• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Differentiating a summation

H

hatton02

Member
On the GLM chapter and on one of the answers it goes from:

ln L (mu_ij) = sum over i sum over j (- mu_ij + y_ij ln mu_ij) + const

Then:

d ln L/d mu_ij = -1 + y_ij/mu_ij = 0.

Why have the summations been ignored? I was trying to put some values of i and j in there to get rid of the summations but I got confused with what it means.

Indeed in the next question it's a very similar thing but with no ij subscripts on the mu but they keep the summations. Anyone help please?

(Apr 2004 question 9)
 
hatton02 said:
On the GLM chapter and on one of the answers it goes from:

ln L (mu_ij) = sum over i sum over j (- mu_ij + y_ij ln mu_ij) + const

Then:

d ln L/d mu_ij = -1 + y_ij/mu_ij = 0.

Why have the summations been ignored? I was trying to put some values of i and j in there to get rid of the summations but I got confused with what it means.

Indeed in the next question it's a very similar thing but with no ij subscripts on the mu but they keep the summations. Anyone help please?

(Apr 2004 question 9)
Click to expand...

Suppose we consider mu13 - only one of all the 12 summations has this particular term - so when we differentiate with respect to mu13 we'll only get that particular part of the summation.

Whereas mu is in all of the 12 summations - so they stay when we differentiate.

Does that help?
 
You must log in or register to reply here.
Back
Top