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I have a dataset with one dependent variable and several independent categorical variables.

I want to explore the amount of variability each of the independent variables explain in the dependent variable.

This can be done by entering all the variables in a one-way ANOVA and calculating the proportions of explained variability of each factor (SSeffect / SStotal).

However, I am also interested in partitioning the proportion of explained variability of a specific independent variable between the different levels of that variable to see if some levels of a factor have more effect on the dependent variable than others.

How can I approach this task?

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First of all, you stated something like

entering all the variables in a one-way ANOVA

Probably, you would like to use multiway ANOVA (maybe you mistaken multiway with Multivariate MANOVA?).

For example, you have a such situation:

  • DV: FlatPrice
  • IVs: City, District, Street, SquareMeters, Storey.

The District is nested in City and Street is nested in District as well as in City. In R environment it's expressed as FlatPrice ~ City/District + ...

Those IVs are properly nested and not crossed, so you could nested ANOVA or hierarchical ANOVA. Look, at this http://www.biostathandbook.com/nestedanova.html

By the way, you said something about assessing the severity of each IV. Maybe you could look at this question and answer, because it may help you Tests I sequential and III marginal

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