ApolloChoiceModelling forum

Dear sir or madam,

Hi, I am trying to estimate mixed logit model w/ truncated normal distribution.

I made code based on example 14.

I had no problem when estimating mixed logit model w/ normal distribution or lognormal distribution. But confronted problem w/ truncated normal distribution.

I used truncated normal distribution random parameter reference with the previous apollo forum (https://groups.google.com/g/apollo-choi ... qyGEJsBQAJ)

I came up with "Error in value[[3L]](cond)" error during apollo_estimate().

Here's my code of random parameter part.

### Set parameters for generating draws
apollo_draws = list(
interDrawsType = "halton",
interNDraws = 500,
# interUnifDraws = c(),
interUnifDraws = c("eta1", "eta2"),
interNormDraws = c(),
# interNormDraws = c("draws_time","draws_fee"),
intraDrawsType = "halton",
intraNDraws = 0,
intraUnifDraws = c(),
intraNormDraws = c()
)

### Create random parameters
apollo_randCoeff = function(apollo_beta, apollo_inputs){

## truncated norm setting.
time_lower = pnorm(-Inf, mean=mu_beta_time, sd=sigma_beta_time)
time_upper = pnorm(0, mean=mu_beta_time, sd=sigma_beta_time)
fee_lower = pnorm(-Inf, mean=mu_beta_fee, sd=sigma_beta_fee)
fee_upper = pnorm(0, mean=mu_beta_fee, sd=sigma_beta_fee)

randcoeff = list()

## lognorm
# randcoeff[["beta_time_rd"]] = -exp( mu_beta_time + sigma_beta_time * draws_time )
# randcoeff[["beta_fee_rd"]] = -exp( mu_beta_fee + sigma_beta_fee * draws_fee )

## norm
# randcoeff[["beta_time_rd"]] = mu_beta_time + sigma_beta_time * draws_time
# randcoeff[["beta_fee_rd"]] = mu_beta_fee + sigma_beta_fee * draws_fee

## truncated norm variable
randcoeff[['beta_time_rd']] = qnorm(time_lower + eta1*(time_upper-time_lower), mu_beta_time, sigma_beta_time)
randcoeff[['beta_fee_rd']] = qnorm(fee_lower + eta2*(fee_upper-fee_lower), mu_beta_fee, sigma_beta_fee)

return(randcoeff)
}

Can you tell me what's wrong with my code? Thanks!

Best regards,
Hong

Dear All members and Professor Stephane.

Regarding the Apollo library in R. At the moment I am working with random coefficients and I am using the different types of distributions.

In the Apollo manual, in section "12.4 Model Specification"-(pg 142), several types of distributions are indicated, among them the truncated normal distribution; however, I have not been able to obtain it. Maybe you can help me with some kind of instruction or library that I could use to get the truncated normal?

I attached the specification of my mixed logit model with random parameters for a single variable "cs"

Later, I added in row 48 the following specification
sigma_cs = 0,
mu_cs = 0)

### Vector with names (in quotes) of parameters to be kept fixed at their starting value in apollo_beta, use apollo_beta_fixed = c() if none
apollo_fixed = c("asc_alt2","mu_cs")

I thought that I could truncate the distribution this way, but later I noticed that I am only setting the mean of the distribution to 0.

Thanks All for your kind help.

Best regards,

Hi

you need to start of with uniform draws, and then use a formula for translating these into truncated normals. See e.g. https://people.sc.fsu.edu/~jburkardt/pr ... normal.pdf

Stephane

Hi

could you please reproduce your entire code file, including the starting values, etc, and the on screen output

Thanks

Stephane

Thank you very much for your kind help professor Stephane.
Any person can continue to collaborate if there is any improvement
I share the code, the file and the processed results with the instructions and the shared article.

# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #
### Clear memory
#rm(list = ls())

### Load libraries
library(apollo)
library(EnvStats)
library(stats) # This library allows to use some functions created to work with distributions and especially to truncate (qnorm)

### Initialise code
apollo_initialise()

### Set core controls
apollo_control = list(
modelName ="ML-Random Parameters",
modelDescr ="MixedLogit_Random Parameters",
indivID ="id",
panelData=TRUE,
mixing = TRUE,
workInLogs=TRUE,
nCores =8)

# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #

setwd("file directory")
database = read.csv("CSP5.csv",header=TRUE,sep=",") #File attached so that any user can execute

# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #

### Vector of parameters, including any that are kept fixed in estimation
apollo_beta=c(asc_alt1 = 0,
asc_alt2 = 0.05,
asc_alt3 = 0.05,

#The specification contains five principal parameters:
#1."b_ev" green zones density, 2."b_cp" pedestrian density, 3."b_cv" traffic flow, 4."b_cs"sound pollution4 and 5."cost" for fee rent of a dweling

b_ev = 0.60, #Green zone density (green spaces/m2)
b_cp = -0.49, # Crowdedness (pedestrian/m2)
b_cv = -1.03, #Traffic flow (volume/capacity ratio)
#This variable b_cs is selected for truncation of the values of normal distribution
#b_cs = 1.5, # Equivalent sound pressure level (LAeq) - This varia
b_cost = -0.002, #Rent Fee
sigma_cs = 0.005,
mu_cs =0.05)

### Vector with names (in quotes) of parameters to be kept fixed at their starting value in apollo_beta, use apollo_beta_fixed = c() if none
apollo_fixed = c("asc_alt1")

# ################################################################# #
#### DEFINE RANDOM COMPONENTS ####
# ################################################################# #

### Set parameters for generating draws
apollo_draws = list(

interDrawsType = "halton",
interNDraws = 500,
#Uniform distribution
interUnifDraws = c("draw_cs"),
#Normal distribution
interNormDraws = c(),

intraDrawsType = "halton",
intraNDraws = 0,
intraUnifDraws = c(),
intraNormDraws = c()

)

### Create random parameters
apollo_randCoeff = function(apollo_beta, apollo_inputs){

## truncated norm setting.
##in this case I am interested in negative distribution values
b_cs_low = pnorm(-Inf, mean = mu_cs, sd=sigma_cs)
b_cs_upper = pnorm(0, mean = mu_cs, sd=sigma_cs)

randcoeff = list()

#### NORMAL DISTRIBUTION##########
#randcoeff[["b_cs"]] = mu_cs + sigma_cs * draws_cs

####TRUNCATED NORMAL DISTRIBUTION##########
## truncated norm variable
randcoeff[["b_cs"]] = qnorm(b_cs_low + draw_cs * (b_cs_upper - b_cs_low), mean = mu_cs , sd = sigma_cs)

####LOGNORMAL DISTRIBUTION#########
#randcoeff[["b_cs"]] = -exp ( mu_cs + sigma_cs * draws_cs )

return(randcoeff)
}

# ################################################################# #
#### GROUP AND VALIDATE INPUTS ####
# ################################################################# #

#validar inputs
apollo_inputs = apollo_validateInputs()

# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD FUNCTION ####
# ################################################################# #

#definir apollo probabilities function
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){

### Function initialisation: do not change the following three commands
### 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 mnl_settings, order is irrelevant
V = list()
##My goal is to know the importance of the attributes independently of the selected alternatives.
V[['alt1']] = asc_alt1 + b_cv * alt1_cv + b_ev * alt1_ev + b_cs * alt1_cs + b_cp * alt1_cp + b_cost * alt1_c
V[['alt2']] = asc_alt2 + b_cv * alt2_cv + b_ev * alt2_ev + b_cs * alt2_cs + b_cp * alt2_cp + b_cost * alt2_c
V[['alt3']] = asc_alt3 + b_cv * alt3_cv + b_ev * alt3_ev + b_cs * alt3_cs + b_cp * alt3_cp + b_cost * alt3_c

### Define settings for MNL model component
mnl_settings = list(
alternatives = c(alt1=1, alt2=2, alt3=3),
avail = list(alt1=1, alt2=1, alt3=1),
choiceVar = choice,
V = V
)

### Compute probabilities using MNL model
P[['model']] = apollo_mnl(mnl_settings, functionality)

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

### Average across inter-individual draws
P = apollo_avgInterDraws(P, apollo_inputs, functionality)

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

# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #

model = apollo_estimate(apollo_beta, apollo_fixed,
apollo_probabilities, apollo_inputs,
estimate_settings=list(hessianRoutine="maxLik"))

# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #

# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO SCREEN) ----
# ----------------------------------------------------------------- #
apollo_modelOutput(model)

# ----------------------------------------------------------------- #
#---- CONDITIONALS AND UNCONDITIONALS ----
# ----------------------------------------------------------------- #
#Error term distribution
unconditionals <- apollo_unconditionals(model,apollo_probabilities, apollo_inputs)

#Drawing of the distribution density function of the parameter
plot(density(as.vector(unconditionals[["b_cs"]])))

# ----------------------------------------------------------------- #
#---- OUTPUT ----
# ----------------------------------------------------------------- #

Model run using Apollo for R, version 0.2.4 on Windows by andre
www.ApolloChoiceModelling.com

Model name : ML-Random Parameters
Model description : MixedLogit_Random Parameters
Model run at : 2021-07-07 11:57:50
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 543
Number of rows in database : 1629
Number of modelled outcomes : 1629

Number of cores used : 8
Number of inter-individual draws : 500 (halton)

LL(start) : -1758.017
LL(0) : -1789.639
LL(final) : -1653.133
Rho-square (0) : 0.0763
Adj.Rho-square (0) : 0.0718
AIC : 3322.27
BIC : 3365.43

Estimated parameters : 8
Time taken (hh:mm:ss) : 00:02:57.84
pre-estimation : 00:00:15.68
estimation : 00:01:55.55
post-estimation : 00:00:46.61
Iterations : 42
Min abs eigenvalue of Hessian : 0.000231

Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_alt1 0.000000 NA NA NA NA
asc_alt2 0.066425 0.07065 0.9402 0.07272 0.9135
asc_alt3 0.159065 0.07090 2.2436 0.08327 1.9103
b_ev 0.600499 0.07321 8.2019 0.08162 7.3571
b_cp -0.647385 0.08224 -7.8722 0.08724 -7.4208
b_cv -0.513378 0.08433 -6.0880 0.08471 -6.0601
b_cost -0.004889 7.9720e-04 -6.1322 8.3563e-04 -5.8502
sigma_cs 5.907047 6.31581 0.9353 2.95235 2.0008
mu_cs 29.139463 65.49067 0.4449 28.61342 1.0184

> mean(unconditionals[["b_cs"]])
[1] -1.114828
>
> sd(unconditionals[["b_cs"]])
[1] 1.08024