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## In the GLM 'Parameter Estimates' table, is the missing parameter a baseline level?

Hi everyone, I am currently trying to run and interpret a binomial GLM using JMP. I have several categorical predictors. In the Parameter Estimates output table, I noticed that the table presents 1 fewer parameter estimate than the number of levels in the predictor. For example, I have a predictor "year" that has two levels, 1 and 2. Under parameter estimates, only "1" shows up for year with an estimate. Does this mean that "2" is a baseline level which "1" is compared against? If so, does that mean that "2" technically has a parameter estimate of 1.0?

Thanks for the help! Sorry if I am completely misunderstanding how this works.

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## Re: In the GLM 'Parameter Estimates' table, is the missing parameter a baseline level?

This is the same answer to your question regarding the Poisson distribution in GLM:

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 a variable with three levels are -6 and 12 for the first two levels. The parameter estimate for the last level 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
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Staff

## Re: In the GLM 'Parameter Estimates' table, is the missing parameter a baseline level?

This is the same answer to your question regarding the Poisson distribution in GLM:

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 a variable with three levels are -6 and 12 for the first two levels. The parameter estimate for the last level 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
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