ordinal logit using second-order latent variables

[idserrano]

Dear developers of Apollo, first, thanks for this powerful and flexible package. It’s amazing!

I’m trying to estimate an ordinal logit using second-order latent variables (LVs). I attached de path diagram of the model to explain me better. The idea is to describe how specific groups can change the purchase habits of respondents due to covid 19. Each group is measured through two indicators: knowledge and trust. Each indicator is ordinal on a four-point Likert scale. For example, nat_gov (national government) group is measured with know_natgov and trust_natgov. I specified the ol_settings like this:

ol_settings_know_natgov = list(outcomeOrdered=know_natgov,
V=zeta_know_natgov*nat_gov,
tau=c(tau_1_know_natgov, tau_2_know_natgov, tau_3_know_natgov),
rows=(task==1))
ol_settings_trust_natgov = list(outcomeOrdered=trust_natgov,
V=zeta_trust_natgov*nat_gov,
tau=c(tau_1_trust_natgov, tau_2_trust_natgov, tau_3_trust_natgov),
rows=(task==1))

For another latent group: loc_gov (local government), I did the same, and so on with all the groups:

ol_settings_know_logov = list(outcomeOrdered=know_logov,
V=zeta_know_logov*loc_gov,
tau=c(tau_1_know_logov, tau_2_know_logov, tau_3_know_logov),
rows=(task==1))
ol_settings_trust_logov = list(outcomeOrdered=trust_logov,
V=zeta_trust_logov*loc_gov,
tau=c(tau_1_trust_logov, tau_2_trust_logov, tau_3_trust_logov),
rows=(task==1))

Then, the latent groups are grouped to form another latent group, for example, government (gov) is formed through the latent groups nat_gov and loc_gov. To make this, I used apollo_randCoeff and son on with all the groups:

randcoeff[["gov"]] = gamma_nat_gov * nat_gov + gamma_loc_gov * loc_gov + eta_gov

My utility function is:

ol_settings_change = list(outcomeOrdered=change,
V= asc + beta_gov * gov + beta_loc_rpnd_org * loc_rpnd_org + beta_int_rpnd_org * int_rpnd_org + beta_news * news + beta_pol_fire * pol_fire,
tau=c(tau_1_change, tau_2_change),
rows=(task==1))
P[["change"]] = apollo_ol(ol_settings_change, functionality)

However, the apollo_inputs function output the error: “Error in f(apollo_beta, apollo_inputs) : objeto 'nat_gov' no encontrado”. I suppose that since 'nat_gov' is latent, the package does not understand that it is. I would like to know why?. Thank you. Best regards

IS
_______________________
The full code is:
library(apollo)
database<-read_csv("bd.csv",col_names=TRUE)
apollo_initialise()
apollo_control = list(
modelName ="Ordinal hybrid model Change v0",
modelDescr ="Ordinal hybrid model Change v0",
indivID ="id",
mixing = TRUE,
nCores = 8
)
apollo_beta=c(asc =0,
gamma_nat_gov =0,
gamma_loc_gov =0,
gamma_health_off =0,
gamma_loc_emer_rpnd =0,
gamma_loc_rlf_org =0,
gamma_int_rlf_org =0,
gamma_red_crs =0,
gamma_trad_news =0,
gamma_elec_news =0,
gamma_poli =0,
gamma_fire =0,
zeta_know_natgov =0,
tau_1_know_natgov =-1,
tau_2_know_natgov =0,
tau_3_know_natgov =1,
zeta_trust_natgov =0,
tau_1_trust_natgov =-1,
tau_2_trust_natgov =0,
tau_3_trust_natgov =1,
zeta_know_logov =0,
tau_1_know_logov =-1,
tau_2_know_logov =0,
tau_3_know_logov =1,
zeta_trust_logov =0,
tau_1_trust_logov =-1,
tau_2_trust_logov =0,
tau_3_trust_logov =1,
zeta_know_health =0,
tau_1_know_health =-1,
tau_2_know_health =0,
tau_3_know_health =1,
zeta_trust_health =0,
tau_1_trust_health =-1,
tau_2_trust_health =0,
tau_3_trust_health =1,
zeta_know_localem =0,
tau_1_know_localem =-1,
tau_2_know_localem =0,
tau_3_know_localem =1,
zeta_trust_localem =0,
tau_1_trust_localem =-1,
tau_2_trust_localem =0,
tau_3_trust_localem =1,
zeta_know_localrelief =0,
tau_1_know_localrelief =-1,
tau_2_know_localrelief =0,
tau_3_know_localrelief =1,
zeta_trust_localrelief =0,
tau_1_trust_localrelief =-1,
tau_2_trust_localrelief =0,
tau_3_trust_localrelief =1,
zeta_know_ingo =0,
tau_1_know_ingo =-1,
tau_2_know_ingo =0,
tau_3_know_ingo =1,
zeta_trust_ingo =0,
tau_1_trust_ingo =-1,
tau_2_trust_ingo =0,
tau_3_trust_ingo =1,
zeta_know_redcross =0,
tau_1_know_redcross =-1,
tau_2_know_redcross =0,
tau_3_know_redcross =1,
zeta_trust_redcross =0,
tau_1_trust_redcross =-1,
tau_2_trust_redcross =0,
tau_3_trust_redcross =1,
zeta_know_news =0,
tau_1_know_news =-1,
tau_2_know_news =0,
tau_3_know_news =1,
zeta_trust_news =0,
tau_1_trust_news =-1,
tau_2_trust_news =0,
tau_3_trust_news =1,
zeta_know_social =0,
tau_1_know_social =-1,
tau_2_know_social =0,
tau_3_know_social =1,
zeta_trust_social =0,
tau_1_trust_social =-1,
tau_2_trust_social =0,
tau_3_trust_social =1,
zeta_know_police =0,
tau_1_know_police =-1,
tau_2_know_police =0,
tau_3_know_police =1,
zeta_trust_police =0,
tau_1_trust_police =-1,
tau_2_trust_police =0,
tau_3_trust_police =1,
zeta_know_fire =0,
tau_1_know_fire =-1,
tau_2_know_fire =0,
tau_3_know_fire =1,
zeta_trust_fire =0,
tau_1_trust_fire =-1,
tau_2_trust_fire =0,
tau_3_trust_fire =1,
beta_gov =0,
beta_loc_rpnd_org =-1,
beta_int_rpnd_org =0,
beta_news =1,
beta_pol_fire=0,
tau_1_change=-1,
tau_2_change=0)
apollo_fixed = c("asc")
apollo_draws = list(
interDrawsType="halton",
interNDraws=500,
interUnifDraws=c(),
interNormDraws=c("eta_gov","eta_loc_rpnd_org","eta_int_rpnd_org","eta_news","eta_pol_fire"),
intraDrawsType='',
intraNDraws=0,
intraUnifDraws=c(),
intraNormDraws=c()
)
apollo_randCoeff=function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["gov"]] = gamma_nat_gov * nat_gov + gamma_loc_gov * loc_gov + eta_gov
randcoeff[["loc_rpnd_org"]] = gamma_health_off * health_off + gamma_loc_emer_rpnd * loc_emer_rpnd + gamma_loc_rlf_org * loc_rlf_org + eta_loc_rpnd_org
randcoeff[["int_rpnd_org"]] = gamma_int_rlf_org * int_rlf_org + gamma_red_crs * red_crs + eta_int_rpnd_org
randcoeff[["news"]] = gamma_trad_news * trad_news + gamma_elec_news * elec_news + eta_news
randcoeff[["pol_fire"]] = gamma_poli * poli + gamma_fire * fire + eta_pol_fire
return(randcoeff)
}
apollo_inputs = apollo_validateInputs()
#definir apollo probabilities function
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))
P = list()
### Likelihood of indicators
#####gov
ol_settings_know_natgov = list(outcomeOrdered=know_natgov,
V=zeta_know_natgov*nat_gov,
tau=c(tau_1_know_natgov, tau_2_know_natgov, tau_3_know_natgov),
rows=(task==1))
ol_settings_trust_natgov = list(outcomeOrdered=trust_natgov,
V=zeta_trust_natgov*nat_gov,
tau=c(tau_1_trust_natgov, tau_2_trust_natgov, tau_3_trust_natgov),
rows=(task==1))
ol_settings_know_logov = list(outcomeOrdered=know_logov,
V=zeta_know_logov*loc_gov,
tau=c(tau_1_know_logov, tau_2_know_logov, tau_3_know_logov),
rows=(task==1))
ol_settings_trust_logov = list(outcomeOrdered=trust_logov,
V=zeta_trust_logov*loc_gov,
tau=c(tau_1_trust_logov, tau_2_trust_logov, tau_3_trust_logov),
rows=(task==1))
ol_settings_know_health = list(outcomeOrdered=know_health,
V=zeta_know_health*health_off,
tau=c(tau_1_know_health, tau_2_know_health, tau_3_know_health),
rows=(task==1))
ol_settings_trust_health = list(outcomeOrdered=trust_health,
V=zeta_trust_health*health_off,
tau=c(tau_1_trust_health, tau_2_trust_health, tau_3_trust_health),
rows=(task==1))
ol_settings_know_localem = list(outcomeOrdered=know_localem,
V=zeta_know_localem*loc_emer_rpnd,
tau=c(tau_1_know_localem, tau_2_know_localem, tau_3_know_localem),
rows=(task==1))
ol_settings_trust_localem = list(outcomeOrdered=trust_localem,
V=zeta_trust_localem*loc_emer_rpnd,
tau=c(tau_1_trust_localem, tau_2_trust_localem, tau_3_trust_localem),
rows=(task==1))
ol_settings_know_localrelief = list(outcomeOrdered=know_localrelief,
V=zeta_know_localrelief*loc_rlf_org,
tau=c(tau_1_know_localrelief, tau_2_know_localrelief, tau_3_know_localrelief),
rows=(task==1))
ol_settings_trust_localrelief = list(outcomeOrdered=trust_localrelief,
V=zeta_trust_localrelief*loc_rlf_org,
tau=c(tau_1_trust_localrelief, tau_2_trust_localrelief, tau_3_trust_localrelief),
rows=(task==1))
ol_settings_know_ingo = list(outcomeOrdered=know_ingo,
V=zeta_know_ingo*int_rlf_org,
tau=c(tau_1_know_ingo, tau_2_know_ingo, tau_3_know_ingo),
rows=(task==1))
ol_settings_trust_ingo = list(outcomeOrdered=trust_ingo,
V=zeta_trust_ingo*int_rlf_org,
tau=c(tau_1_trust_ingo, tau_2_trust_ingo, tau_3_trust_ingo),
rows=(task==1))
ol_settings_know_redcross = list(outcomeOrdered=know_redcross,
V=zeta_know_redcross*red_crs,
tau=c(tau_1_know_redcross, tau_2_know_redcross, tau_3_know_redcross),
rows=(task==1))
ol_settings_trust_redcross = list(outcomeOrdered=trust_redcross,
V=zeta_trust_redcross*red_crs,
tau=c(tau_1_trust_redcross, tau_2_trust_redcross, tau_3_trust_redcross),
rows=(task==1))
ol_settings_know_news = list(outcomeOrdered=know_news,
V=zeta_know_news*trad_news,
tau=c(tau_1_know_news, tau_2_know_news, tau_3_know_news),
rows=(task==1))
ol_settings_trust_news = list(outcomeOrdered=trust_news,
V=zeta_trust_news*trad_news,
tau=c(tau_1_trust_news, tau_2_trust_news, tau_3_trust_news),
rows=(task==1))
ol_settings_know_social = list(outcomeOrdered=know_social,
V=zeta_know_social*elec_news,
tau=c(tau_1_know_social, tau_2_know_social, tau_3_know_social),
rows=(task==1))
ol_settings_trust_social = list(outcomeOrdered=trust_social,
V=zeta_trust_social*elec_news,
tau=c(tau_1_trust_social, tau_2_trust_social, tau_3_trust_social),
rows=(task==1))
ol_settings_know_police = list(outcomeOrdered=know_police,
V=zeta_know_police*poli,
tau=c(tau_1_know_police, tau_2_know_police, tau_3_know_police),
rows=(task==1))
ol_settings_trust_police = list(outcomeOrdered=trust_police,
V=zeta_trust_police*poli,
tau=c(tau_1_trust_police, tau_2_trust_police, tau_3_trust_police),
rows=(task==1))
ol_settings_know_fire = list(outcomeOrdered=know_fire,
V=zeta_know_fire*fire,
tau=c(tau_1_know_fire, tau_2_know_fire, tau_3_know_fire),
rows=(task==1))
ol_settings_trust_fire = list(outcomeOrdered=trust_fire,
V=zeta_trust_fire*fire,
tau=c(tau_1_trust_fire, tau_2_trust_fire, tau_3_trust_fire),
rows=(task==1))
P[["indic_know_natgov"]] = apollo_ol(ol_settings_know_natgov, functionality)
P[["indic_trust_natgov"]] = apollo_ol(ol_settings_trust_natgov, functionality)
P[["indic_know_logov"]] = apollo_ol(ol_settings_know_logov, functionality)
P[["indic_trust_logov"]] = apollo_ol(ol_settings_trust_logov, functionality)
P[["indic_know_health"]] = apollo_ol(ol_settings_know_health, functionality)
P[["indic_trust_health"]] = apollo_ol(ol_settings_trust_health, functionality)
P[["indic_know_localem"]] = apollo_ol(ol_settings_know_localem, functionality)
P[["indic_trust_localem"]] = apollo_ol(ol_settings_trust_localem, functionality)
P[["indic_know_localrelief"]] = apollo_ol(ol_settings_know_localrelief, functionality)
P[["indic_trust_localrelief"]] = apollo_ol(ol_settings_trust_localrelief, functionality)
P[["indic_know_ingo"]] = apollo_ol(ol_settings_know_ingo, functionality)
P[["indic_trust_ingo"]] = apollo_ol(ol_settings_trust_ingo, functionality)
P[["indic_know_redcross"]] = apollo_ol(ol_settings_know_redcross, functionality)
P[["indic_trust_redcross"]] = apollo_ol(ol_settings_trust_redcross, functionality)
P[["indic_know_news"]] = apollo_ol(ol_settings_know_news, functionality)
P[["indic_trust_news"]] = apollo_ol(ol_settings_trust_news, functionality)
P[["indic_know_social"]] = apollo_ol(ol_settings_know_social, functionality)
P[["indic_trust_social"]] = apollo_ol(ol_settings_trust_social, functionality)
P[["indic_know_police"]] = apollo_ol(ol_settings_know_police, functionality)
P[["indic_trust_police"]] = apollo_ol(ol_settings_trust_police, functionality)
P[["indic_know_fire"]] = apollo_ol(ol_settings_know_fire, functionality)
P[["indic_trust_fire"]] = apollo_ol(ol_settings_trust_fire, functionality)

ol_settings_change = list(outcomeOrdered=change,
V= asc + beta_gov * gov + beta_loc_rpnd_org * loc_rpnd_org + beta_int_rpnd_org * int_rpnd_org + beta_news * news + beta_pol_fire * pol_fire,
tau=c(tau_1_change, tau_2_change),
rows=(task==1))
P[["change"]] = apollo_ol(ol_settings_change, functionality)
### Likelihood of the whole model
P = apollo_combineModels(P, apollo_inputs, 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)
}
#estimar el modelo
# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #

### Optional: calculate LL before model estimation
apollo_llCalc(apollo_beta, apollo_probabilities, apollo_inputs)

### Estimate model
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)

[stephanehess]

Hi

the problem is that you have not created nat_gov anywhere. This needs to be included in apollo_randCoeff.

Hope this helps

Stephane

[idserrano]

Thanks for the reply prof Hess, I created the randCoeff nat_gov this:

apollo_draws = list(
interDrawsType="mlhs",
interNDraws=1000,
interUnifDraws=c(),
interNormDraws=c("eta_nat_gov"),
intraDrawsType='',
intraNDraws=0,
intraUnifDraws=c(),
intraNormDraws=c()
)
randcoeff[["nat_gov"]] = eta_nat_gov

However, I got the same Error:

Error in f(apollo_beta, apollo_inputs) : objeto 'nat_gov' no encontrado

[stephanehess]

Can you please show us the whole code again, not just the extracts

[idserrano]

Prof Hess, I solved the problem in my code. It was that I specified the second-order latent variable in the wrong form:

randcoeff[["gov"]] = gamma_nat_gov * nat_gov + gamma_loc_gov * loc_gov

And the correct form is:

randcoeff[["gov"]] = gamma_nat_gov * randcoeff[["nat_gov"]] + gamma_loc_gov * randcoeff[["loc_gov"]].

Also, I deactivated (analyticGrad=FALSE). The code ran without a problem.

Professor, I have another doubt. Should I create an error term of the second-order variable or not? I mean, for example:

Lv1 = gama*x1 + eta1;
Lv2 = gama*x2 + eta2;

Lv3 = Lv1 + Lv2; or
Lv3 = Lv1 + Lv2 + eta3;

Being eta_i a normal random draw.

Thanks for the guidance,

Bests,

IS

[stephanehess]

Hi

regarding your question of creating an additional error for LV3, this depends on whether in your model, LV1 and LV2 are used separately from LV3 too as this will determine whether you can identify an additional source of error

Stephane

[idserrano]

Thanks, prof very useful your suggestion

Bests