Actuarial Outpost Poisson Regression
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#1
12-03-2018, 03:53 PM
 we7dude Member Join Date: Jan 2009 College: Temple Alumni Posts: 325
Poisson Regression

HI all,

Let's say that I am modeling number of claim count an insurance company have. I vaguely remember that if the deviacne/DF is approx 1.000 (in SAS Genmod) and we can safely assume the data fits Poisson well. In the case where the data doesn't fit Poisson, we can throw in the command "scale=deviance or pearson" to "fix" it. What is this command is doing? any explanation is appreciated. Ideally I want to be able to calculate by hand to fully understand it. Thanks in advance.
#2
12-03-2018, 04:00 PM
 CuriousGeorge Member CAS SOA Join Date: Dec 2005 Posts: 1,453

From the SAS documentation, you are setting the scale parameter per the option you select:
Quote:
 sets the value used for the scale parameter where the NOSCALE option is used. For the binomial and Poisson distributions, which have no free scale parameter, this can be used to specify an overdispersed model. In this case, the parameter covariance matrix and the likelihood function are adjusted by the scale parameter. See the section Dispersion Parameter and the section Overdispersion for more information. If the NOSCALE option is not specified, then number is used as an initial estimate of the scale parameter. Specifying SCALE=PEARSON or SCALE=P is the same as specifying the PSCALE option. This fixes the scale parameter at the value 1 in the estimation procedure. After the parameter estimates are determined, the exponential family dispersion parameter is assumed to be given by Pearson’s chi-square statistic divided by the degrees of freedom, and all statistics such as standard errors and likelihood ratio statistics are adjusted appropriately. Specifying SCALE=DEVIANCE or SCALE=D is the same as specifying the DSCALE option. This fixes the scale parameter at a value of 1 in the estimation procedure. After the parameter estimates are determined, the exponential family dispersion parameter is assumed to be given by the deviance divided by the degrees of freedom. All statistics such as standard errors and likelihood ratio statistics are adjusted appropriately.