ApolloChoiceModelling forum

Dear Prof. Hess,

I am developing a latent class model containing two latent classes. In the example model, I have noticed two parameters, "delta_a" and "delta_b" in the apollo beta and the output has provided the estimated for the deltas. My question is: do we need to employ deltas in the apollo beta, how do they affect the outcome estimates, and how to interpret them? Are they default mandatory variables to keep in the latent class model? And are they proportionate to the number of classes, for example, three deltas for three latent classes model?
We have run the same model in the NLogit, but we did not have to use deltas or any variables equivalent to deltas. FYI, our data has an opt-out option. Below is the code we have used to develop the model.
Thank you for your help.

apollo_beta = c(asc_1 = 0,
asc_2 = 0,
asc_optout = 0,
beta_rec_a = 0,
beta_rec_b = 0,
beta_eff_a = 0,
beta_eff_b = 0,
beta_sideno_a =0,
beta_sideno_b =0,
beta_sidemild_a =0,
beta_sidemild_b =0,
beta_sidesev_a =0,
beta_sidesev_b =0,
beta_cost_a=0,
beta_cost_b=0,
delta_a = 0,
delta_b = 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_optout","delta_b")

# ################################################################# #
#### DEFINE LATENT CLASS COMPONENTS ####
# ################################################################# #

apollo_lcPars=function(apollo_beta, apollo_inputs){
lcpars = list()

lcpars[["beta_rec"]] = list(beta_rec_a, beta_rec_b)
lcpars[["beta_eff"]] = list(beta_eff_a, beta_eff_b)
lcpars[["beta_sideno"]] = list(beta_sideno_a, beta_sideno_b)
lcpars[["beta_sidemild"]] = list(beta_sidemild_a, beta_sidemild_b)
lcpars[["beta_sidesev"]] = list(beta_sidesev_a, beta_sidesev_b)
lcpars[["beta_cost"]] = list(beta_cost_a, beta_cost_b)

V=list()
V[["class_a"]] = delta_a
V[["class_b"]] = delta_b

classAlloc_settings = list(
classes = c(class_a=1, class_b=2),
utilities = V
)

lcpars[["pi_values"]] = apollo_classAlloc(classAlloc_settings)

return(lcpars)
}

# ################################################################# #
#### 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()

### 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 = Choice
)

### Loop over classes
for(s in 1:2){

### Compute class-specific utilities
V=list()
V[["alt1"]] = asc_1+beta_rec[[s]]*REC1 + beta_eff[[s]]*Eff1 + beta_sideno[[s]]*sideno1 + beta_sidemild[[s]]*sidemild1+beta_sidesev[[s]]*sidesev1+beta_cost[[s]]*cost1
V[["alt2"]] = asc_2+beta_rec[[s]]*REC2 + beta_eff[[s]]*Eff2 + beta_sideno[[s]]*sideno2 + beta_sidemild[[s]]*sidemild2+beta_sidesev[[s]]*sidesev2+beta_cost[[s]]*cost2
V[["alt3"]] = asc_optout

mnl_settings$utilities = V
#mnl_settings$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 ####
# ################################################################# #

### Optional starting values search
# apollo_beta=apollo_searchStart(apollo_beta, apollo_fixed,apollo_probabilities, apollo_inputs)

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

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

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

apollo_modelOutput(model)

apollo_beta = apollo_searchStart(apollo_beta,
apollo_fixed,
apollo_probabilities,
apollo_inputs)
# searchStart_settings)

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

apollo_saveOutput(model)

Hi

a latent class model uses a class allocation model. This needs to have constants in it. Please look at the details in the manual (http://apollochoicemodelling.com/manual.html) and the references to the theory on latent class models therein

Stephane