[R] Simulate type I error

[Chao Liu]

Hi Jeff,

Thanks for the reminder. I will post my question there. I did post the
plain text but maybe the default font of my gmail makes it look like being
formatted.

Best,

Chao

On Wed, Jan 26, 2022 at 2:49 PM Jeff Newmiller <jdnewmil using dcn.davis.ca.us>
wrote:

> You might get a response here, but the R-sig-mixed-models mailing list is
> a more appropriate place for this. See the Posting Guide mentioned in the
> footer.
>
> Also, post using plain text... formatted email may not communicate what
> you expected it to communicate.
>
> On January 26, 2022 11:12:36 AM PST, Chao Liu <psychaoliu using gmail.com>
> wrote:
> >Dear R-help community,
> >
> >I would like to simulate type I error for a random-effects model I
> >generated.
> >
> >The statistic of interest is standard deviations of the random intercept
> >and random slope. Specifically, for random intercept, H_{0}: lambda_{0} =2
> >and H_{1}: lambda_{0} not equal to 2; for random slope, H_{0}: lambda_{1}
> >=1 and H_{1}: lambda_{1} not equal to 1. I assume the test would be
> >likelihood ratio test but please correct me if I am wrong. How do I assess
> >type I error for the random-effects model I specified below:
> >
> >set.seed(323)
> >#The following code is to specify the structure and parameters of the
> >random-effects model
> >dtfunc = function(nsub){
> >  time = 0:9
> >  rt = c()
> >  time.all = rep(time, nsub)
> >  subid.all = as.factor(rep(1:nsub, each = length(time)))
> >
> >  # Step 1:  Specify the lambdas.
> >  G = matrix(c(2^2, 0, 0, 1^2), nrow = 2)
> >  int.mean = 251
> >  slope.mean = 10
> >  sub.ints.slopes = mvrnorm(nsub, c(int.mean, slope.mean), G)
> >  sub.ints = sub.ints.slopes[,1]
> >  time.slopes = sub.ints.slopes[,2]
> >
> >  # Step 2:  Use the intercepts and slopes to generate RT data
> >  sigma = 30
> >  for (i in 1:nsub){
> >    rt.vec = sub.ints[i] + time.slopes[i]*time + rnorm(length(time), sd =
> >sigma)
> >    rt = c(rt, rt.vec)
> >  }
> >
> >  dat = data.frame(rt, time.all, subid.all)
> >  return(dat)
> >}
> >
> >#Here I run one random-effects model
> >set.seed(10)
> >dat = dtfunc(16)
> >lmer(rt~time.all + (1+time.all |subid.all), dat)
> >
> >Assuming the test for significance is likelihood ratio test and so in the
> >end, I want to see if I run the test 1000 times, what is the probability
> of
> >rejecting null hypothesis when it is TRUE. Also, how do I plot the
> behavior
> >of type I error if I change the values of standard deviations?
> >
> >Any help is appreciated!
> >
> >Best,
> >
> >Chao
> >
> >       [[alternative HTML version deleted]]
> >
> >______________________________________________
> >R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> >https://stat.ethz.ch/mailman/listinfo/r-help
> >PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> >and provide commented, minimal, self-contained, reproducible code.
>
> --
> Sent from my phone. Please excuse my brevity.
>

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