multinomial logit. I found that there is a package in R
called mlogit. I am not sure whether I have already found the correct
package or software. May I ask am I correct?
? Basically, let's say
? I have observations of n outcomes, for each outcome 1<=i<=n, they
were selected by a choice from a set S_i = { H(i,j) | 1 <= j <= m_i }
with utility U(i,j)
??Assuming each outcome was chosen by maximizing?the utility.
? Let U*(i) = max{ 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*(i) }
? where P*(i) =?exp(U*(i)) / sum_{j=1}^{m_i} ( exp(U(i,j))
? I believe I can create a data.frame similar to this:
outcome ?observe V1 V2 V3 V4
1 1 ....
0 1 ....
0 1 ....
0 1 ...
1 2 ...
0 2 ...
0 2 ...
0 2 ...
0 2 ..
0 2 ...
1 3 ...
0 3 ...
0 3 ...
? and then convert it by mlogit.data method by specifying
chld.var="observe"
mdata <-
mlogit.data(data,choice="outcome",shape="long",chid.var="observe")
? Am I right? and then I could use mlogit to fit my model.
? Furthermore, I am also quite puzzled with the mFormula and the
probit boolean flag, am I correct to use
fit <- mlogit(outcome ~ V1 + V2 + V3 + V4,data=mydata)
? and then compute my probability estimate from the?coefficients??What
are the difference if I put variable between the?separator?| ??
? Thank you very much.
Best regards,
WONG Hang.
