Assorted questions - help appreciated!

[12345]

Hello there,

Few q's that I haven't been able to resolve:

1. Q&A bank 2.19, part (i) - in this proof is there a missing theta in the penultimate line before the "so" comment on p15. Shouldn't it be = theta^2 - 2(blah)theta + constant?

2. Truncated moments for lognormal distribution - if U = infinity, we assume that phi(U) is 1 but what if k does not equal 1, e.g. what does phi(U,2) equal? I haven't seen this up in the q's but just wondered for peace of mind.

3. Q&A bank 3.18 - I don't quite follow the logic here, why are there only 4 parameters in model 1? I initially assumed that it is because each parameter can only have 1 or 0 so total can only be 0,1,2 or 3, i.e. we ignore individual cases where YO=1 or FS=1 etc. but in this case why does model 2 have 5 parameters? There are only 2 results for the 2 x 2 combinations of YO and FS i.e. 1 or 0 are there not? Just thought actually, is this now defined as a new parameter with 4 separate results, i.e. =1 if YO = 0 and FS =0, 2 if YO =1 and FS =0, etc?

4. Are the formulas relating to scaled deviance in the yellow book? Couldn't see them.

Sorry for the long post, thanks in advance!

 

[John Lee]

Hello there,

Few q's that I haven't been able to resolve:

1. Q&A bank 2.19, part (i) - in this proof is there a missing theta in the penultimate line before the "so" comment on p15. Shouldn't it be = theta^2 - 2(blah)theta + constant?

Yup! I'll pass it on to get corrected for the 2009 version and put in the corrections document. Thanks for that.

2. Truncated moments for lognormal distribution - if U = infinity, we assume that phi(U) is 1 but what if k does not equal 1, e.g. what does phi(U,2) equal? I haven't seen this up in the q's but just wondered for peace of mind.

Will still give 1. The ln(infinity) is infinity and the minus part won't change that! So phi(infinity) = 1.

Similarly if L =0, we get ln0 = -infinity and phi(-infinity) = 0.

3. Q&A bank 3.18 - I don't quite follow the logic here, why are there only 4 parameters in model 1? I initially assumed that it is because each parameter can only have 1 or 0 so total can only be 0,1,2 or 3, i.e. we ignore individual cases where YO=1 or FS=1 etc. but in this case why does model 2 have 5 parameters? There are only 2 results for the 2 x 2 combinations of YO and FS i.e. 1 or 0 are there not? Just thought actually, is this now defined as a new parameter with 4 separate results, i.e. =1 if YO = 0 and FS =0, 2 if YO =1 and FS =0, etc?

Every time you add a new rating factor you lose 1 parameter as the "constants combine". The calculation would be:

2 + (2-1) + (2-1) = 4

However, I think the confusion arises from the question - the 1, 0 idea seems to indicate the we have the estimated values - when it's trying to tell us that YO1 = constant, YO0 = another constant.

As an example suppose we have a single term model YO and when we estimate the unknowns we get:

YO1 = +50 and YO0 = +10

So 2 parameters.

Now we add on the Fast/Slow factor.

When we change the model and estimate the parameters the Young/Old parameters will change as well. Suppose we have the following data:

Suppose we have a Young driver with a Fast car and his/her total constant is +80

An Old driver with a Fast car has total constant +45

A Young driver with a Slow car has total constant +50

An Old driver with a Slow car has total constant + 15

In equations we have:

YO1 + FS1 = 80
YO0 + FS1 = 45
YO1 + FS0 = 50
YO0 + FS0 = 15

The trouble is that they're not linearly independent (rather like when solving NCD stable state) and so we can't actually solve unless we assume 1 of the values (the so called "base level"). So we only estimate 3 parameters - we have lost one parameter.

4. Are the formulas relating to scaled deviance in the yellow book? Couldn't see them.

Nope the scaled deviance and the test are not in the tables. Sorry!