efficent rppanel or bayesian rp model?

[mdann]

Good morning everyone,

I`ve a question relating the choice between two models for my study. I`ve created on the one hand an efficient rppanel design and on the other a bayesian rp model (a rppanel bayesian design does not work). So which one would you declare as the better alternative? Or in other words: is it more desirable to have bayesian or rppanel.

For more explanation: I´ve done a pilot with an orthogonal design. From that I got the priors for my final model and gave them to Ngene.

Thanks for your help.

Micha

[Michiel Bliemer]

In Bliemer and Rose (2010) we showed that RP models yield very different results to RPPANEL models, so I would not suggest using an RP model if you will estimate an RPPANEL model in the end (which is preferable).
Unfortunately, RPPANEL efficient designs are very difficult to generate since they require many repetitions, and therefore it is in most cases not feasible, except for the smallest of models. What we found in Bliemer and Rose (2010) is that an efficient design for the MNL model is in many cases also quite efficient for the RPPANEL model. Further, I would advise to use Bayesian priors as much as possible.

Therefore, I would suggest the following:
- Estimate an MNL model and obtain the parameter estimates and standard errors. Call this model1
- Specify a syntax for model_mnl in Ngene for generating a Bayesian efficient design for this MNL model using normal distributions with a mean set to the parameter estimate and a standard deviation set to the standard error
- Estimate an RPPANEL model and obtain the parameter estimates (means and standard deviations in case you estimate all normally distributed parameters). Call this model2
- Specify a syntax for model_rppanel in Ngene for evaluating an efficient design (with fixed priors) for this RPPANEL model using the parameter estimates.
- Optimise on model_mnl, and evaluate in model_rppanel

The syntax will look something like:

Code: Select all

Design
;alts(model1) = al1, alt2
;alts(model2) = alt1, alt2
;eff = model1(mnl,d,mean)
;rdraws = gauss(3)
;bdraws = gauss(3)
;rep = 1000
;model(model):
U(alt1) = b1[(n,1.2,0.1)] * A[1,2,3] + b2.dummy[(n,0.5,0.1)|(n,1.5,0.2)] * B[1,2,3] + ... /
U(alt2) = ...
;model(model2l):
U(alt1) = b1[n,1.0,0.3] * A[1,2,3] + b2.dummy[n,0.8,0.2|n,1.2,0.1] * B[1,2,3] + ... /
U(alt2) = ...
$


Note that your utility functions and priors will look different, this is just an example. What this syntax will do is it will generate a Bayesian efficient design for the MNL model (model1). But when you click on one of the generated designs, it will evaluate this design for all models that you have specified, hence also model2, which is the RPPANEL model (this may take a little bit of time), so you can see how the design will perform when you would estimate an RPPANEL model without optimising on the RPPANEL model (which is extremely time consuming and usually infeasible). I have specified Gaussian quadrature for the random and Bayesian draws, because these are most efficient, see Bliemer et al. (2008). Note that Gaussian draws are only consistent with the mean, if you would like to use the median, then you need to use quasi-Monte Carlo draws. I would suggest using Sobol draws in that case (which perform better than Halton draws).

Bliemer, M.C.J., and J.M. Rose (2010) Construction of experimental designs for mixed logit models allowing for correlation across choice observations. Transportation Research Part B, Vol. 44, No. 6, pp. 720-734.

Bliemer, M.C.J., J.M. Rose, and S. Hess (2008) Approximation of Bayesian efficiency in experimental choice designs. Journal of Choice Modelling, Vol. 1, pp. 98-127.

[mdann]

Thank you a lot.

What I´d not understand till now is, where is the command for the rppanel in this syntax?

Michael

[Michiel Bliemer]

You can simply use:
;eff = (rppanel,d,mean)
or something similar

[mdann]

Is the 3 after gauss(3) saying, that there are three random parameters?

[Michiel Bliemer]

No it is the number of absciccas

;rdraws = gauss(n) means n^K draws where K is the number of random distributed parameters (Ngene counts them automatically).
;bdraws = gauss(m) means m^L draws where L is the number of Bayesian priors.

The total number of draws is n^K * m^L * rep per design.

[Michiel Bliemer]

Responding again to your comment where rppabel is in the syntax, it need not be there. If you run this syntax, Ngene will automatically report all possible models it can estimate given the information in the syntax. With model2 it can estimate an rppanel model so it automatically reports it when you double click on a design. Give it a try.