truncated normal for random parameters
Posted: 06 Mar 2026, 09:38
Dear all,
I need to estimate a model with random parameters, imposing a strictly negative or positive distribution for the parameters. I have tried with the negative log-normal distribution in the mixed logit specification, but it has too heavy tail and produces unrealistic marginal rates of substitution. I would like to impose a truncated normal below zero (and I also need a truncated normal above zero for a different parameter). I found a couple of questions in the forum related to this topic, but the issue was not solved.
Below is my code, which now includes normally distributed parameters. I need always negative parameters for ild, diarrea, alop and nausea (they are adverse effects), and always positive coefficient for fs (it represents the efficacy of the treatment); thanks for any help:
I need to estimate a model with random parameters, imposing a strictly negative or positive distribution for the parameters. I have tried with the negative log-normal distribution in the mixed logit specification, but it has too heavy tail and produces unrealistic marginal rates of substitution. I would like to impose a truncated normal below zero (and I also need a truncated normal above zero for a different parameter). I found a couple of questions in the forum related to this topic, but the issue was not solved.
Below is my code, which now includes normally distributed parameters. I need always negative parameters for ild, diarrea, alop and nausea (they are adverse effects), and always positive coefficient for fs (it represents the efficacy of the treatment); thanks for any help:
Code: Select all
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta=c(fs_mu = 0,
fs_sigma = 0,
diarrea_mu = 0,
diarrea_sigma = 0,
alop_mu = 0,
alop_sigma = 0,
nausea_mu = 0,
nausea_sigma = 0,
ild_mu = 0,
ild_sigma = 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()
apollo_draws = list(
interDrawsType = "halton",
interNDraws = 500,
interUnifDraws = c(),
interNormDraws = c("draws_fs","draws_alop","draws_nausea","draws_diarrea","draws_ild")
)
apollo_randCoeff = function(apollo_beta, apollo_inputs){
randcoeff = list()
# NORMAL
randcoeff[["fs"]] = fs_mu + fs_sigma * draws_fs
randcoeff[["diarrea"]] = diarrea_mu + diarrea_sigma * draws_diarrea
randcoeff[["alop"]] = alop_mu + alop_sigma * draws_alop
randcoeff[["nausea"]] = nausea_mu + nausea_sigma * draws_nausea
return(randcoeff)
}
# ################################################################# #
#### 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()
### List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["A"]] = fs*fs_A + diarrea * diarrea_A + alop*alopecia_A + nausea*nausea_A + ild *ild_A
V[["B"]] = fs*fs_B + diarrea * diarrea_B + alop*alopecia_B + nausea*nausea_B + ild *ild_B
### Define settings for MNL model component
mnl_settings = list(
alternatives = c(A=1, B=2),
#avail = list(),
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)
### Media sui draw inter-individuali
P = apollo_avgInterDraws(P, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}