[R] Simulate type I error

[Jeff Newmiller]

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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]]
>
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-- 
Sent from my phone. Please excuse my brevity.