This vignette provides examples of some of the hypothesis tests that can be specified in
simr. The function
doTest can be used to apply a test to an input model, which lets you check that the test works before running a power simulation.
Documentation for the test specification functions can be found in the help system at
The first example comes from the help page for
glmer. The data frame
cbpp contains data on contagious bovine pleuropneumonia. An observation variable is added to allow for overdispersion. Note that the response is specified using
simr expects a binomial model to be in this form.
cbpp$obs <- 1:nrow(cbpp) gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd) + (1|obs), data=cbpp, family=binomial) summary(gm1)$coef
period is a categorical variable with 4 levels, which enters the model as 3 dummy variables. To test all 3 dummy variables simultaneously, you can use a likelihood ratio test.
doTest(gm1, fixed("period", "lr"))
If you were (for some reason) especially interested in the significance for the dummy variable
period2 you could use a z-test. This test uses the value
Pr(>|z|) reported in the summary above.
doTest(gm1, fixed("period2", "z"))
Suppose your model also has a continuous predictor. You can use
fixed to choose which fixed effect to apply tests to.
gm2 <- glmer(cbind(incidence, size - incidence) ~ period + size + (1 | herd), data=cbpp, family=binomial) doTest(gm2, fixed("size", "z"))
Once you have chosen your tests, you can run a power analysis by replacing
powerSim. Don't forget to specify an appropriate effect size.
fixef(gm2)["size"] <- 0.05 powerSim(gm2, fixed("size", "z"), nsim=50)
As your models become more complex, it can be easier to explicitly specify your null hypothesis using the
This example uses the
fm1 <- lmer(angle ~ recipe * temp + (1|recipe:replicate), data=cake, REML=FALSE)
Main effects should not be tested when they appear in an interaction term. Using the
fcompare function, we can specify a comparison with a simpler model (without having to re-type the random effects specification).
doTest(fm1, fcompare(~ recipe + temp))
This also works for polynomial terms:
fm2 <- lmer(angle ~ recipe + poly(temp, 2) + (1|recipe:replicate), data=cake, REML=FALSE) summary(fm2)$coef doTest(fm2, fcompare(~ recipe + temp))
We can do similar things with the
budworm data in the
data(budworm, package="pbkrtest") bw1 <- glm(cbind(ndead, ntotal-ndead) ~ dose*sex, family="binomial", data=budworm) summary(bw1)$coef
Of course we don't want to retype the
doTest(bw1, compare(. ~ dose + sex))
dose is continous and
sex is binary we could also use a Z-test on the single interaction term.
doTest(bw1, fixed("dose:sexmale", "z"))
random function gives you access to tests from the
RLRsim package. No additional arguments are needed for a single random effect.
re1 <- lmer(Yield ~ 1|Batch, data=Dyestuff) doTest(re1, random())
Where the model has multiple random effects,
compare can be used to test alternative specifications.
fm1 <- lmer(Reaction ~ Days + (Days | Subject), data=sleepstudy)
doTest(fm1, compare( ~ Days + (1 | Subject)))
The LRT is fast but only approximate. In fact, when testing random effects, the test is conservative[^1] because the null hypothesis is at a boundary of the parameter space. This means that you will underestimate power if you use the LRT. For more accurate results you can use
compare with a parametric bootstrap test from the
pbkrtest package. These can be quite slow, so you may want to use the LRT to exploring designs, and then double check with the parametric bootstrap.
doTest(fm1, compare( ~ Days + (1 | Subject), "pb"))
Note that the shortcut
rcompare saves you from retyping the fixed effect specification.
doTest(fm1, rcompare( ~ (1 | Subject), "pb"))
During a simulation study, some iterations may fail due to some sort of error. When this happens,
simr treats that iteration as a failed (i.e. not significant) test. In the following example there are 50 simulations, with 14 successes, 34 failures, and 2 non-results. The power is calculated as 14/50, i.e. 28%:
binFit <- glm(formula = cbind(z, 10 - z) ~ x + g, family = binomial, data = simdata) poisSim <- glm(formula = z ~ x + g, family = poisson, data = simdata) coef(poisSim)[1:2] <- c(1, -0.05) powerSim(binFit, sim=poisSim, nsim=50, seed=1)
Rather than interrupting part-way through an analysis,
simr traps and logs errors and warnings. You can access these logs using
$errors. If you didn't assign your analysis to a variable, you can recover it with the
ps <- lastResult() ps$errors
[^1]: See, e.g., Pinheiro, J.C., Bates D.M. (2000) Mixed-Effects Models in S and S-PLUS, Springer, New York (p84).
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