[R] fixed effects following lmer and mcmcsamp - which to present?

[Henrik Parn]

Dear all,

I am running a mixed model using lmer. In order to obtain CI of 
individual coefficients I use mcmcsamp. However, I need advice which 
values that are most appropriate to present in result section of a 
paper. I have not used mixed models and lmer so much before so my 
question is probably very naive. However, to avoid to much problems with 
journal editors and referees addicted to p-values, I would appreciate 
advice of which values of the output for the fixed factor that would be 
most appropriate to present in a result section, in order to convince 
them of the p-value free 'lmer-mcmcsamp'-approach!

Using the example from the help page on lmer:

fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)

...I obtain the following for 'Days':


summary(fm1)
...
            Estimate Std. Error  t value

Days         10.4673     1.5458    6.771


...and from mcmcsamp:

summary(mcmcsamp(fm1 , n = 10000))

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

                        Mean     SD Naive SE Time-series SE
Days                 10.4695 1.7354 0.017354       0.015921

2. Quantiles for each variable:
                        2.5%       25%       50%       75%    97.5%
Days                  7.0227    9.3395   10.4712   11.5719   13.957



The standard way of presenting coefficients following a 'non-lmer' 
output is often (beta=..., SE=..., statistic=..., P=...). What would be 
the best equivalent in a 'lmer-mcmcsamp-context'? (beta=..., CI=...) is 
a good start I believe. But which beta? And what else?

I assume that the a 95% CI in this case would be 7.0227-13.957 (please, 
do correct me I have completely misunderstood!). But which would be the 
corresponding beta? 10.4673?, 10.4695? 10.4712? Is the t-value worth 
presenting or is it 'useless' without corresponding degrees of freedom 
and P-value? If I present the mcmcsamp-CI, does it make sense to present 
any of the three SE obtained in the output above? BTW, I have no idea 
what Naive SE, Time-series SE means. Could not find much in help and 
pdfs to coda or Matrix, or in Google.

Thanks in advance for any advice and hints to help-texts I have missed!


Best regards,

Henrik