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X3.10

T

tatos

Member
Why are the parameters equal to 2+(10-1) = 11, for model SA + PT
Similarly why are there 20 + (6-1) = 25 parameters for model SA*PT + NB?
i.e. please explain the LHS of the equations above..

Also, why does model SA + PT + SA.PT become SA*PT?

Lastly, the parameterised form of the linear predictor for model SA*PT+NB.. why is B_j at the end? Shouldn't there rather be some parameter (and not the factor itself?)
 
Hi tatos,

SA has 2 parameters, one of which is a constant
PT has 10 parameters (10 different constants) - so one of these constants can be abosorbed into the constant for SA

eg if we have the 3 possible numbers... 7, 8 and 9 and then we add 3 - why not just consider the 3 possible numbers 10, 11 and 12 - ie we only need 3 parameters not 4

Hopefully this clears up your second question too as it's the same idea

Now SA*PT = SA + PT + SA.PT by definition. SA.PT considers just the interaction between SA and PT wheeras SA*PT considers SA, PT and the interaction SA.PT. SA*PT will need 2*10 parameters

I'm sorry but I'm not sure I understand your last question. What linear predictor parameterisation would you propose instead? Maybe I could try and help on this one by explaining what would be wrong with it?

John
 
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