# Specifying special poisson maximum likelihood

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## Specifying special poisson maximum likelihood

 Hi everyone I am stuck on specifying my own maximum likelihood function for a special poisson model. My poisson model is as follow: O ~ Pois(b*N + b*RR*E) With O = observed cases b = constant (known) N = number of unexposed persons (known) E = number exposed persons (known) RR = relative risk (value is assumed under a scenario, e.g. RR=2.0) I used rpois to simulate the values of O for several years with known values of b, N,  E and RR. Hence, an example simulated data set would look like: O <- c(173, 184, 154, 162, 158, 196, 203, 230, 240, 252, 252, 268, 255, 297, 265, 270, 265, 283) N <- c(1345246.66,1325945.58,1311490.16,1301155.99,1212731.00,1052598.42,889413.52,592314.47,31694.02,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00) E <- c(1387.337,7294.417,13634.838,24372.007,120172.455,290369.579,471271.484,796911.525,1388343.975,1445355.000,1464523.000,1482467.000,1492197.000,1494862.000,1489437.000,1478092.000,1468076.000,1458794.000) In this dataset, I now want to estimate RR under the above model with known values for E and N (the ones above) and the constant b should be treated as nuisance parameter. In addition, no intercept should be estimated. The model formula would thus be: O = b1*N + b2*E Then, I would use a nonlinear combination of the estimates to calculate the RR: RR = (b2/b1) Can anybody help me specifying my own likelihood function to be used with optim? That would help me alot. Thank you. Denis _____________________________________________ Denis Aydin, MSc Swiss Tropical and Public Health Institute Socinstrasse 57, P.O. Box 4002 Basel, Switzerland T +41 (0)61 284 86 09 F +41 (0)61 284 81 01 [hidden email] _____________________________________________ Postal address: Denis Aydin, MSc Swiss Tropical and Public Health Institute Socinstrasse 57, P.O. Box 4002 Basel, Switzerland Visitors address: Eulerstrasse 68 4051 Basel, Switzerland _____________________________________________ www.swisstph.ch         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.