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I have created a linear mixed model and am using emtrends to determine the impact of a dichotomous variable on the effect of a continuous variable, across levels of a categorical variable. Is it expected for the standard errors (& 95% CIs) to be uniform across the categorical variable? I wish I understood more about the underpinnings of how contrasts work mathematically, and want to make sure I am doing it correctly. I have included the code and output below.

The idea, is to determine if a baker being an expert or not (dichotomous, 1/0) impacts the effect of time (cont) on freshness (cont) of bread, after baked. Also if so, which types of bread (10 level nominal), are affected more than others. The types of breads vary in freshness at time 0 and at follow up, and decrease in freshness at different rates. I would think their standard errors would differ by the magnitude of their freshness, but instead they are all the same. By using contrasts is it normal to have a constant error across the 'by' group levels?

Thanks for your help!

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  • $\begingroup$ In your question, you have time, group1, and group2. In your output, you have skill and type. It looks like type is group2. But if you stratify by a variable that is in an interaction, things will get weird. Can you show your code? Or explain what you did in more detail? $\endgroup$
    – Peter Flom
    Commented Jun 11 at 17:22
  • $\begingroup$ Hi Peter, I clarified the question a bit, and added my code and output. I hope it's more clear to understand. As seen in the output, bread freshness over time for types 2, and 5 are positively impacted by the baker being an expert. This I feel is correct as it can be seen in boxplots. However, all of the standard errors are the same regardless of the magnitude of each contrast estimate, so some have extremely wide confidence intervals in relation to their estimate, if that makes sense? Or is the SE based on the original mixed model, and a product of partial pooling? Thanks again for your help! $\endgroup$
    – Jackson
    Commented Jun 12 at 4:35
  • $\begingroup$ That is a lot clearer; unfortunately, I don't know the answer. $\endgroup$
    – Peter Flom
    Commented Jun 12 at 11:47

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It's normal. I happens because a) you are using a model that assumes homogeneous error variance and b) apparently your design is balanced (i.e. you have equal number of observations in each type x expertise cell).

There are several answers explaining this: here, here, and here

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