Scaled Logitic Model

[#1]

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.

[#2]

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.

[#3]

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.

[#4]

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).

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.

[#5]

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