CT6 IFoA April 2013 Q7

[pbrown]

Hi John

I am hoping that you can help me with the second part of this question. I do not understand how they have calculated the 10, 7 and 1 degrees of freedom for those three models. I understand that the first model has 4 x 3 = 12 degrees of freedom because there are 4 groups for location and three groups for age.

I have watched your review of the paper on youtube and you don't seem to explain it.

Would appreciate your help

Peter

 

[John Lee]

the YouTube video is just an overview - detailed solutions are included in our ASET (ActEd's Solutions with Exam Technique).

1 stands for a single parameter.

Age is a factor with 3 categories - so it will have 3 parameters (one for each category).

Location is a factor with 4 categories - so it will have 4 parameters (one for each category).
However when you add another covariate we lose a parameter so age + location = 3 + 4 - 1 = 6 parameters.

When we have a * term we multiply the parameters, so age*location = 3*4 = 12 parameters.

No need to calculate degrees of freedom as the difference in the degrees of freedom will be the same as the difference in the parameters. Which is all we need to carry out the test.

 

[pbrown]

Thanks John
It makes sense now!
Peter

 

[uniquenewyork]

Hi John,

Just on this question - in the Subject Notes, when going through an example similar to this question, it mentions that the total number of degrees of freedom for the Null model (Model "1") is the "total number of non-empty cells, less one". (Referring to Page 39 of Chapter 10).

Here, wouldn't the DF for Model "1" then be 12-1=11?

I understand that it won't affect the results but I'm just a bit confused.

Thanks!

 

[John Lee]

I worked with parameters - the degrees of freedom for each model will simply be cells - parameters. So they will be:

1 = 11
age = 9
age + location = 6
age * location = 0

This will give us the same degrees of freedom for the tests as before of 2, 3 and 6.

 

[uniquenewyork]

I worked with parameters - the degrees of freedom for each model will simply be cells - parameters. So they will be:

1 = 11
age = 9
age + location = 6
age * location = 0

This will give us the same degrees of freedom for the tests as before of 2, 3 and 6.

Thanks for clearing that up John. The Examiner's Report says that the degrees of freedom are 12, 10, 7 and 1.