Nested Logit-location choice joint with mode utility

[lucia]

Dear Prof. Hess,

Thanks for your Apollo package!

I have encountered an issue with a nested logit mode framework using Apollo. For the nest logit mode structure, the upper level is the choice of the zones and zone alternatives, and the lower level is the utility of different travel modes. We have alternative-specific parameters (population & employment) and mode-specific parameters(beta for different travel modes).

I have two questions regarding the model. First, I estimated the mode without alternative specific variables (attached code file), and nesting parameters for two nests are always minus zero. I've tried searching for initial values for beta, but the nesting parameters become far from the range of (0-1). I've also tested increasing the maximum iterations; however, the nesting parameter results are still below zero.

The second question is, what would be the correct way to set alternative specific variables in the utility function? I've searched keywords in the forum but only found alternative specific constant examples. Please correct me if I missed the existing answers to this topic.

Thanks for your time!

The code I am testing is attached below:

library(apollo)

{
rm(list = ls())

apollo_initialise()

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

#### LOAD DATA AND APPLY ANY TRANSFORMATIONS

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

database = read.csv("E:\\...\\testmatrix.csv", header = TRUE)

apollo_control = list(
modelName ="Apollo_NL_Model",
modelDescr ="Two-level NL model ",
nCores = 1,
panelData=FALSE,
indivID = "ID"
)

apollo_beta=c(
asc_AutoPassen1 = 0,
asc_Rideshare1 = 0,
asc_PT1 = 0,
asc_AutoPassen2 = 0,
asc_Rideshare2 = 0,
asc_PT2 = 0,
asc_AutoPassen3 = 0,
asc_Rideshare3 = 0,
asc_PT3 = 0,
asc_AutoPassen4 = 0,
asc_Rideshare4 = 0,
asc_PT4 = 0,
#C_AutoPassUtil = 0,
#C_Rideshare = 0,
#C_PTUtil = 0,
#b_LogEmploy = -3,
#b_Logpop = -3,
lamda1 = 0.5,
lamda2 = 0.5,
lamda3 = 0.5,
lamda4 = 0.5
)


apollo_fixed =c()

apollo_inputs <- apollo_validateInputs()

apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){


### Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))

### Create list of probabilities P


P = list()

### List of utilities: these must use the same names as in nl_settings, order is irrelevant
V = list()

# Nest 1: alt1
V[['Auto1']] = 0


V[['Passenger1']] = asc_AutoPassen1
#b_LogEmploy*log(Employ1) + b_Logpop*log(Pop1)
#C_AutoPassUtil*Auto_util1

V[['Rideshare1']] = asc_Rideshare1
#b_LogEmploy*log(Employ1) + b_Logpop*log(Pop1)
# C_Rideshare*Auto_util1*0.8

V[['PT1']] = asc_PT1
#b_LogEmploy*log(Employ1) + b_Logpop*log(Pop1)
#C_PTUtil*PT_util1

#----------------------------------------------------------------------------------------------------
# Nest 2: alt2

V[['Auto2']] = 0


V[['Passenger2']] = asc_AutoPassen2
#b_LogEmploy*log(Employ2) + b_Logpop*log(Pop2)
#C_AutoPassUtil*Auto_util2

V[['Rideshare2']] = asc_Rideshare2
#b_LogEmploy*log(Employ2) + b_Logpop*log(Pop2)
# C_Rideshare*Auto_util2*0.8

V[['PT2']] = asc_PT2
#b_LogEmploy*log(Employ2) + b_Logpop*log(Pop2)
# C_PTUtil*PT_util2

#----------------------------------------------------------------------------------------------------
# Nest 3: alt3

V[['Auto3']] = 0

V[['Passenger3']] = asc_AutoPassen3
#b_LogEmploy*log(Employ3) + b_Logpop*log(Pop3) #+
#C_AutoPassUtil*Auto_util3

V[['Rideshare3']] = asc_Rideshare3
#b_LogEmploy*log(Employ3) + b_Logpop*log(Pop3) #+
#C_Rideshare*Auto_util3*0.8

V[['PT3']] = asc_PT3
#b_LogEmploy*log(Employ3) + b_Logpop*log(Pop3) #+
#C_PTUtil*PT_util3

### Specify nests for NL model

#----------------------------------------------------------------------------------------------------
# Nest 4: alt4

V[['Auto4']] = 0

V[['Passenger4']] = asc_AutoPassen4
#b_LogEmploy*log(Employ4) + b_Logpop*log(Pop4) #+
#C_AutoPassUtil*Auto_util4

V[['Rideshare4']] = asc_Rideshare4
#b_LogEmploy*log(Employ4) + b_Logpop*log(Pop4) #+
#C_Rideshare*Auto_util4*0.8

V[['PT4']] = asc_PT4
#b_LogEmploy*log(Employ4) + b_Logpop*log(Pop4) #+
#C_PTUtil*PT_util4

### Specify nests for NL model

nlNests = list(root = 1,
alt1 = lamda1,
alt2 = lamda2,
alt3 = lamda3,
alt4 = lamda4)

### Specify tree structure for NL model
nlStructure= list()
nlStructure[["root"]] = c("alt1","alt2","alt3","alt4")
nlStructure[["alt1"]] = c("Auto1","Passenger1","Rideshare1","PT1")
nlStructure[["alt2"]] = c("Auto2","Passenger2","Rideshare2","PT2")
nlStructure[["alt3"]] = c("Auto3","Passenger3","Rideshare3","PT3")
nlStructure[["alt4"]] = c("Auto4","Passenger4","Rideshare4","PT4")

# Define settings for NL model
nl_settings <- list(
alternatives = c(Auto1=1, Passenger1=2, Rideshare1=3, PT1=4,
Auto2=5, Passenger2=6, Rideshare2=7, PT2=8,
Auto3=9, Passenger3=10, Rideshare3=11, PT3=12,
Auto4=13, Passenger4=14, Rideshare4=15, PT4=16),

avail = 1, #always the first zone (alt1) being selected
choiceVar = modechoice,
V = V,
nlNests = nlNests,
nlStructure = nlStructure
)

### Compute probabilities using NL model

P[["model"]] = apollo_nl(nl_settings, functionality)

## Take product across observation for same individual
#P = apollo_panelProd(P, apollo_inputs, functionality)

### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}

estimate_settings <- list(maxIterations = 5000)

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

#### MODEL ESTIMATION

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

NLmodel = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)
}

apollo_modelOutput(NLmodel)


The estimation results are as follows:
***** Singular convergence *****

Estimated parameters:
Estimate
asc_AutoPassen1 11.09500
asc_Rideshare1 7.07276
asc_PT1 -12.79277
asc_AutoPassen2 -10.56887
asc_Rideshare2 -0.74122
asc_PT2 -0.74122
asc_AutoPassen3 -0.75133
asc_Rideshare3 -0.75133
asc_PT3 -0.75133
asc_AutoPassen4 -0.75136
asc_Rideshare4 -0.75136
asc_PT4 -0.75136
lamda1 15.18385
lamda2 -0.15593
lamda3 0.06352
lamda4 0.06906

Final LL: -1340.4552

WARNING: Estimation failed. No covariance matrix to compute.

Current process will resume in 3 seconds unless interrupted by the user...

Nesting structure for model component :
Nest: root (1)
|-Nest: alt1 (15.1839)
| |-Alternative: Auto1
| |-Alternative: Passenger1
| |-Alternative: Rideshare1
| '-Alternative: PT1
|-Nest: alt2 (-0.1559)
| |-Alternative: Auto2
| |-Alternative: Passenger2
| |-Alternative: Rideshare2
| '-Alternative: PT2
|-Nest: alt3 (0.0635)
| |-Alternative: Auto3
| |-Alternative: Passenger3
| |-Alternative: Rideshare3
| '-Alternative: PT3
'-Nest: alt4 (0.0691)
|-Alternative: Auto4
|-Alternative: Passenger4
|-Alternative: Rideshare4
'-Alternative: PT4

WARNING: The nesting parameter for nest "alt1" should be between 0 and 1 (the nesting parameter for nest "root"), yet its value is 15.1839.
WARNING: The nesting parameter for nest "alt2" should be between 0 and 1 (the nesting parameter for nest "root"), yet its value is -0.1559.

Calculating log-likelihood at equal shares (LL(0)) for applicable models...
Calculating log-likelihood at observed shares from estimation data (LL(c)) for applicable models...
Calculating LL of each model component...
Calculating other model fit measures

[stephanehess]

Hi

I think the reason your model is not working at the moment is that you only have constants in the utilities, which makes it impossible to estimate a nesting structure

Regarding your second question, can you explain a bit more what you mean, please?

Thanks