ApolloChoiceModelling forum

Dear all,

I’m working with a choice experiment that includes two alternatives (product A and product B), plus an opt-out (no purchase) option. Each product is described by two attributes: *price* and a *binary characteristic* (e.g., a product feature that is either present or not).

We are particularly interested in assessing the *level of substitution* between products A and B. One idea we’re exploring is to estimate a mixed multinomial logit model in the WTP space, using the following specification:


apollo_beta=c(asc_A_mu = 0, asc_A_sig = 0,
asc_B_mu = 0, asc_B_sig = 0,
lambda_mu =-1, lambda_sig= 0,
char_mu = 0, char_sig = 0)

apollo_draws = list(
interDrawsType = "mlhs",
interNDraws = 1000,
interNormDraws = c("draws_asc_A","draws_asc_B",
"draws_lambda",
"draws_char")
)

apollo_randCoeff = function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["asc_A"]] = asc_A_mu + _asc_A_sig * draws_asc_A
randcoeff[["asc_B"]] = asc_B_mu + _asc_B_sig * draws_asc_B
randcoeff[["lambda"]] = -exp(lambda_mu + lambda_sig * draws_lambda)
randcoeff[["char"]] = char_mu + char_sig * draws_char
return(randcoeff)
}

And utility:

V = list()
V[["pA"]] = lambda * (price1 + asc_A + char * (char1 == 1))
V[["pB"]] = lambda * (price2 + asc_B + char * (char2 == 1))
V[["optout"]] = 0


Then, we interpret the *difference between the estimated alternative-specific constants (ASCs)* for A and B as the *willingness to pay (WTP) to keep product A instead of B*, using:

r
subs = apollo_deltaMethod(model, list(operation = "diff", parName1 = "asc_A", parName2 = "asc_B"))


We’d really appreciate your thoughts on this approach:

1. *Is this a valid interpretation* in the WTP space model—i.e., treating the ASC difference as a WTP for choosing A over B, holding all else constant?
2. Are there any *caveats or identification issues* we should keep in mind when interpreting ASC differences this way?
3. Would you recommend any *alternative or complementary approaches* for quantifying substitution between A and B (e.g., cross-elasticities or marginal rates of substitution)?

Many thanks for your time and insights!

Best regards,

Hi

you don't need WTP space to compute WTP from mixed logit, you could use preference space with appropriate distributions.

But in general, WTP for ASC is not generally something I would recommend as ASCs capture a range of different factors, incuding possible ordering effects

Stephane