[Limdep Nlogit List] Generating Orthogonal Experiment

[John Rose]

Dear Anat

Your requirement for an orthogonal design should depend upon the type of model you are after. If you are estimating a regression model, then the variance covariance matrix is sigma^2(X'X)-1 where X is your design. An orthogonal design will generally minimise this matrix and hence minimise the standard errors (maximise your t-ratios) and produce zero covariances. If you are estimating a discrete choice model however, the VC matrix is NOT sigma^2(X'X)-1, and you will not minimise the standard errors (maximise your t-ratios) or produce zero covariances using an orthogonal design, unless there are a special set of circumstances that exist. 

Basically, the reason people use orthogonal designs is because they want to obtain independent estimates (zero covariances). If you are using an orthogonal design for DCMs (logits and probits), then you will only get zero covariances if all the parameters are zero. The minute the parameters are not zero, then you will get non-zero covariances. This is because the formulas for the VC matrix of DCM are not those of linear regression models. They actually have probabilities in them, and only if the parameters are zero (and hence the probabilities all go to 1/J) will the covariances go to zero. Thus, talk of main effects and interaction effects designs for DCMs is really meaningless, as the designs ability to get independent main effects and interaction effects (zero covariances) depends upon the parameter estimates (which influence the probabilities). This terminology has meaning only for linear models (which historically is where all the experimental design literature came from - ANOVA to be precise which is simply nothing more than a regression model). There is a huge literature now on this exact issue (mainly in marketing but also in other areas).
 
There are other software available to do orthogonal designs beyond SAS as well as well as software that is specifically designed to construct designs for DCMs. I am happy to discuss these with you outside of the Limdep list if you wish to contact me (johnr at itls.usyd.edu.au).

John

-----Original Message-----
From: limdep-bounces at limdep.itls.usyd.edu.au [mailto:limdep-bounces at limdep.itls.usyd.edu.au] On Behalf Of Leif
Sent: Tuesday, 24 February 2009 12:13 PM
To: Limdep and Nlogit Mailing List
Subject: Re: [Limdep Nlogit List] Generating Orthogonal Experiment

Anat,

I believe the answer to your question about Limdep is no, but I might be able to help if you have access to SAS.

I'd need more details to truly be of any help.  Orthogonal isn't specific enough.  Are you looking for a main effects only or a higher resolution? I assume you'd want a design built for a choice model but there are numerous examples in the literature where choice models have been estimated on designs built for linear models as well so that would be up to you.  After I learned more about what type of design you're seeking I could walk you through the steps associated with creating an experimental design in SAS.

Cheers,

Leif Anderson
leifand at u.washington.edu





On Mon, 23 Feb 2009, Dr. Anat Tchetchik wrote:

> Dear all!
>
>
>
> Does anyone know whether NLOGIT have a routine for creating an Orthogonal
> design (specifically, we have 4 alternatives and 4 characteristics that
> describe each alternative)
>
> Thanks in advance for any guiding help
>
>
>
> Best,
>
> Anat Tchetchik, Ph.D.
>
> The Department of Agricultural Economics
>
> The Hebrew University of Jerusalem
>
> Tel: 08-9489231
>
> cell: 054-4928740
>
>
>
>
>
> _______________________________________________
> Limdep site list
> Limdep at limdep.itls.usyd.edu.au
> http://limdep.itls.usyd.edu.au
>


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