Interpretation of ASC shifts in Mixed logit model

[KHMackenzie]

Hello,
Please may I ask for some guidance on interpreting the parameters of the ASC shifts. I have estimated a Mixed logit with deterministic heterogeneity based on socio-demographics, and random heterogeneity for the attributes (Normal / Log Normal for costs). What I am not too sure on is interpreting the ASC shifts (interacted with the socio-demographics). Are they interpreted in comparison to the fixed ASC, or in relation to the base ASC?

Thank you,

My code is as follows:
# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #

### Loading data from package
### if data is to be loaded from a file (e.g. called data.csv),
### the code would be: database = read.csv("data.csv",header=TRUE)
library(readxl)
database= read_excel("~/Desktop/5.PhD Data Analysis/Final data March 24/GEMS_full_data_clean_072024.xlsx")
database <- as.data.frame(database)


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

### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c (asc_GDH = 0,
asc_HB_base = -0.417987981078515,
asc_HB_shift_age = -0.000006576788541,
asc_HB_shift_own_home = -0.172911424845596,
asc_HB_shift_time_home = 0.005804949359464,
asc_HB_shift_time_home_exp = 0.011078526872732,
asc_HB_shift_energy_eff = 0.401480915827985,
asc_HB_shift_heat_type_SEB = -0.378367338786279,
asc_HB_shift_vehicle = 0.129490126151764,
asc_SEB_base = 0.036123749627697,
asc_SEB_shift_age = -0.007876528078052,
asc_SEB_shift_hh_size = 0.030708165261368,
asc_SEB_shift_own_home = -0.406770861915822,
asc_SEB_shift_time_home = -0.017861791384544,
asc_SEB_shift_time_home_exp = 0.005958891796782,
asc_SEB_shift_energy_eff = 0.562745824365959,
asc_SEB_shift_heat_type_SEB = 0.931629474692535,
asc_ASHP_base = 0.294174276687739,
asc_ASHP_shift_age = -0.021291954519979,
asc_ASHP_shift_bedrooms = -0.190503565914332,
asc_ASHP_shift_own_home = -0.406627539945095,
asc_ASHP_shift_time_home = -0.024110068663101,
asc_ASHP_shift_time_home_exp = 0.025144789672796,
asc_ASHP_shift_energy_eff = 0.693991577526987,
asc_ASHP_shift_heat_type_ASHP = 0.928449838191297,
b_income = 0.035507623124387,
b_ic_mu = -0.097310888453008,
b_ic_sig = 0.007572013090580,
b_mc_mu = -0.774384919567975,
b_mc_sig = 0.023587111440034,
b_rp_mu = 0.033464397621852,
b_rp_sig = 0.003104653980893,
b_co2_mu = -0.078783918091262,
b_co2_sig = 0.005352128606680,
b_jc_mu = 0.006782241699742,
b_jc_sig = 0.001142904793546)

### 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_GDH")

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

### Set parameters for generating draws
apollo_draws = list(
interDrawsType = "halton",
interNDraws = 1000,
interNormDraws = c("draws_ic","draws_mc","draws_rp", "draws_co2","draws_jc")
)

### Create random parameters
apollo_randCoeff = function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["b_inv_cost"]] = -exp(b_ic_mu + b_ic_sig * draws_ic)
randcoeff[["b_monthly_cost"]] = -exp(b_mc_mu + b_mc_sig * draws_mc)
randcoeff[["b_replace_period"]] = b_rp_mu + b_rp_sig * draws_rp
randcoeff[["b_CO2"]] = b_co2_mu + b_co2_sig * draws_co2
randcoeff[["b_job"]] = b_jc_mu + b_jc_sig * draws_jc
return(randcoeff)
}

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

apollo_inputs = apollo_validateInputs()

# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD 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()

### Create alternative specific constants and coefficients with interactions with socio-demographics
asc_HB = asc_HB_base + asc_HB_shift_age*Q22_age + asc_HB_shift_own_home*Q34_own_home + asc_HB_shift_time_home*Q37_time_home + asc_HB_shift_time_home_exp*Q38_time_home_exp + asc_HB_shift_energy_eff*Q41_energy_eff + asc_HB_shift_heat_type_SEB*Q39_heat_type_SEB + asc_HB_shift_vehicle*Q33_vehicle
asc_SEB = asc_SEB_base + asc_SEB_shift_age*Q22_age + asc_SEB_shift_hh_size*Q25_hh_size + asc_SEB_shift_own_home*Q34_own_home + asc_SEB_shift_time_home*Q37_time_home + asc_SEB_shift_time_home_exp*Q38_time_home_exp + asc_SEB_shift_energy_eff*Q41_energy_eff + asc_SEB_shift_heat_type_SEB*Q39_heat_type_SEB
asc_ASHP = asc_ASHP_base + asc_ASHP_shift_age*Q22_age + asc_ASHP_shift_bedrooms*Q36_bedrooms + asc_ASHP_shift_own_home*Q34_own_home + asc_ASHP_shift_time_home*Q37_time_home + asc_ASHP_shift_time_home_exp*Q38_time_home_exp + asc_ASHP_shift_energy_eff*Q41_energy_eff + asc_ASHP_shift_heat_type_ASHP*Q39_heat_type_ASHP


### List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["GDH"]] = asc_GDH + b_inv_cost*(inv_cost_GDH_/1000) + b_monthly_cost*(monthly_cost_GDH_/100) + b_replace_period*replace_period_GDH_ + b_CO2*(CO2_GDH_/1000) + b_job*job_GDH_
V[["HB"]] = asc_HB + + b_inv_cost*(inv_cost_HB_/1000) + b_monthly_cost*(monthly_cost_HB_/100) + b_replace_period*replace_period_HB_ + b_CO2*(CO2_HB_/1000) + b_job*job_HB_ + b_income*(Q32_income/10000)
V[["SEB"]] = asc_SEB + b_inv_cost*(inv_cost_SEB_/1000) + b_monthly_cost*(monthly_cost_SEB_/100) + b_replace_period*replace_period_SEB_ + b_CO2*(CO2_SEB_/1000) + b_job*job_SEB_ + b_income*(Q32_income/10000)
V[["ASHP"]] = asc_ASHP + b_inv_cost*(inv_cost_ASHP_/1000) + b_monthly_cost*(monthly_cost_ASHP_/100) + b_replace_period*replace_period_ASHP_ + b_CO2*(CO2_ASHP_/1000) + b_job*job_ASHP_+ b_income*(Q32_income/10000)

### Define settings for MNL model component
mnl_settings = list(
alternatives = c(GDH=1, HB=2, SEB=3, ASHP=4),
choiceVar = choice,
utilities = 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 ####
# ################################################################# #

### Optional speedTest
#speedTest_settings=list(
# nDrawsTry = c(100, 200, 500),
# nCoresTry = c(1,3,5,7),
# nRep = 30
#)

#apollo_speedTest(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs, speedTest_settings)

model = apollo_estimate(apollo_beta, apollo_fixed,
apollo_probabilities, apollo_inputs)

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

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

apollo_modelOutput(model)

# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO FILE, using model name) ----
# ----------------------------------------------------------------- #

apollo_saveOutput(model)

# ################################################################# #
##### POST-PROCESSING ####
# ################################################################# #

### Print outputs of additional diagnostics to new output file (remember to close file writing when complete)
apollo_sink()

[stephanehess]

Hi

only differences in utility matter, so everything is relative to the base.

In your case, you have a negative constant for the HB option for a person in the base socio-demographic group. Then you have a negative interaction for age, which simply means that for older respondents, the constant for HB is more negative than for younger respondents, all still relative to the base of course

Stephane

[KHMackenzie]

Thank you