[Limdep Nlogit List] Structure of Variance-Covariance Matrix of ECM with panel data

[David Hoyos]

Dear all,

I am running some simulations using discrete choice models and I am
not sure about the structure of the variance-covariance matrix of the
error terms when panel data structure is defined, so maybe somebody
can give me some advice.

1) Starting with the basic MNL, I understand that the utility
functions are defined as:

U(Alt1)= beta_1 + beta_2 * A1 + epsilon_1
U(Alt2)=          beta_2 * A1 + epsilon_2
U(Alt3)=          beta_2 * A1 + epsilon_3

and so, the VC matris would be as follows:
s^2 0  0
0  s^2 0
0  0   s^2

2) moving to the ECM, correlation between two alternatives can be
included [e.g. ; ECM= (Alt1, Alt2) ] so that:

U(Alt1)= beta_1 + beta_2 * A1 + epsilon_1
U(Alt2)=                 beta_2 * A1 + theta + epsilon_2
U(Alt3)=                 beta_2 * A1 + theta + epsilon_3

and so, the VC matris would be as follows:

s^2 0  0
0  s^2  s_11
0  s_11 s^2

3) Now, when the previous models includes a panel data structure [e.g.
;pts=2] so that the same respondent is giving two choices, how exactly
is defined the VC matrix?

s^2  0  0     |s_PD  0    0
0  s^2  s_11  |0     s_PD 0
0  s_11 s^2   |0     0    s_PD
----------------------------
s_PD    0     | s^2  0     0
0  s_PD 0     | 0    s^2   s_11
0  0   s_PD   | 0    s_11  s^2


Thank-you very much,

-- 
David Hoyos
University of the Basque Country