[Rasch] Permissible Transformations

Anthony James luckyantonio2003 at yahoo.com
Thu Mar 19 03:14:22 EST 2009

Dear folks,
It is said that linear transformations in the from of X' = a + bX are permissible for interval scales. What does this mean? If we multiply a set of numbers by a constant and add them with another constant we will get a new different set. What properties does this new set have and how is it related to the first set that makes it a linear transformation?
Why isn’t multiplication permissible? Isn’t multiplication a linear transformation where the additive component is zero? So it must be a linear transformation? (or probably zero isn’t allowed to be the multiplicative component). When a scale in linearly transformed the distances between the objects are increased ‘a’ times the distances in the first scales. 
I don’t understand how interval and ratio scales are different in relation to permissible transformations. I’d be thankful for comments.

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