Advancing a monster = advancing caster level?

[Vahktang]

Well, my heroes are getting into that rarefied atmosphere where I have to advance the monsters to be competitive.
When I add Challenge Ratings (HD, saves, skills, etc) does the caster level of the monster increase also?
Or I do I have to add an associtive level (MM pg 294)?
And would that be a character level or up the caster level of the monster?
(Yes, there are many monsters that only advance by character level. This is not about that)

For example, we have a Night Hag, advancement by HD (not character level)
It has 8 HD and it's caster level is 8, it's CR is 9.
It can do spell like abilities including magic missle, which would be 4 missles.
I want it to do the max number of missles: 5.
If I advance this outsider a CR, it's HD would be 10, it would get another feat, it's base attack would increase, etc, but would it's caster level increase?

If not, how do I advance the caster level, if it is possible at all?

Thanks for any help.

More later,

Vahktang

 

[UltimaGabe]

Generally (as in your example), monsters have a Caster Level equal to their Hit Dice or their Hit Dice x 1/2. If they do, it's simple- advancing Hit Dice (which includes adding class levels, I believe) also advances their caster level. If their Caster Level doesn't seem to be dependant on their Hit Dice (or, rather, if you can't seem to find a way to tie the two together), then generally their Hit Dice don't affect their caster level at all.

Unless the description says otherwise, that is.