Chapter 13 confusion!

Hi all,

Really struggling with chapter 13, in particular the section linear predictors and question 9.
For part a, im very confused as to where the markscheme got to those models. for example i would have said that model 2 (YO+FS+YO.FS+TC) where \alpha=YO, \beta=FS and \gamma=TC would have been
\alpha_i +\beta_k +\gamma_j _\sigma_ij
where \sigma_ij is the interaction term between \alpha and \beta.
But this isnt the case, the answer is \alpha_ij + \gamma_j. How did they get this model?
The model 3 equation makes no sense to me either, the course notes say "when an interaction term is used in a model, both main effects must also be included", but the answer for the interaction Y0*FS*TC is simply \alpha_ijk. How is this possible?

Finally, im very confused how they have got their parameters. Is there a formula for parameters or a rule i am missing?
I would have said that there is 6 parameters, as we have two options for each YO, FS, TC, but this isnt the case... even in the course notes the treatment of parameters is very unclear, for example on page 653 they combine parameters but there isnt any explanation on why they chose those specific ones to combine

Please can someone help clear this up?

 

Hi Andrea, thank you so so much for this - your answer has really cleared this up for me!

 

Hi Andrea, this is also confusing me as well.

Section 3.3, p25 - where is this? Is this another thread on the forums? Or a page in the CMP?

Thanks!

 

I guess is CMP,it show possible parameters of question. 3.3-p25 has only one question.

 

Hi Andrea, thank you again for this. i feel very happy with the parameters for a factor now , im just a little confused on how we would compute n for variables?
Thanks

 

ah, thank you so much, i understand what you mean!

 

Thank you Molly for the question, I have finally understood this thanks to you. I am still facing challenges however on how they went on to calculate the degrees of freedom for Que 13.9 (iv). I cannot seem to understand how the degrees of freedom for the models were calculated. Can someone please explain that.

 

Hi Tinashe,

I also find this very confusing!

the base model has two parameters (for this i am unsure why, could someone explain this)
we then add (n-1) parameters for each factor added where n is the number of categories in the factor

so with YO+FS+TC we have YO as the base, FS we then add (2-1) and then a further (2-1) for TC
=4 parameters

then YO+FS+YO.FS+TC
can also be written as YO+FS+TC+YO.FS
so we have the 4 parameters from above covering the first three terms
then we have an interactive factor this adds (n-1)(m-1) where again n and m are the respective categories
both YO and FS have 2 categories ie (2-1)(2-1)=1
so we have 5 parmeters

i cannot help you with the last one, as i dont understand it myself, i get to seven parameters but the answer is 8. if anyone can help up on this that would be really appreciated!

Thanks

 

I guess it will helpful for understanding relationship about df and parameters.
https://www.acted.co.uk/forums/index.php?threads/assignment-x4-8.19082/

There are two method of claculating parameters(df),factor and variable.

About last one,they are factors,so I guess it is 8 possible parameters(2*2*2),
all same category:YO0.FS0.TC0,YO1.FS1.TC1
one 1 category:YO0.FS0.TC1,YO1.FS1.TC0,YO1.FS0.TC0
two 1 category:YO1.FS1.TC0,YO1.FS0.TC1,YO0.FS1.TC1

In linear predictor, it may be y=factor_ijk,value of factor are above.factor is like intercept,coefficient.

If I made a mistake, please tutors correct my mistakes.

 

I guess official calculation way is YO*FS*TC=YO+FS+TC+YO.FS+FS.TC+YO.TC+YO.FS.TC
=(2-1)+(2-1)+(2-1)
+(2-1)*(2-1)+(2-1)*(2-1)+(2-1)*(2-1)
+(2-1)*(2-1)*(2-1)=7
Mode3 has 7 more parameters than constant model, so we calculated as 7-7.
Although I guess the official calculation is probably like this, but I still want to ask the tutor where the 1 comes from in the official calculation?

 

What I mean is that 1 which is deducted from model1~3 in official calculation,except for constant model.

 

Thanks so much Ykai!!

ive been looking at this for a whilec, i think i can make sense of it:
we have
YO*FS*TC
focusing on first two terms
YO*FS=YO+FS+YO.FS
now subbing this in to the desired equation
(YO+FS+YO.FS)*TC
= YO+FS+YO.FS+TC+ YO.TC+FS.TC+YO.FS.TC

=2 params for base model YO
+(2-1)=1 for FC
+(2-1)(2-1)=1 for YO.FC
+(2-1)=1 for TC
+(2-1)(2-1)=1 for YO.TC
+(2-1)(2-1)=1 for FS.TC
+(2-1)(2-1)(2-1)=1 YO.FS.TC

=2+1+1+1+1+1+1= 8 params as required

please can a tutor verify this method is ok?

Thanks

 

also, have absolutely no idea how we would calcualte degrees of freedom. it seems that dof are in a sense top down (as in we can lose dofs), while params are bottom up.

but what would be the initial dof to start subtracting from?

thanks
molly

 

i think what has happened here is that you havent left YO as a base model... i guess? definitely not 100% on this

 

I just can't sure about where 1 df of constant model come from.Why is constant model is -1df?I want to know it.

 

I type wrong,the extra 1df of model1~3.

 

i am unsure on this too...

 

But when we calculate model1~3, don’t the constant parameters disappear? Just like assignment X4-8, the constant parameter is merged in the later models, doesn't it?or could you give me parameterised form of the linear predictor of this question or what I do in assignment X4-8? I may understand more clearly.