number of choice tasks needed in estimating MXL, LCM

[Yana]

Hi
I have a question about the number of choice tasks (number of rows) needed in estimating mixed logit models, latent class models etc.

I learn from Ngene manual and this forum that when talking about the number of choice tasks, it should be at minimum S, where S*(J-1)>=K. In our study, the J =3 (two alternative and 1 opt-out, though I am not sure if opt-out should count as in J in this equation); K has 3-4 attributes (depending on versions of survey). Considering we are interested in some interactions, I would say that S=8 or 12 is more than enough. Moreover, when I tried bigger designs with 18, 24 rows for the version with 3 attributes, Ngene report it difficult to generate efficient design with "not having enough attributes or attribute levels for the number of rows required". Therefore, I think S=8, 12 can work.

Then going back to the question about estimating mixed logit models, latent class models. I read related literature and understand that for these models, data richness is beneficial for capturing e.g., taste heterogeneity, but how rich is enough richness in these models is not clear to me. One of my colleagues has used much larger designs (with 64 tasks, though attribute number is bigger, it is 5.) and suggests me that number of rows =8 or 12 seems quite low and therefore is not sure whether it will work with all possible models we way want to run... I don't have a direct answer to this. Therefore any ideas on our concern will be very much appreciated.

[Michiel Bliemer]

An opt-out counts as an alternative in J, yes.
K is essentially the number of parameters you are estimating. If you estimate dummy or effects coded parameters, then K is larger than the number of attributes. Also, if you are estimating a mixed logit model, you estimate a mean and standard deviation for each coefficient, again increasing the number of parameters. So for mixed logit models and latent class models with say 3 classes, you need at minimum double the number of choice tasks.

There is no easy guideline to state how many is enough, but often Ngene can give you an idea when you increase the number of rows and see what this does to your D-error. If you normalise the D-error by correcting it for the number of choice tasks, you can see whether this normalised D-error stabilises. Once it has stabilised, you have enough 'richness'. We have done this in one of our papers:

Rose, J.M. and M.C.J. Bliemer (2013) Sample size requirements for stated choice experiments. Transportation, Vol. 40, No. 5, pp. 1021-1041

On the other hand, if you are not sure, it does not harm to use a larger design and simply block/split this design into smaller pieces to give to a respondent. It is more harmful using a too small design than to use a design that is large.