ApolloChoiceModelling forum

Hi,

I have a question about calculating the characteristics across classes. For example, I have the covariate age in my model, this is divided into three categories: youth, young-adults and middle-aged adults. I've managed to find the most likely value per class:

X1 X2 X3
2.107134 2.281334 1.961140

However, I would like to find how many respondents (in %) of class 1 fall within category 1 (youth), how many in category 2 (young-adults) and how many in category 3 (middle-aged adults). Do you have some advice on how to calculate this?

Kind regards

This is my code:

rm(list = ls())

### Load Apollo library

library(apollo)

### Initialise code

apollo_initialise()


### Set core controls
apollo_control = list(
modelName = "LCCM_covariates",
modelDescr = "LCCM_covariates",
indivID = "ID"
)


### Load data
database = read.delim("LCCMcovariates.dat",sep=',',header=TRUE)

###
apollo_beta = c(BETA_env_a = 0,
BETA_env_b = 0,
BETA_env_c = 0,
BETA_nutri_a = 0,
BETA_nutri_b = 0,
BETA_nutri_c = 0,
BETA_price_a = 0,
BETA_price_b = 0,
BETA_price_c = 0,
BETA_taste_a = 0,
BETA_taste_b = 0,
BETA_taste_c = 0,
BETA_tex_a = 0,
BETA_tex_b = 0,
BETA_tex_c = 0,
BETA_app_a = 0,
BETA_app_b = 0,
BETA_app_c = 0,
BETA_AW_a = 0,
BETA_AW_b = 0,
BETA_AW_c = 0,
delta_a = 0,
delta_b = 0,
delta_c = 0,
gamma_diet_a = 0,
gamma_diet_b = 0,
gamma_diet_c = 0,
gamma_age_a = 0,
gamma_age_b = 0,
gamma_age_c = 0,
gamma_prep_a = 0,
gamma_prep_b = 0,
gamma_prep_c = 0,
gamma_promeat_a = 0,
gamma_promeat_b = 0,
gamma_promeat_c = 0,
gamma_sustainablebehaviour_a = 0,
gamma_sustainablebehaviour_b = 0,
gamma_sustainablebehaviour_c = 0,
gamma_EnvConcern_a = 0,
gamma_EnvConcern_b = 0,
gamma_EnvConcern_c = 0,
gamma_HealthConscious_a = 0,
gamma_HealthConscious_b = 0,
gamma_HealthConscious_c = 0,
gamma_objknow_a = 0,
gamma_objknow_b = 0,
gamma_objknow_c = 0)

apollo_fixed = c("delta_c","gamma_diet_c","gamma_age_c",
"gamma_prep_c","gamma_promeat_c" ,
"gamma_sustainablebehaviour_c","gamma_EnvConcern_c", "gamma_HealthConscious_c",
"gamma_objknow_c")



### Defining Latent Class Parameters
apollo_lcPars=function(apollo_beta, apollo_inputs){
lcpars = list()
lcpars[["BETA_env"]] = list(BETA_env_a, BETA_env_b, BETA_env_c)
lcpars[["BETA_nutri"]] = list(BETA_nutri_a, BETA_nutri_b, BETA_nutri_c)
lcpars[["BETA_price"]] = list(BETA_price_a, BETA_price_b, BETA_price_c)
lcpars[["BETA_taste"]] = list(BETA_taste_a, BETA_taste_b, BETA_taste_c)
lcpars[["BETA_tex"]] = list(BETA_tex_a, BETA_tex_b, BETA_tex_c)
lcpars[["BETA_app"]] = list(BETA_app_a, BETA_app_b, BETA_app_c)
lcpars[["BETA_AW"]] = list(BETA_AW_a, BETA_AW_b, BETA_AW_c)

V=list()
V[["class_a"]] = delta_a + gamma_diet_a*diet + gamma_age_a * AgeCategory + gamma_prep_a * prep1 +
gamma_promeat_a * promeat +
gamma_sustainablebehaviour_a * sustainablebehaviour + gamma_EnvConcern_a * EnvConcern +
gamma_HealthConscious_a * HealthConscious + gamma_objknow_a * objknow

V[["class_b"]] = delta_b + gamma_diet_b*diet + gamma_age_b * AgeCategory + gamma_prep_b * prep1 +
gamma_promeat_b * promeat +
gamma_sustainablebehaviour_b * sustainablebehaviour + gamma_EnvConcern_b * EnvConcern +
gamma_HealthConscious_b * HealthConscious + gamma_objknow_b * objknow

V[["class_c"]] = delta_c + gamma_diet_c*diet + gamma_age_c * AgeCategory + gamma_prep_c * prep1 +
gamma_promeat_c * promeat +
gamma_sustainablebehaviour_c * sustainablebehaviour + gamma_EnvConcern_c * EnvConcern +
gamma_HealthConscious_c * HealthConscious + gamma_objknow_c * objknow




mnl_settings = list(
alternatives = c(class_a=1, class_b=2, class_c=3),
avail = 1,
choiceVar = NA,
V = V
)


lcpars[["pi_values"]] = apollo_mnl(mnl_settings, functionality = "raw")
lcpars[["pi_values"]] = apollo_firstRow(lcpars[["pi_values"]], apollo_inputs)
return(lcpars)
}



### VALIDATING AND PREPARING INPUTS
apollo_inputs = apollo_validateInputs()



### Model definition
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()

## Define settings for MNL model component that are generic across classes
mnl_settings= list(
alternatives = c(alt1=1, alt2=2, alt3=3),
avail = list(alt1=1, alt2=1, alt3=1),
choiceVar = value
)


### Loop over classes
for(s in 1:3){

### Compute class-specific utilities
V = list()
V[['alt1']] = env1 * BETA_env[[s]] + nutri1 * BETA_nutri[[s]] + price1 * BETA_price[[s]] +
taste1 * BETA_taste[[s]] + tex1 * BETA_tex[[s]] + app1 * BETA_app[[s]] + AW1 * BETA_AW[[s]]
V[['alt2']] = env2 * BETA_env[[s]] + nutri2 * BETA_nutri[[s]] + price2 * BETA_price[[s]] +
taste2 * BETA_taste[[s]] + tex2 * BETA_tex[[s]] + app2 * BETA_app[[s]] + AW2 * BETA_AW[[s]]
V[['alt3']] = env3 * BETA_env[[s]] + nutri3 * BETA_nutri[[s]] + price3 * BETA_price[[s]] +
taste3 * BETA_taste[[s]] + tex3 * BETA_tex[[s]] + app3 * BETA_app[[s]] + AW3 * BETA_AW[[s]]

mnl_settings$V = V
mnl_settings$componentName = paste0("Class_",s)

### Compute within-class choice probabilities using MNL model
P[[paste0("Class_",s)]] = apollo_mnl(mnl_settings, functionality)

### Take product across observation for same individual
P[[paste0("Class_",s)]] = apollo_panelProd(P[[paste0("Class_",s)]], apollo_inputs, functionality)

}

### Compute latent class model probabilities
lc_settings = list(inClassProb = P, classProb=pi_values)
P[["model"]] = apollo_lc(lc_settings,
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,modelOutput_settings=list(printPVal=TRUE))

###apollo_saveOutput(model)


unconditionals = apollo_unconditionals(model,apollo_probabilities,apollo_inputs)

conditionals = apollo_conditionals(model,apollo_probabilities, apollo_inputs)

summary(conditionals)

summary(as.data.frame(unconditionals[["pi_values"]]))

diet_n = apollo_firstRow(database$diet, apollo_inputs)
age_n = apollo_firstRow(database$AgeCategory, apollo_inputs)

post_diet=colSums(diet_n*conditionals)/colSums(conditionals)
post_age=colSums(age_n*conditionals)/colSums(conditionals)

post_diet

post_age

post_diet[2:4]

post_age[2:4]

The command
would tell you the posterior probability of someone in class 1 being in age group 1. Then you could do the same for other age groups and other classes

Then multiplying the posterior probability for people in group 1 being in age group 1 by the size of class 1 would tell you how many of the age group 1 people you would expect to fall into class 1. Just remember that this is all probabilistic, so it's an expectation, rather than an observation

Stephane