ok, I've lost it - I used to feed Science Diet years ago to previous dogs not Iams.
But back to your concern, I'm not sure that fat would have an effect like that or the lack of it. I would be more concerned about the corn and chicken by products that is Bil Jac. You might want to look at this site that compares dog food and ingredients. I 4 or 5 star is probably best for a yorkie. 6 star may be too much for these little babies.
www.dogfoodanalysis.com
Also, there are many members here who home-cook, something I'm considering doing, here's a link to some recipes
http://www.yorkietalk.com/forums/showthread.php?t=75933
Also, many are feeding raw.
There are so many alternatives out there, but I believe often the problems on the outside have more to do with what we're putting on the inside