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Level II

## Scaled Logitic Model

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.

4 REPLIES 4
Super User

## Re: Scaled Logitic Model

Hi @vincem : That is the Logistic 3p model in the Nonlinear platform Model Library, where lambda (your model) = theta1, alpha ( your model) = ln(theta2), beta (your model) = theta3.

Level II

## Re: Scaled Logitic Model

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.

Super User

## Re: Scaled Logitic Model

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/772...

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

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

Questions, come back.

Level II

## Re: Scaled Logitic Model

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/

 titres vaccine n N prop 5 Non-Flu 6 119 0.05042 20 Non-Flu 0 2 0 40 Non-Flu 0 1 0 80 Non-Flu 0 4 0 160 Non-Flu 0 7 0 320 Non-Flu 0 13 0 453 Non-Flu 0 1 0 640 Non-Flu 0 4 0 2560 Non-Flu 0 1 0 3620 Non-Flu 0 1 0 5 TIV Control 2 25 0.08 10 TIV Control 2 36 0.055556 20 TIV Control 4 47 0.085106 28 TIV Control 0 1 0 40 TIV Control 2 42 0.047619 57 TIV Control 0 1 0 80 TIV Control 4 28 0.142857 113 TIV Control 0 1 0 160 TIV Control 0 32 0 226 TIV Control 0 1 0 320 TIV Control 0 17 0 640 TIV Control 0 16 0 905 TIV Control 0 2 0 1280 TIV Control 0 35 0 1810 TIV Control 0 4 0 2560 TIV Control 0 19 0 3620 TIV Control 0 2 0 5120 TIV Control 0 4 0 5 TIV adj 0 4 0 40 TIV adj 0 1 0 80 TIV adj 0 1 0 160 TIV adj 0 21 0 226 TIV adj 0 2 0 320 TIV adj 0 63 0 453 TIV adj 0 7 0 640 TIV adj 1 76 0.013158 905 TIV adj 0 4 0 1280 TIV adj 1 63 0.015873 1810 TIV adj 0 4 0 2560 TIV adj 0 46 0 3620 TIV adj 0 9 0 5120 TIV adj 0 10 0