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Plotting means and error bars for fixed effects in a ME model

4 messages · Paul Johnson, Ché Lucero, Dan Mirman

Original
Ché Lucero
# 
Hello, list.

I have a question about error bars on barplotted means of data that has
been analyzed with mixed effects models.

Mixed effects models allow us to simultaneously model variance from
multiple random-effects sources (such as Subjects and Items), a much needed
solution to a problem pointed out (most potently) in my field by Herb Clark
in 1973.

However, to my knowledge, calculating confidence interval/SEM for means has
not advanced to take this modeling approach into account. A series of
papers - Loftus and Masson 94 (Using confidence intervals in within-subject
designs)  Cousineau 05  (Confidence intervals in within-subject designs: a
simpler solution) and Morey 05 (Confidence Intervals from Normalized Data:
A correction to Cousineau)   has specified ways to calculate error bars in
which the within-Subject error has been accounted for.

That approach to calculating error bars for plotting seems to be well
matched for when the statistical procedure is a simple repeated measures
(for Subjects OR Items) ANOVA. But what about the case where I have both
within-Subjects and within-Items (and within-XYZ random factors too)? Is
there a way to construct standard errors of the mean for levels of a fixed
factor (e.g. Condition) taking more than one random-effect into account as
mixed effects models do? It would be really great to have the charts
visually suggest the same inferences that the ME statistics do, but I can't
find any literature about it.

Thanks for your time.

-Ch?
Paul Johnson
#
On Sun, Feb 7, 2016 at 2:56 PM, Ch? Lucero <chelucero at uchicago.edu> wrote:
Hi.

You will get better help if you rephrase your question with a fitted
lme4 object and let us see what you are trying to do.  As it is, your
question asks us to wade throught a lot of ANOVA jargon. I'd rather
see your model, data, and the number for which you want the CI.

It appears that even for glm without random effects, there is no
settled upon idea for CI on predicted values. You can fall down a
rabbit hole reading math articles about that. I don't think the
presence of random effects makes that tougher, its just another
element to add in the error bands.  The model you specify when you fit
dictates what's correlated.

I had to improvise some CIs last semester. In the package "arm"
(support for the Gelman & Hill textbook), there's a function called
se.coef and they do the usual plus or minus 2 of those to make error
bars that look like CIs for predicted values. That works because if
you calculate some linear sum, you can use the variances of individual
elements to get a Wald type CI.

I am pretty sure the best answer is simulation with lme4 objects,
however. But don't have code to share to you.

Good luck, think about showing everybody code and such that they can focus on.

pj

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Ché Lucero
    

    

      
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Hi PJ.

An example:

library(lme4)
dat <- expand.grid(Condition = c('A', 'B'), Subject = 1:10,
                   Item = c('popcorn', 'butter', 'rosemary', 'salt',
'yeast'))
dat$Subject <- factor(dat$Subject)
size <- nrow(dat)
dat$DV <- numeric(size)
dat[dat$Condition == 'A', 'DV'] <- rnorm(size/2, 8, 1)
dat[dat$Condition == 'B', 'DV'] <- rnorm(size/2, 9, 1)

barplot(tapply(dat$DV, dat$Condition, FUN=mean))

m.1 <- lmer(DV ~ Condition + (1|Subject) + (1|Item), data=dat)
m.2 <- update(m.1, . ~ . - Condition)
anova(m.1, m.2)

I don't want a standard error on anything from the model per se. I want to
build a standard error of the mean for the two Condition means for
charting. My example lmer model takes two random effects into account:
Subject and Item. I want to make a plot in which the standard error of the
mean takes into account both the Subject and Item variance (like my model).
I am only aware of how construct the standard error of the mean taking one
of those into account at a time. Hope I was clearer this time!

Thanks,

-Ch?

        
On Sun, Feb 7, 2016 at 3:21 PM Paul Johnson <pauljohn32 at gmail.com> wrote:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

  
  


  


      

    

    

      
      

        


  

        

      Dan Mirman
    

    

      
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I think both the effects and lsmeans packages can do this for you:

library(effects)
as.data.frame(effect("Condition", m.1))

library(lsmeans)
lsmeans(m.1, "Condition")

        
On Sun, Feb 7, 2016 at 4:51 PM, Ch? Lucero <chelucero at uchicago.edu> wrote: