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What type of statistical tests should I look into for determining which of several nominal predictor variables have the largest effect on a discrete/ordinal response variable?

Say that the five nominal predictors are X1 - X5, each of which are comprised of 5 to 30 unordered categories (say X1 = Employee, X2 = Customer, X3 = Order Type, etc). The response variable, in this case, is the number of errors per order. I want to determine which of the nominal predictors have a statistically significant impact on, say, the number of errors per order.

What are the common ways to approach this type of problem?

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Do you have repeated measurements for each level of these variables? For example, if every single observation has a different value for "Customer" and for "Employee", then you won't be able to separate their effects – Macro Jun 2 '12 at 15:52

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