Errors when estimating a LC model with random components allowed for one of the classes

[arohamirai]

Dear Stephane and David,

Thank you very much for inventing the Apollo package and creating the forum allowing our users to communicate.

I recently run a latent class model, but allow for inter-individual heterogeneity only within one of the classes (i.e., preferences are assumed to be non-random in the other classes). The model ends up with an error saying

"Error in apollo_avgInterDraws(P[[s]], apollo_inputs, functionality) :
No Inter-individuals draws to average over! "

I think the problem is the following: R tries to average across inter-individual draws for class, but the problem occurs when estimating the two non-random classes where no draws are generated.

My questions are:

(1) Is this model theoretically valid and/or practically sensible?

(2) If yes to (1), How can I code the model such as this (where let's say, attributes follow are random in one class, and non-random in the other two classes)?

I have attached my R code below.

Thank you very much.


Tim
-------------------------------------------




# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #

### Clear memory
rm(list = ls())

### Load Apollo library
library(apollo)

### Initialise code
apollo_initialise()

### Set core controls
apollo_control = list(
modelName ="RPL_coop_LC3_ENVgroupRPL",
modelDescr ="RPL_coop_LC3_ENVgroupRPL",
indivID ="pool_ID",
nCores = 3,
mixing = TRUE,
noDiagnostics = TRUE
)

# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #
#load the data
database = read.csv("R_for_coop.csv",header=TRUE)


##renames##
#names(database)[names(database)=="id"] <- "ID"

database= subset(database, database$dce_valid_CB1==1&dce_valid_CB2==1&
dce_valid_CB3==1&dce_valid_CB4==1&dce_valid_T2B1==1
&dce_valid_T2B2==1&dce_valid_T2B3==1&dce_valid_T2B4==1)




############################T1############################################

####T1 and control only
database= subset(database, database$T2==0)



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

### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c(asc_I = 0,



asc_III_1 = 0,
asc_III_2_mu = 0,
asc_III_2_sig = 0,
asc_III_3 = 0,


project_1 = 0,
project_2_mu = 0,
project_2_sig = 0,
project_3 = 0,



carbon_1 = 0,
carbon_2_mu = 0,
carbon_2_sig = 0,
carbon_3 = 0,


location_Wregion_1 = 0,
location_Wregion_2_mu = 0,
location_Wregion_2_sig = 0,
location_Wregion_3 = 0,


location_Wcountry_1 = 0,
location_Wcountry_2_mu = 0,
location_Wcountry_2_sig = 0,
location_Wcountry_3 = 0,

location_Ocountry_1 = 0,
location_Ocountry_2_mu = 0,
location_Ocountry_2_sig = 0,
location_Ocountry_3 = 0,


min_invest_1 = 0,
min_invest_2_mu = 0,
min_invest_2_sig = 0,
min_invest_3 = 0,

duration_I_1 = 0,
duration_I_2_mu = 0,
duration_I_2_sig = 0,
duration_I_3 = 0,

duration_II_1 = 0,
duration_II_2_mu = 0,
duration_II_2_sig = 0,
duration_II_3 = 0,


duration_V_1 = 0,
duration_V_2_mu = 0,
duration_V_2_sig = 0,
duration_V_3 = 0,

Q_participation_1 = 0,
Q_participation_2_mu = 0,
Q_participation_2_sig = 0,
Q_participation_3 = 0,



A_participation_1 = 0,
A_participation_2_mu = 0,
A_participation_2_sig = 0,
A_participation_3 = 0,



e_return_1 = 0,
e_return_2_mu = 0,
e_return_2_sig = 0,
e_return_3 = 0,

delta_a = 0,
delta_b = 0,
delta_c = 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("delta_b", "asc_I") #fix the scale of the control treatment


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

### Set parameters for generating draws
apollo_draws = list(
interDrawsType = "mlhs",
interNDraws = 500,
interUnifDraws = c(),
interNormDraws = c("draws_project_2",
"draws_carbon_2",
"draws_location_Wregion_2",
"draws_location_Wcountry_2",
"draws_location_Ocountry_2",
"draws_min_invest_2",
"draws_duration_I_2",
"draws_duration_II_2",
"draws_duration_V_2",
"draws_Q_participation_2",
"draws_A_participation_2",
"draws_asc_2",
"draws_Ereturn_2"
),

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

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

randcoeff[["asc_III_2"]] = asc_III_2_mu + asc_III_2_sig*draws_asc_2

randcoeff[["project_2"]] = project_2_mu + project_2_sig*draws_project_2
randcoeff[["carbon_2"]] = carbon_2_mu + carbon_2_sig*draws_carbon_2
randcoeff[["location_Wregion_2"]] = location_Wregion_2_mu + location_Wregion_2_sig*draws_location_Wregion_2
randcoeff[["location_Wcountry_2"]] = location_Wcountry_2_mu + location_Wcountry_2_sig*draws_location_Wcountry_2
randcoeff[["location_Ocountry_2"]] = location_Ocountry_2_mu + location_Ocountry_2_sig*draws_location_Ocountry_2
randcoeff[["min_invest_2"]] = min_invest_2_mu + min_invest_2_sig*draws_min_invest_2
randcoeff[["duration_I_2"]] = duration_I_2_mu + duration_I_2_sig*draws_duration_I_2
randcoeff[["duration_II_2"]] = duration_II_2_mu + duration_II_2_sig*draws_duration_II_2
randcoeff[["duration_V_2"]] = duration_V_2_mu + duration_V_2_sig*draws_duration_V_2
randcoeff[["Q_participation_2"]] = A_participation_2_mu + A_participation_2_sig*draws_Q_participation_2
randcoeff[["A_participation_2"]] = A_participation_2_mu + A_participation_2_sig*draws_A_participation_2
randcoeff[["e_return_2"]] = e_return_2_mu + e_return_2_sig*draws_Ereturn_2


return(randcoeff)
}


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

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


lcpars[["asc_III"]] = list(asc_III_1, asc_III_2,asc_III_3)
lcpars[["project"]] = list(project_1, project_2,project_3)
lcpars[["carbon"]] = list(carbon_1, carbon_2,carbon_3)
lcpars[["location_Wregion"]] = list(location_Wregion_1, location_Wregion_2,location_Wregion_3)
lcpars[["location_Wcountry"]] = list(location_Wcountry_1, location_Wcountry_2,location_Wcountry_3)
lcpars[["location_Ocountry"]] = list(location_Ocountry_1, location_Ocountry_2,location_Ocountry_3)
lcpars[["min_invest"]] = list(min_invest_1, min_invest_2,min_invest_3)
lcpars[["duration_I"]] = list(duration_I_1, duration_I_2,duration_I_3)
lcpars[["duration_II"]] = list(duration_II_1, duration_II_2,duration_II_3)
lcpars[["duration_V"]] = list(duration_V_1, duration_V_2,duration_V_3)
lcpars[["Q_participation"]] = list(Q_participation_1, Q_participation_2,Q_participation_3)
lcpars[["A_participation"]] = list(A_participation_1, A_participation_2,A_participation_3)
lcpars[["e_return"]] = list(e_return_1, e_return_2,e_return_3)



V=list()
V[["class_a"]] = delta_a
V[["class_b"]] = delta_b
V[["class_c"]] = delta_c #more classes need change


mnl_settings = list(
alternatives = c(class_a=1, class_b=2,class_c=3), #more classes need change
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)
}



# ################################################################# #
#### 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
s=1
while(s<=3){ #change when there are more classes


### Compute class-specific utilities
V=list()
V[['alt1']] = asc_I + project[[s]]*project1 + carbon[[s]]*rescaled_Land_co21 +
location_Wregion[[s]]*location_region_1 + location_Wcountry[[s]]*location_within_country_1 +
location_Ocountry[[s]]*location_out_country_1 + min_invest[[s]]*rescaled_min_invest1 +
duration_I[[s]]*duration_one_1 + duration_II[[s]]*duration_two_1 +
duration_V[[s]]*duration_five_1 + Q_participation[[s]]*participation_quarter_1 +
A_participation[[s]]*participation_annual_1 +
e_return[[s]]*e_return1

V[['alt2']] = asc_I + project[[s]]*project2 + carbon[[s]]*rescaled_Land_co22 +
location_Wregion[[s]]*location_region_2 + location_Wcountry[[s]]*location_within_country_2 +
location_Ocountry[[s]]*location_out_country_2 + min_invest[[s]]*rescaled_min_invest2 +
duration_I[[s]]*duration_one_2 + duration_II[[s]]*duration_two_2 +
duration_V[[s]]*duration_five_2 + Q_participation[[s]]*participation_quarter_2 +
A_participation[[s]]*participation_annual_2 +
e_return[[s]]*e_return2

V[['alt3']] = asc_III[[s]]

mnl_settings$V = V

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

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

### Average across inter-individual draws within classes
P[[s]] = apollo_avgInterDraws(P[[s]], apollo_inputs, functionality)


s=s+1
}

### 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)

Error in apollo_avgInterDraws(P[[s]], apollo_inputs, functionality) :
No Inter-individuals draws to average over!
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #

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

apollo_modelOutput(model)

[stephanehess]

Hi Tim

you are right that this happens because there is no continuous heterogeneity in class 1 and 3.

There are two solutions:

1. You create random coefficients also for the other classes, but with a standard deviation of zero. So for example, you could do:

randcoeff[["project_1"]] = project_1_mu + 0*draws_project

Note that I have changed the name of your draws so you can use the same draws across classes. The project_1_mu parameter will then take on the role of your current project_1 parameter

2. The other option is to make a change inside apollo_probabilities by writing the part for each class separately. So not using a loop, but explicitly writing the code for P[[1]], P[[2]] and P[[3]] and only using apollo_avgInterDraws inside P[[2]]

Solution 1 is probably easier

Best wishes

Stephane

[arohamirai]

Dear Stephane,

Thank you vey much for your help. The model runs successfully, but the standard errors for all parameters are "Inf". This actually happened before when I was running some complex models (e.g., imposing complex distributions such as Johnson SB distribution or polynomial-normal distribution, or latent class with random parameters allowed within each class).

My question is: how should I interpret this "Inf"? Does that imply this model is too complicated and my current dataset is too small to support this kind of complex analysis?

Thank you very much.

Best wishes,
Tim

[stephanehess]

Tim

first, I talked with David yesterday, and he suggested a much simpler solution, which I should have thought of too - thanks, David.

Just replace your line

P[[s]] = apollo_avgInterDraws(P[[s]], apollo_inputs, functionality)

by

if(s==2) P[[s]] = apollo_avgInterDraws(P[[s]], apollo_inputs, functionality)

Then the averaging will only be used in the class where you have draws

Regarding Inf, there are many reasons, have you had a look at the FAQ section in the manual or on the website?

Stephane

[arohamirai]

Hi Stephane,

Thank you very much for your email and David's solution. Also thank you for reminding me reading the corresponding section in the manual which actually helps to solve my problem.

Thank you again.

Best wishes,
Tim