[R-sig-ME] Assessing whether sigma for a random effects parameter is equal to 0

[Ben Bolker]

On 10/13/20 4:56 PM, Sammie Haskin wrote:
> Hello! Given the pistonrings data set from the qcc package in R, I produced the following code to assess whether the standard deviation of random effect of the model was equal to 0. Here is my code:
> 
> library(lme4)
> library(qcc)
> library(RLRsim)
> library(nlme)
> library(data.table)
> 
> fit.pistons <- lmer(formula=diameter ~  sample + (1 | sample), data = pistonrings,REML=T)
> fit.pistons0 <- lm(diameter ~ sample, data = pistonrings)
> exactLRT(fit.pistons,fit.pistons0)
> 
> Here is the output:
> 
> LRT = 8.1423, p-value = 0.0014
> 
> Is this result implying that the standard deviation for the random effect is significant such that we reject the null hypothesis 

    Yes, if we're using a standard alpha-level cutoff of 0.05 (or 0.01).

and that H0: sigma = 0 is false?

   For what it's worth I would argue that the null hypothesis is 
(almost??) *always* false, whatever the results of null-hypothesis 
testing are.


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