dummy variables in hlm

This is a question which applies equally well to classical / non 
hierarchical models, so you can also use resources for those. That said, 
I'll answer here anyway.

The answer is "maybe", for a few reasons.

First, we often don't need to / bother worrying about multiple 
comparisons within a single regression model (Gelman, Hill and Yajima 
2012; 
http://www.stat.columbia.edu/~gelman/research/published/multiple2f.pdf). 
That said, for large models, especially those with lots of interactions, 
multiple comparisons issues can become a problem, see e.g. this blog 
post 
https://deevybee.blogspot.com/2013/06/interpreting-unexpected-significant.html 
, which is presented with ANOVA, but which holds for multiple regression.

Speaking of ANOVA ... the dummy variables don't all test the null 
hypothesis of the categorical variable per se, but instead test the null 
hypothesis for a single contrast derived from that categorical variable. 
If you want an omnibus test for your categorical variable, then you need 
to do something like ANOVA / analysis of deviance or a likelihood-ratio 
test. Since these yield a single test across all levels of the 
categorical variable, they don't have the multiple comparisons problem.

In all cases, note that your choice of contrast coding has a big impact 
on the hypotheses that you're testing and whether or not things 
car::Anova() yield meaningful results.

Phillip

PS: I would recommend avoiding the Level 1 / Level 2 terminology. For 
many R packages, you don't need a strict nesting of levels and so the 
Level # terminology doesn't make much sense. I also generally find it 
quite confusing. Instead, try talking about fixed/population-level 
effects and random effects / variance components.

  Dear Prof. Bob,

I have run an HLM model that contains an independent categorical variable
(5 categories) at level 2. Four dummy variables entered into the model to
represent the categorical variable. Since the dummy variables all test the
null hypothesis of the categorical variable, do I need to adjust P-values
to control the type-I error rate?

Best,
Shoeayb

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