Scaled Logitic Model

Question

Hi- need to fit the following logistic model to data, where Y=binary (1=diseased, 0=no-disease) and X is continuous. The model is similar to a logistic but with an added parameter, lambda. Any advice on how to proceed in JMP will be appreciated.

vincem · Answer

Thanks again..I have fitted  the nonlinear model and fitted the below, where prop=n/N in below table. Parameter estimates noted below. i think its worked as its should..

Data is from the publication

https://pubmed.ncbi.nlm.nih.gov/21983214/

titresvaccinenNprop5Non-Flu61190.0504220Non-Flu02040Non-Flu01080Non-Flu040160Non-Flu070320Non-Flu0130453Non-Flu010640Non-Flu0402560Non-Flu0103620Non-Flu0105TIV Control2250.0810TIV Control2360.05555620TIV Control4470.08510628TIV Control01040TIV Control2420.04761957TIV Control01080TIV Control4280.142857113TIV Control010160TIV Control0320226TIV Control010320TIV Control0170640TIV Control0160905TIV Control0201280TIV Control03501810TIV Control0402560TIV Control01903620TIV Control0205120TIV Control0405TIV adj04040TIV adj01080TIV adj010160TIV adj0210226TIV adj020320TIV adj0630453TIV adj070640TIV adj1760.013158905TIV adj0401280TIV adj1630.0158731810TIV adj0402560TIV adj04603620TIV adj0905120TIV adj0100

MRB3855 · Answer

Hi @vincem  It can be done via the method described by @peng_liu  here. The log-likelihood will be different though. See here.

https://community.jmp.com/t5/Discussions/fitting-truncated-data-to-a-continuous-distribution/m-p/772507#M95290

And see section 12.2.1 here (you will need to adapt it slightly to include lambda).

https://www.stat.cmu.edu/~cshalizi/uADA/12/lectures/ch12.pdf

for the log-likelihood function (use the negative log-likelihood as @peng_liu explains)

Questions, come back.

vincem · Answer

thank you very much. however my response is biinary (diseased =1, or not diseased=0) im unsure whether the non-linear platfrom can handle a binary response. appreciate your help. thanks again.