This paper is organized as follows. First the concept of robust profile likelihood functions
that motivates the RPR model is briefly described in Section 2. In Section 3 the adjustment
that makes the Poisson working model robust for the population mean parameter is given
for independent and identically distributed (iid) count data. RPR models for the identity
link and for the log link functions are presented in Sections 4 and 5, respectively. Section
6 includes simulation studies that demonstrate the effectiveness of the RPR model
for data actually generated from non-Poisson distributions. Concluding remarks are given
in Section 7