[R-sig-ME] pvalues & model inference

[Anthony R. Ives]

Stephanie,

The short answer is that a bootstrap can address both bias (problems with estimates) and hypothesis testing. It is often the case that, even though estimates are unbiased, a bootstrap is still needed for hypothesis testing.

If you are interested in p-values, I'd perform bootstraps under the null hypothesis. Standard bootstraps are generally performed using the estimates, and if there is bias, this can still give you incorrect p-values. 

There are several examples of different types of bootstraps and randomizations here: https://leanpub.com/correlateddata

Cheers, Tony

______________
Anthony R. Ives
UW-Madison
459 Birge Hall
608-262-1519
 

-----Original Message-----
From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> on behalf of Stephanie Rivest <srive046 using uottawa.ca>
Date: Thursday, November 1, 2018 at 11:03 AM
To: "r-sig-mixed-models using r-project.org" <r-sig-mixed-models using r-project.org>
Subject: [R-sig-ME] pvalues & model inference

    Hi there,
    
    I am having some trouble understanding all the documentation that I've read
    regarding how to do hypothesis testing and model inference for a glmm with
    zero-inflation. I'm hoping someone can clarify. For a little background, I
    fit a model with the package glmmTMB for a response that is a count and is
    zero-inflated, random effects were included.
    
    From what I understand, the Wald Z tests that are reported in the output of
    a model fit with glmmTMB cannot be fully trusted for several reasons: (1)
    df are difficult to calculate, yet are used to do hypothesis testing, (2)
    Wald z tests make assumptions that can be violated (asymptotic null
    distributions), and (3) boundary effects can occur, especially for the
    random effects. To me, this sounds like the parameter estimates are ok, but
    the standard errors and p-values cannot be trusted. Therefore, its the
    *prediction
    intervals* that are incorrect, but not the estimates themselves. Is this
    interpretation right? I may have misinterpreted some of the terminology
    used as well, any guidance on this would be appreciated.
    
    I understand that a bootstrap is the next logical step, and my dataset is
    small enough that this option is feasible for me. What I don't understand
    is the purpose of the bootstrap. Is the aim to obtain more accurate
    prediction intervals and correct p-values? OR, are model estimates also
    made more reliable?
    
    Thanks in advance for taking the time to respond.
    
    Cheers,
    Stephanie
    
    Stephanie Rivest
    Ph.D. Candidate | Candidate au Doctorat
    Dept. of Biology | Dép. de Biologie
    University of Ottawa | Université d'Ottawa
    
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