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Is there a way to perform a Two-way Welch Anova? I have not found an implementation of it.

My dependent variable is continuous and normal, and my independent variables are all categorical and ordinal with unequal sample size and some of them presenting unequal variances (checked with levines test).

I am not interested in predictions, but more in evaluating the effect of the features on the outcome. Would it be acceptable to perform a linear regression with the categorical and ordinal variables and directly evaluate the coefficients? How could I consider their possible interactions?

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  • $\begingroup$ Are your residual variances unequal? Otherwise it's not clear to me, how the categorical and oridnal variables can have variances. Further, the variances of independent variables can be different as long as the response variance within the groups (= residuals) is equal (this is what's meant by homoscedasticity). Unequal sample sizes could be more of a problem, since it reduces statistical power and robustness of the model (if assumptions, especially homoscedasticity, are violated). $\endgroup$
    – tintiverde
    Feb 17 at 12:50
  • $\begingroup$ What do you mean by "evaluate the coefficients"? Catgorial predictors are encoded with dummy variables, so testing for these individual dummy variables is usually not hat you want. That is the point of ANOVA that it checks whether any of the levels has an effect and thereby evaluates teh predictor as an entity. And linear regression does not circumvent the problem (two-way ANOVA is a special case of linear regression), because it assumes homoscedsticity too. $\endgroup$
    – cdalitz
    Feb 17 at 13:44
  • $\begingroup$ I meant to look into the weights associated to each dummy variable and use them to interpret how much each variable influenced the outcome. But I agree that my priority was to study N-way Anova, however, given the heteroscedasticity of my data I was unsure on how to perform a N-way Welch Anova. $\endgroup$
    – s223
    Feb 17 at 14:08
  • $\begingroup$ Some approaches at this link may be applicable to the two-way case: stats.stackexchange.com/questions/91872/alternatives-to-one-way-anova-for-heteroskedastic-data/ $\endgroup$ Feb 17 at 14:10

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