Currently I am working on the sample size determination of Discrete Choice Experiment. We thought of using mixed logit model . For the sample size determination, initial value parameter is one of the factors. My understanding is that for mixed logit model the initial value parameter for each individual needs to be obtained. But I am not understanding how initial value parameter is obtained? Also, how can we take Asymptotic Variance Co-Variance matrix in mixed logit model for sample size determination?
In ideal condition for discrete distribution (1,0), say one flips a coin---ultimately one should obtain 50/50 for heads and tails in a so-called "fair coin." If so then ideally, P = 0.50 and Q = 0.50; using Cochran's sample equation for discrete data:
n = (Z2PQ) / e2
where Z = critical value at a specific confidence interval; P = 0.50 and Q = 0.50. The error term e = 0.05 for 95% confidence interval. Assume e = 0.05, Z = 1.65 then:
n = [(1.652)(0.5)(0.50)] / 0.502
n = [(2.7225)(0.25)] / 0.0025
n = 0.68 / 0.0025
n = 272 >>>>>> This is you minimum sample size for discrete variable. NO IT IS NOT n = 30; THAT IS FOR "CONTINUOUS" data. In the calculation, if Z = 1.97, then the result would be n = 388 which is almost the same as under finite population scenario under Yamane sample size where n = 400 (approximately).
I was going to give you some theory but this might be easier. Do a rough pilot expt. Run the data. From this you get rough estimates of the coefs, SEs and your var-Cov matrix. Use these in your sample size program to get estimates of your sample size for each term in your model. Choose the biggest of these sample sizes. OK?
Best wishes, David Booth
Paul Louangrath Thank you for your replay .But I am searching for sample size determination for Discrete Choice Experiment . It will be good if you could help me with that.
Thank you
David Eugene Booth Thank you for your replay.We created a dummy data, worked on it using R.We got variance-Co variance matrix but we have some doubts about estimates. It will be helpful for our research if you can share any documents regarding the R code of mixed logit model in discrete choice experiments.
Thank you
Hi, I do not have any current code myself but some of the papers in the following link reference R packages etc which you might find helpful. I don't know how you built your dummy data set, but please be sure that it gets you roughly close to the parameters you want to estimate so that your sample size will be approx. Correct. If you can take a small sample of real data by whatever means you have available that might be best. Wish you good luck and may the force be with you. David Booth Here is the promised link:
https://www.google.com/search?q=mixed+logit+model+for+discrete+choice+experiment+in+R&rlz=1C1CHBF_enUS847US847&oq=mixed+logit+model+for+discrete+choice+experiment+in+R&aqs=chrome..69i57j33.37686j0j8&sourceid=chrome&ie=UTF-8
David Eugene Booth
We are trying to find the sample size in an electricity data. We got the this data from the package mlogit in R. Here the data set consist of 359 individuals each having 12 choice set. There are six attributes having 4 levels each and the number of alternatives are 4. When got the output as estimate of the parameter ( sd.param.param )which we took as the asymptotic variance covariance matrix matix.By using this information we calculated sample size,but we are getting very small sample size.Maximum value we got is 10.While reading some document we came across Cholesky decomposition.IS this decomposition is necessary to find the AVC matix.Also how can we get Cholesky decomposition in mixed logit.
Wow . 30 years ago Cholesky decomposition was very popular in variable selection circles. Ah ha this link tells us that cholesky is often used with sparse matrices There is a book that might help, see this link:https://b-ok.cc/s/?q=statistical+learning+sparsity. Sparse matrices have been associated with variable selection for some time. My guess is that the algorithm you are using uses sparse matrices which may be why say, if this result was intermediate, you might get smaller estimates. This link might help as well: https://cran.r-project.org/web/packages/mlogit/mlogit.pdf It is the documentation for mlogit and gives the email of the maintainer who should know everything about the package. Email him, explain your problem and see what he can tell you. He may know where in the computations larger sample size estimates are hiding. I hope some of this is of value to you. For sure-check out that book and e-mail the maintainer. Let me know what happens, please? May the Force be with you, David
This may be of help
Yinmei Li ( 2006) Power analysis for a mixed effects logistic regression model
https://pdfs.semanticscholar.org/236e/473be39268e31f313e4280b727b004f340fc.pdf
@ David Eugene Booth We have referred the book you shared and waiting for the reply from the maintainer.
Thank you
David Eugene Booth The code was working now but we have some confusion regarding the number of choice sets we need to provide. Our understanding is that from full factorial design we need to subset and obtain the optimal number of choice set.
We got 36 as an optimal design from full factorial design. Since it is very difficult for an individual to answer all the 36 choice set, for convenience we divide it into 3 blocks (36/3=12). We referred the below document for the sample size determination. Here, for finding the sample size, number of choice set is an important criterion. We need some clarification regarding the number of choice set need to provide ie whether we need to give the choice set of the block ( n=12) or choice set of the subset from full factorial(n=36) .
https://link.springer.com/content/pdf/10.1007%2Fs40271-015-0118-z.pdf
Can you help us with this ?
Thank you
@ David Eugene Booth
The code was working now but we have some confusion regarding the number of choice sets we need to provide. Our understanding is that from full factorial design we need to subset and obtain the optimal number of choice set.
We got 36 as an optimal design from full factorial design. Since it is very difficult for an individual to answer all the 36 choice set, for convenience we divide it into 3 blocks (36/3=12). We referred the below document for the sample size determination. Here, for finding the sample size, number of choice set is an important criterion. We need some clarification regarding the number of choice set need to provide ie whether we need to give the choice set of the block ( n=12) or choice set of the subset from full factorial(n=36) .
https://link.springer.com/content/pdf/10.1007%2Fs40271-015-0118-z.pdf
Can you help us with this ?
Thank you
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