Identification issue

[Dali Hajilari]

Dear Prof. Bierlaire,

As presented below, I developed a random parameter ordinal logit model, but I receive the identification issue. How can I address this issue?

Best,

Dali

Code:

sigma_s1 = Beta('sigma_s1', 1, None, None, 1)

B_ADT = \
     ASC_ADT \
   + b_Weather_Con_4 * Weather_Con_4 \
   + sigma_s1 * bioDraws('EC', 'NORMAL_MLHS')

######################################################################## 

sigma_s2 = Beta('sigma_s2', 1, None, None, 1)
B_Collision_Type_2 = \
      ASC_Collision_Type_2 \
    + b_Accident_Cause_9 * Accident_Cause_9 \
    + sigma_s2 * bioDraws('FC', 'NORMAL_MLHS')
######################################################################## 

tau1 = Beta('tau1', -1, None, 0, 0)

delta1 = Beta('delta1', 2, 0, None, 0)
tau2 = tau1 + delta1
########################################################################

U =   ASC_Severity + \
      B_Collision_Type_2 * Collision_Type_2 + \
      b_ADT * ADT + \
      b_Accident_Type_3 * Accident_Type_3 + \
      b_Accident_Type_4 * Accident_Type_4 + \
      b_Collision_Type_3 * Collision_Type_3 + \
      b_Collision_Type_5 * Collision_Type_5 + \
      b_Collision_Type_6 * Collision_Type_6 + \
      b_Collision_Type_8 * Collision_Type_8 + \
      b_Accident_Cause_8 * Accident_Cause_8 + \
      b_Road_Section_3 * Road_Section_3 + \
      b_Road_Section_7 * Road_Section_7 + \
      b_Season_03 * Season_03 + \
      b_Season_04 * Season_04 + \
      b_Involved_Veh01_Type_2 * Involved_Veh01_Type_2 + \
      b_Involved_Veh01_Type_3 * Involved_Veh01_Type_3 + \
      b_Involved_Veh_Type_3 * Involved_Veh_Type_3 + \
      b_Holiday * Holiday + \
      b_Hour_catogery_1 * Hour_catogery_1
########################################################################

the_proba = ordered_logit(continuous_value = U, list_of_discrete_values = [1, 2, 3], tau_parameter = tau1)
the_chosen_proba = Elem(the_proba, Severity)
loglike = log(MonteCarlo(the_chosen_proba))
the_biogeme = bio.BIOGEME(database, loglike, numberOfDraws = 250)

[Michel Bierlaire]

My guess is that you are trying to estimate both the constant and the thresholds. One of them must be normalized to set the zero.

In any case, try first to estimate the ordered logit with fixed parameters before investigating the random version.

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Michel Bierlaire
Transport and Mobility Laboratory
School of Architecture, Civil and Environmental Engineering
EPFL - Ecole Polytechnique Fédérale de Lausanne
http://transp-or.epfl.ch
http://people.epfl.ch/michel.bierlaire