Frequently Asked Questions
How to Calculate Power
Power can be calculated using the power.rmcorr function. This function modifies pwr.r.test from the pwr package to use the rmcorr degrees of freedom. It is not presently included in the rmcorr package.
Notation: N is the sample size, k is the (average) number of repeated measures for each individual, and rrm is the rmcorr effect size.
power.rmcorr Example
N = 100, k = 3, and rrm = 0.20. This design has 82% power.
install.packages("pwr")
require(pwr)
power.rmcorr <- function(k, N, effectsizer, sig)
{pwr.r.test(n = ((N)*(k-1))+1, r = effectsizer, sig.level = sig)}
power.rmcorr(k = 3, N = 100, effectsizer = 0.20, sig = 0.05)
#>
#> approximate correlation power calculation (arctangh transformation)
#>
#> n = 201
#> r = 0.2
#> sig.level = 0.05
#> power = 0.8156984
#> alternative = two.sidedSee Power curves for more information.
For G*Power (Faul et al. 2009) or other
software, power can be calculated by substituting the rmcorr degrees of
freedom for a Pearson correlation. Instead of sample size, use the
degrees of freedom for rmcorr plus two (effective sample size). This is
because a Pearson correlation has N - 2 degrees of
freedom.
- Rmcorr exact degrees of freedom = N x (k - 1) - 1
- Approximate degrees of freedom = (N -1) x (k - 1)
Exact Degrees of Freedom Example
Values: N = 100, k = 3 , and
rrm = 0.20 (same as above)
rmcorr df =
100 x (3 - 1) - 1 = 200 - 1 = 199
Add two (kludge): 199 + 2 = 201
Enter N = 201 as the effective sample size in G*Power
G*Power will calculate the degrees of freedom as N - 2 = 201 -
2 = 199. Thus, using the correct degrees of freedom for rmcorr.
Note power is just slighty different than the same calculation in R, which uses an arctan approximation.
Approximate Degrees of Freedom Example
Values: N = 100, k = 3, and
rrm = 0.20 (again, same as above)
approx rmcorr df = (100 - 1) x (3 - 1) = 99 x 2 = 198
Note the
small difference between the approximate vs. exact calculation:
one degree of freedom
Add two (same kludge) for G*Power,
entering a sample size of N = 200
Note power is slighty different than the exact formula
above. 
How to Extract the Slope and its Confidence Interval
my.rmc <- rmcorr(participant = Subject, measure1 = PaCO2, measure2 = pH,
dataset = bland1995)
#> Warning in rmcorr(participant = Subject, measure1 = PaCO2, measure2 = pH, :
#> 'Subject' coerced into a factor
# Structure of rmcorr object
#str(my.rmc)
# Extract rmcorr model coefficients
coef.rmc <- my.rmc$model$coefficients
coef.rmc
#> (Intercept) Participant1 Participant2 Participant3 Participant4 Participant5
#> 7.65590848 -0.72605418 -0.02144291 0.22395850 0.24550355 0.13432752
#> Participant6 Participant7 Measure1
#> 0.20037424 -0.03394863 -0.10832305
slope.rmc <- coef.rmc[length(coef.rmc)] #Last value in coefficients is the slope
slope.rmc
#> Measure1
#> -0.108323
# Confidence intervals around all estimates
coef.CIs <- stats::confint(my.rmc$model)
coefs.all <- cbind(coef.rmc, coef.CIs)
coefs.all
#> coef.rmc 2.5 % 97.5 %
#> (Intercept) 7.65590848 7.34994594 7.96187102
#> Participant1 -0.72605418 -0.83211999 -0.61998837
#> Participant2 -0.02144291 -0.11116705 0.06828123
#> Participant3 0.22395850 0.16049969 0.28741732
#> Participant4 0.24550355 0.16448903 0.32651806
#> Participant5 0.13432752 0.05868538 0.20996967
#> Participant6 0.20037424 0.12673292 0.27401556
#> Participant7 -0.03394863 -0.17148111 0.10358385
#> Measure1 -0.10832305 -0.16883787 -0.04780822isa Error
We have had reports of this error when running rmcorr:
Error in isa(Participant, "character") : could not find function "isa" Updating R to version 4.1.0 or later resolves this error.
Transformations
Transformations can be used to make the data (errors) more normal. We highly recommend graphing both the raw and transformed data. It may be appropriate to only transform one measure or transform both measures. “Consider transforming every variable in sight” (Gelman and Hill 2007, 548).