Initial log-likelihood is too low

[mdmosab...@gmail.com]

Hi all,

I am a novice in PythonBiogeme. Just started to use it a couple of days back.

My problem is, I have run a multinomial logit model with a set of data, however, when I am using the same data set to estimate a nested logit model it stops and shows the error: "There is a numerical problem with the intial log likelihood.......". I don't understand why this is happening because it is the same data set I was using to estimate MNL. Could you please explain why this may happen?

After following some other questions on the same topic I tried to run a simulation and getting "nan" for all probabilities. I also have no idea how to find the solution from simulation results.

Thanks in advance.

Best,

Pasha

This is the code for simulation:

*******************************************************************************************************************************************************************************************************************************************************************************************************************************

from biogeme import *

from headers import *

from nested import *

from loglikelihood import *

from statistics import *

for i in range(1,7):

  

    status = 1 if (i==3) else 0

    vars()['ASC_'+str(i)] = Beta('ASC_'+str(i),0,-1000,1000,status)

B_TIME = Beta('B_TIME',0,-10000,10000,0,'Travel time')

B_COST = Beta('B_COST',0,-10000,10000,0,'Travel cost')

MU = Beta('MU',0,-10000,10000,0)

V1 = ASC_1 + B_TIME * BUS_TT_Minutes + B_COST * BUS_COST_AUD 

V2 = ASC_2 + B_TIME * TRAIN_TT_Minutes + B_COST * TRAIN_COST_AUD 

V3 = ASC_3 + B_TIME * CAR_TT_Minutes + B_COST * CAR_COST_AUD 

V4 = ASC_4 + B_TIME * SHUTTLE_TT_Minutes + B_COST * SHUTTLE_COST_AUD 

V5 = ASC_5 + B_TIME * TAXI_TT_Minutes + B_COST * TAXI_COST_AUD 

V6 = ASC_6 + B_TIME * UBER_TT_Minutes + B_COST * UBER_COST_AUD 

# Associate utility functions with the numbering of alternatives

V= {1: V1,

2: V2,

3: V3,

4:V4,

5:V5,

6:V6}

# Associate the availability conditions with the alternatives

av= {1: SP,

2: SP,

3: SP,

4:SP,

5:SP,

6:SP}

Public = MU , [1,2,3,4,5]

Private = 1.0 , [6]

nests = Public,Private

prob1 = lognested(V,av, nests,1)

prob2 = lognested(V,av, nests,2)

prob3 = lognested(V,av, nests,3)

prob4 = lognested(V,av, nests,4)

prob5 = lognested(V,av, nests,5)

prob6 = lognested(V,av, nests,6)

genelas1 = Derive(prob1,'BUS_TT_Minutes') * BUS_TT_Minutes / prob1

genelas2 = Derive(prob2,'TRAIN_TT_Minutes') * TRAIN_TT_Minutes / prob2

genelas3 = Derive(prob3,'CAR_TT_Minutes') * CAR_TT_Minutes / prob3

genelas4 = Derive(prob4,'SHUTTLE_TT_Minutes') * SHUTTLE_TT_Minutes / prob4

genelas5 = Derive(prob5,'TAXI_TT_Minutes') * TAXI_TT_Minutes / prob5

genelas6 = Derive(prob6,'UBER_TT_Minutes') * UBER_TT_Minutes / prob6

# Second, the elasticity of logit models. See Ben-Akiva and Lerman for

# the formula

#logitelas1 = TRAIN_AV_SP * (1.0 - prob1) * TRAIN_TT_SCALED * B_TIME

#logitelas2 = SM_AV * (1.0 - prob2) * SM_TT_SCALED * B_TIME

#logitelas3 = CAR_AV_SP * (1.0 - prob3) * CAR_TT_SCALED * B_TIME

# Defines an itertor on the data

rowIterator('obsIter') 

simulate = {'Prob. BUS': prob1,

            'Prob. TRAIN': prob2,

            'Prob. CAR':prob3,

'Prob. SHUTTLE': prob4,

            'Prob. TAXI': prob5,

            'Prob. UBER':prob6,

            'generic elas. 1':genelas1,

            'generic elas. 2':genelas2,

            'generic elas. 3':genelas3,

            'generic elas. 4':genelas4,

            'generic elas. 5':genelas5,

            'generic elas. 6':genelas6}

# DEfine the likelihood function for the estimation

BIOGEME_OBJECT.SIMULATE = Enumerate(simulate,'obsIter')

BIOGEME_OBJECT.ESTIMATE = Sum(logprob,'obsIter')

nullLoglikelihood(av,'obsIter')

choiceSet = [1,2,3,4,5,6]

cteLoglikelihood(choiceSet,CHOICE,'obsIter')

availabilityStatistics(av,'obsIter')

#BIOGEME_OBJECT.PARAMETERS['optimizationAlgorithm'] = "BIO"

BIOGEME_OBJECT.PARAMETERS['DumpSensitivityAnalysis'] = "1"

BIOGEME_OBJECT.PARAMETERS['simulateReportForEveryObservation'] = "1"

BIOGEME_OBJECT.PARAMETERS['includeDataWhenSimulate'] = "1"

BIOGEME_OBJECT.FORMULAS['Bus utility'] = V1

BIOGEME_OBJECT.FORMULAS['Train utility'] = V2

BIOGEME_OBJECT.FORMULAS['Car utility'] = V3

BIOGEME_OBJECT.FORMULAS['Shuttle Utility'] = V4

BIOGEME_OBJECT.FORMULAS['Taxi utility'] = V5

BIOGEME_OBJECT.FORMULAS['Uber utility'] = V6

BIOGEME_OBJECT.PARAMETERS['biogemeDisplay'] = "3"

[Bierlaire Michel]

You are mixing code for estimation and simulation. I did not find the definition of logprob. 

Also, MU must be 1.0 or higher, and certainly not negative. Therefore, you should write

MU = Beta('MU’,1,1,10000,0)

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[mdmosab...@gmail.com]

Thanks a lot Michel. Much appreciated.

Pasha