Sample size when using Latent Class Model

[Mayaba]

Dear Michiel,

Thank you for guiding me so far on how to go about generating choice sets using Ngene. Your responses have indeed enhanced my understanding of choice experiments. The last time I posted a question, I forgot to mention I intend to use Latent Class Model to analyse data. I have realised I must change the syntax below to fit the model I intend to use. My questions are as follows:

1. Could you please help change the syntax to suit the intended model?

2. I understand that S - estimate is the minimum sample size requirement, and because I'm using a blocking approach, I have to multiply the S - estimate with the number of blocks. My question is: Do I multiply the main S - estimate with the number of blocks or the S - estimate per parameter?

3. Are the sample size requirements different when using MNL to the Latent Class Model?



Design
;alts = A*, B*, C*, D*, None
;rows = 12
;block = 3, minsum
;eff = (mnl,d)
;alg = mfederov
;reject:


A.nestingperches&scratching = 0 and A.certification = 1,
B.nestingperches&scratching = 0 and B.certification = 1,
C.nestingperches&scratching = 0 and C.certification = 1,
D.nestingperches&scratching = 0 and D.certification = 1,

A.cages = 1 and A.nestingperches&scratching = 0,
B.cages = 1 and B.nestingperches&scratching = 0,
C.cages = 1 and C.nestingperches&scratching = 0,
D.cages = 1 and D.nestingperches&scratching = 0,

A.cages = 0 and A.certification = 1,
B.cages = 0 and B.certification = 1,
C.cages = 0 and C.certification = 1,
D.cages = 0 and D.certification = 1,


A.cages = 1 and A.certification = 0,
B.cages = 1 and B.certification = 0,
C.cages = 1 and C.certification = 0,
D.cages = 1 and D.certification = 0


;model:


U(A) = bcages.dummy [0.145] * cages [1,0] + bnestingperches&scratching.dummy [0.133] * nestingperches&scratching [1,0] + bcertification.dummy [0.15|0.16|0.17] * certification [3,2,1,0] + bmortality.dummy[0.134] * mortality [1,0]
+ bprice[-0.47] * price[4 ,6,8,10](3-5,3-5,3-5,3-5)
/
U(B) = bcages * cages + bnestingperches&scratching * nestingperches&scratching + bcertification * certification + bmortality * mortality + bprice * price /
U(C) = bcages * cages + bnestingperches&scratching * nestingperches&scratching + bcertification * certification + bmortality * mortality + bprice * price /
U(D) = bcages * cages + bnestingperches&scratching * nestingperches&scratching + bcertification * certification + bmortality * mortality + bprice * price /
U(None) = b0[-3]
$

[Michiel Bliemer]

1.
Ngene cannot optimise for estimating a latent class model, and I am not aware anyone else is doing that. It is common to optimise the design for the multinomial logit model, and afterwards estimate multinomial logit, latent class, mixed logit, etc. The data from a design that is optimised for the multinomial logit model can also be used to estimate other model types. The reason that it is generally not practical to optimise for a latent class model is that you would need to obtain parameter priors. Pilot study data is generally not sufficient to estimate such models, which have a very large number of parameters.

If you have 2 classes, you typically have twice as many parameters and therefore your design size (number of rows) needs to be larger and also your sample size needs to be larger (but I cannot tell you how much). If you have 3 classes, you need even larger numbers. You will not know in advance how many classes you need, which again makes practically not possible to optimise the data for estimating the latent class model.

2. You will need to multiply both the main S-estimate as well as the S-estimates per parameter by the number of blocks.

3. Yes, see above, I would increase the number of rows. Sample size estimates can only be computed for the multinomial logit model and we only know that the latent class model needs a large sample.

Michiel

[Mayaba]

Dear Michiel,

Thank you very much for the response, this will help.