Hi everyone! I understood the reason behind alpha_i + beta_j, and the sum of the linear predictors before they combine. I do not understand the logic behind the combinations (as in why we are doing these combinations in the solutions given). Also I would like to ask why the "combination" of gamma_0 and beta_j is not considered? I thought they can be considered too! Please help! Thank you! Regards, Wei Zhe
The reason we combine is because we can't estimate all the parameters otherwise. So every time we add a new covariate will lose one parameter (either think of it being set to zero and other values adjusted, or combined). For example age + sex = \(\gamma_0 + \gamma_1 x + \alpha_i\) has 4 unknowns - the two gammas, and the constant for male and the constant for female. Since there's 4 unknowns surely 4 pieces of information should be able to solve it. So here you go: male age 20 is 61.5 female age 20 is 66.5 male age 30 is 86.5 female age 30 is 91.5
Sir, Thanks for your reply here. I now understand why we combine the parameters. Though what I really want to know is why we do not include \[\gamma_{0} \beta_{j}\] into the new \[\alpha_{i}\] as in the solution. If we were to include it then where will it go? Thank you!
Can you see they have different subscripts? We can't combine them - otherwise that will say the vehicle type is the same category as the gender.
Thank you sir for the clarification regarding why we cannot combine those together. Just one more thing though (Hopefully I did not ask too much, as I struggle at this for quite long already ). Can we combine γ0βj with βj, since they are in a way similar? Note that in the solution that I posted there is no γ0βj. If yes, then I guess the βj in the solution is different with the one in the original equation. Correct? If not, hopefully you can clarify where I went wrong. Thank you!
Yes. You can combine them (as they are both constants with the same subscript). And yes - it will be a different \(\beta_j\) but they've just used the same name (which is confusing!)
