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Star terms - generalised linear models

J

jolien

Member
Hi all
Something that isn't clear to me after reading Chapter 10 is: when you have a star term consisting of 3 covariates, does that imply a three-way interaction term as well as the 3 two-way interaction terms? i.e. is it true that ---
a*b*c
means
a + b + c + a.b + b.c + a.c + a.b.c
???
Obviously the notes cover the situation where there are 2 covariates and explicitly says that
a*b = a + b + a.b
But i have looked back through the notes and can't find any explanation of a*b*c.

The reason why i ask is that when i got to question 3.17 (iv) in the Q&A Bank this uncertainty meant that i couldn't say what the degrees of freedom should be for YO*FS*TC. I think given that the answers say it has zero DF, it must include the three-way interaction term.


Many thanks...
Jolien
 
jolien said:
Hi all
Something that isn't clear to me after reading Chapter 10 is: when you have a star term consisting of 3 covariates, does that imply a three-way interaction term as well as the 3 two-way interaction terms? i.e. is it true that ---
a*b*c
means
a + b + c + a.b + b.c + a.c + a.b.c
???
Obviously the notes cover the situation where there are 2 covariates and explicitly says that
a*b = a + b + a.b
But i have looked back through the notes and can't find any explanation of a*b*c.

The reason why i ask is that when i got to question 3.17 (iv) in the Q&A Bank this uncertainty meant that i couldn't say what the degrees of freedom should be for YO*FS*TC. I think given that the answers say it has zero DF, it must include the three-way interaction term.


Many thanks...
Jolien
Click to expand...

Further to this - in the same Q&A Bank question 3.17 (iv) it has the heading "Deviance" in the table but it actually means "Scaled deviance". Are these terms sometimes used interchangeably - even though the course notes have defined "deviance" to be a different metric altogether?
 
Yes. It would include all interaction terms.

Deviance is the scaled deviance multiplied by the scale parameter \(\phi\). However, the only time it's mentioned in exams is for the Poisson or Exponential where the scale parameter is 1. Hence they are equal.
 
Ah understood thanks. Looking back at question 3.17 it doesn't specifically say it's a Poisson or Expo model. Should i be able to tell given what they have said in the question or is it just assumed?
 
Oops! That's our bad. Apologies - I'll get this into the corrections document. Unfortunately, we've signed off the 2017 materials :(
 
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