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## Question about GLM with Poisson distribution and parameter estimates

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Aug 13, 2014

Hello all, I am trying to conduct a GLM with poisson distribution in JMP. I want to use 2 categorical variables as predictors for count data. However, I notice that in the "Parameter Estimates" report table, 1 fewer than the number of levels I have for each category shows up with an estimate. For example, I am looking at 3 habitat types, types A, B, and C. Parameter estimates only show up for Types A and B, not C. The same happens for my 4 times of day variables, only 3 show up in parameter estimates. I'm not sure I understand why. Can anyone help me with this?

1 ACCEPTED SOLUTION

Accepted Solutions
Solution

This is typical for any regression when you have a categorical input variable. The parameter estimates for each level of a categorical input are "offsets" from the overall mean. This leads to a restriction that the sum of the parameter estimates for each level is zero. Because of this, if you have k-levels of a categorical factor you only need k-1 parameter estimates. The estimate for the last level is -1 times the sum of the other parameter estimates. For example, suppose your estimates for habitat type are -6 and 12 for levels A and B respectively. The parameter estimate for C is then -1*(-6 + 12) = -1*6 = -6.

In standard least squares regression you can ask for the expanded parameter estimates to see all of them (in other words, JMP will do the math for you). Alas, that is not an option for the generalized linear model.

Dan Obermiller
1 REPLY
Solution

This is typical for any regression when you have a categorical input variable. The parameter estimates for each level of a categorical input are "offsets" from the overall mean. This leads to a restriction that the sum of the parameter estimates for each level is zero. Because of this, if you have k-levels of a categorical factor you only need k-1 parameter estimates. The estimate for the last level is -1 times the sum of the other parameter estimates. For example, suppose your estimates for habitat type are -6 and 12 for levels A and B respectively. The parameter estimate for C is then -1*(-6 + 12) = -1*6 = -6.

In standard least squares regression you can ask for the expanded parameter estimates to see all of them (in other words, JMP will do the math for you). Alas, that is not an option for the generalized linear model.

Dan Obermiller