Hybrid Choice Model - Latent Variable Affecting Only One Attribute
Posted: 04 Feb 2025, 10:06
Dear Apollo community,
I am working on a Hybrid Choice Model (HCM) applied to a choice experiment with an unlabeled design. My experiment involves a choice between two alternative products and a no-buy option. A set of attributes describes each alternative, and my goal is to investigate how a latent variable (LV) representing consumer beliefs influences the choices.
Currently, I am estimating this LV using a structural equation that depends on socio-demographic characteristics. I am measuring it through multiple indicators in a measurement model using normal density distributions.
I have collected attitudinal responses from participants to measure their beliefs about the product. These responses indicate the perceived probability (0-100%) that consuming the product:
1. Contributes to reducing food waste.
2. Supports a circular economy.
3. Is safe for health.
4. Brings environmental benefits.
To integrate these beliefs into my choice model, I normalized the responses (0-1 scale) and used them to estimate a latent variable (LV) via a continuous measurement model.
I would like to investigate whether this LV influences only one specific attribute in my choice model—"upcycled".
My current utility specification (excluding LV) is as follows:
My question is: Does it make sense, from a theoretical and practical standpoint, to include the latent variable directly in the utility function affecting only the "upcycled" attribute?
For example, could I modify my model as follows?
Would this approach be correct in representing the effect of the latent variable on only the "upcycled" attribute?
Or is there a more appropriate way to model this relationship within Apollo?
Any feedback or suggestions would be greatly appreciated.
Thank you in advance for your help!
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############ CODE ################
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I am working on a Hybrid Choice Model (HCM) applied to a choice experiment with an unlabeled design. My experiment involves a choice between two alternative products and a no-buy option. A set of attributes describes each alternative, and my goal is to investigate how a latent variable (LV) representing consumer beliefs influences the choices.
Currently, I am estimating this LV using a structural equation that depends on socio-demographic characteristics. I am measuring it through multiple indicators in a measurement model using normal density distributions.
I have collected attitudinal responses from participants to measure their beliefs about the product. These responses indicate the perceived probability (0-100%) that consuming the product:
1. Contributes to reducing food waste.
2. Supports a circular economy.
3. Is safe for health.
4. Brings environmental benefits.
To integrate these beliefs into my choice model, I normalized the responses (0-1 scale) and used them to estimate a latent variable (LV) via a continuous measurement model.
I would like to investigate whether this LV influences only one specific attribute in my choice model—"upcycled".
My current utility specification (excluding LV) is as follows:
Code: Select all
V[['alt1']] <- b_price * alt1.price +
b_olivo * alt1.olivo +
b_upcycled * alt1.upcycled +
b_waste * alt1.waste +
b_bio * alt1.bio +
b_int1 * alt1.upcycled * alt1.waste +
b_int3 * alt1.upcycled * alt1.bio
V[['alt2']] <- b_price * alt2.price +
b_olivo * alt2.olivo +
b_upcycled * alt2.upcycled +
b_waste * alt2.waste +
b_bio * alt2.bio +
b_int1 * alt2.upcycled * alt2.waste +
b_int3 * alt2.upcycled * alt2.bio
V[['no_buy']] <- nobuyFor example, could I modify my model as follows?
Code: Select all
V[['alt1']] <- b_price * alt1.price +
b_olivo * alt1.olivo +
(b_upcycled + lambda_LV * LV) * alt1.upcycled +
b_waste * alt1.waste +
b_bio * alt1.bio +
b_int1 * alt1.upcycled * alt1.waste +
b_int3 * alt1.upcycled * alt1.bio
V[['alt2']] <- b_price * alt2.price +
b_olivo * alt2.olivo +
(b_upcycled + + lambda*LV) * alt2.upcycled +
b_waste * alt2.waste +
b_bio * alt2.bio +
b_int1 * alt2.upcycled * alt2.waste +
b_int3 * alt2.upcycled * alt2.bio
V[['no_buy']] <- nobuyOr is there a more appropriate way to model this relationship within Apollo?
Any feedback or suggestions would be greatly appreciated.
Thank you in advance for your help!
##################################
############ CODE ################
##################################
Code: Select all
### Clear memory
rm(list = ls())
library(apollo)
library(readr)
library(tidyr)
library(dplyr)
library(readxl)
library(writexl)
library(ggplot2)
library(reshape2)
# DATA
#file_path <- "....."
data <- read_csv(file_path)
data$food_waste <- data$belief_1
data$circular_ec <- data$belief_2
data$health_safe <- data$belief_4
data$env_benefit <- data$belief_10
data$age <- data$eta_scr
database <- data[, c("y", "block", "id", "cset", "pid",
"alt1.price", "alt1.upcycled", "alt1.waste","alt1.olivo", "alt1.bio", "alt2.price", "alt2.ingredients", "alt2.waste", "alt2.upcycled", "alt2.olivo" ,"alt2.bio", "food_waste", "circular_ec", "health_safe", "env_benefit", "age","gen", "reddito","istr","reddito", "neoph_total", "nepscale_total", "health_consc")]
# Normalize belief variables
database$food_waste <- database$food_waste / 100
database$circular_ec <- database$circular_ec / 100
database$health_safe <- database$health_safe / 100
database$env_benefit <- database$env_benefit / 100
# Create the 'female' variable (1 if gen = 2, 0 otherwise)
database$female <- ifelse(database$gen == 2, 1, 0)
# Create the 'high_education' variable (1 if istr is among 4, 5, 6, 0 otherwise)
database$high_istr <- ifelse(database$istr %in% c(4, 5, 6), 1, 0)
# Create the 'high_income' variable
database$high_income <- ifelse(database$reddito %in% c(6, 7, 8,9,10), 1, 0)
# Create the 'under35' variable (1 if age is among 2,3, 0 otherwise)
database$under35 <- ifelse(database$age %in% c(2,3), 1, 0)
################### HYBRID MMNL ####################################
# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #
### Initialize code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "Hybrid_MMNL_CREMA_gen_age_istr_income_beliefs_up1",
modelDescr = "Hybrid choice model using continuous measurement model for indicators",
indivID = "id",
nCores = 4,
outputDirectory = "output"
)
# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c( b_price = -0.21183826, # Price coefficient
nobuy = -3.36746925, # "no buy" alternative
# Coefficients for random distributions
b_olivo_mu = 0.68344044, # Estimated mean for b_olivo
b_olivo_sig = 0.1, # Initial estimate for standard deviation
b_upcycled_mu = 0.14579275, # Estimated mean for b_upcycled
b_upcycled_sig = 0.1, # Initial estimate for standard deviation
b_waste_mu = 0.63220937, # Estimated mean for b_waste
b_waste_sig = 0.1, # Initial estimate for standard deviation
b_bio_mu = 0.39202152, # Estimated mean for b_bio
b_bio_sig = 0.1, # Initial estimate for standard deviation
b_int1 = 0.50219241 ,
b_int3 = 0.02165156,
lambda = 0, # Indicates how much the latent variable (LV) influences choices
gamma_female = 1.201601935,
gamma_high_istr = 0.875568049,
gamma_under35 = 0.301690559,
gamma_high_income = 0.581571635,
zeta_food_waste = 1,
zeta_circular_ec = 1,
zeta_health_safe = 1,
zeta_env_benefit = 1,
sigma_food_waste = 1,
sigma_circular_ec = 1,
sigma_health_safe = 1,
sigma_env_benefit = 1)
### 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()
# ################################################################# #
#### DEFINE RANDOM COMPONENTS ####
# ################################################################# #
### Set parameters for generating draws
apollo_draws = list(
interDrawsType="halton",
interNDraws=1000,
interUnifDraws=c(),
interNormDraws=c("eta","draws_olivo","draws_upcycled","draws_waste", "draws_bio"),
intraDrawsType="",
intraNDraws=0,
intraUnifDraws=c(),
intraNormDraws=c()
)
### Create random parameters
apollo_randCoeff=function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["LV"]] = gamma_high_istr * high_istr + gamma_female * female + gamma_under35*under35 + gamma_high_income * high_income + eta
randcoeff[["b_olivo"]] = b_olivo_mu + b_olivo_sig * draws_olivo
randcoeff[["b_upcycled"]] = b_upcycled_mu + b_upcycled_sig * draws_upcycled
randcoeff[["b_waste"]] = b_waste_mu + b_waste_sig * draws_waste
randcoeff[["b_bio"]] = b_bio_mu + b_bio_sig * draws_bio
return(randcoeff)
}
# ################################################################# #
#### GROUP AND VALIDATE INPUTS ####
# ################################################################# #
apollo_inputs = apollo_validateInputs()
# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD FUNCTION ####
# ################################################################# #
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()
### Likelihood of indicators
normalDensity_settings1 = list(outcomeNormal = food_waste,
xNormal = zeta_food_waste*LV,
mu = 0,
sigma = sigma_food_waste,
rows = (pid==1),
# Since each belief question is answered once per respondent
# but repeated in each row of the data for that respondent, we include rows=(pid==1) which
# ensures that the measurement model is only used once for each belief statement and for each
# individual, rather than contributing to the overall model likelihood in each row for that person.
componentName = "Food_Waste")
normalDensity_settings2 = list(outcomeNormal = circular_ec,
xNormal = zeta_circular_ec*LV,
mu = 0,
sigma = sigma_circular_ec,
rows = (pid==1),
componentName = "Circular_economy")
normalDensity_settings4 = list(outcomeNormal = health_safe,
xNormal = zeta_health_safe*LV,
mu = 0,
sigma = sigma_health_safe,
rows = (pid==1),
componentName = "Health_safety")
normalDensity_settings5 = list(outcomeNormal = env_benefit,
xNormal = zeta_env_benefit*LV,
mu = 0,
sigma = sigma_env_benefit,
rows = (pid==1),
componentName = "Env_benefit")
# 4 INDICATORS of the model
P[["Food_Waste"]] = apollo_normalDensity(normalDensity_settings1, functionality)
P[["Circular_economy"]] = apollo_normalDensity(normalDensity_settings2, functionality)
P[["Health_safety"]] = apollo_normalDensity(normalDensity_settings4, functionality)
P[["Env_benefit"]] = apollo_normalDensity(normalDensity_settings5, functionality)
### Likelihood of choices
V <- list()
V[['alt1']] <- b_price * alt1.price +
b_olivo * alt1.olivo +
(b_upcycled + lambda*LV) * alt1.upcycled +
b_waste * alt1.waste +
b_bio * alt1.bio +
b_int1 * alt1.upcycled * alt1.waste +
b_int3 * alt1.upcycled * alt1.bio
V[['alt2']] <- b_price * alt2.price +
b_olivo * alt2.olivo +
(b_upcycled + + lambda*LV) * alt2.upcycled +
b_waste * alt2.waste +
b_bio * alt2.bio +
b_int1 * alt2.upcycled * alt2.waste +
b_int3 * alt2.upcycled * alt2.bio
V[['no_buy']] <- nobuy
### Define settings for MNL model component
mnl_settings <- list(
alternatives = c(alt1 = 1, alt2 = 2, no_buy = 3),
avail = list(alt1 = 1, alt2 = 1, no_buy = 1),
choiceVar = y,
utilities = V
)
### Compute probabilities for MNL model component
P[["choice"]] = apollo_mnl(mnl_settings, functionality)
### Likelihood of the whole model
#This function takes the list P which contains several individual model components and produces
#a combined model
P = apollo_combineModels(P, apollo_inputs, functionality)
### Take product across observation for same individual
#apollo_panelProd which multiplies the probabilities across individual choice observations for the 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)
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #
apollo_modelOutput(model)
apollo_saveOutput(model)
apollo_sink()