The goal of varde is to provide functions for decomposing the variance in multilevel models, e.g., for g studies in generalizability theory or intraclass correlation analyses in interrater reliability.
You can install the development version of varde from GitHub with:
# install.packages("devtools")
devtools::install_github("jmgirard/varde")In the ppa example dataset, 72 human “raters” judged the perceived
physical attractiveness of 36 human “targets” in 6 different conditions
(i.e., stimulus “types”).
library(varde)
# Extract only type 1 observations (to simplify the example)
ppa_type1 <- ppa[ppa$Type == 1, ]# Fit a mixed effects model with target and rater effects
fit_1 <- brms::brm(
formula = Score ~ 1 + (1 | Target) + (1 | Rater),
data = ppa_type1,
chains = 4,
cores = 4,
init = "random",
warmup = 5000,
iter = 10000,
seed = 2022,
file = "m1"
)# Extract variance component estimates
res_1 <- varde(fit_1)
res_1
#> # Variance Estimates
#> # A tibble: 3 × 6
#> component term estimate lower upper percent
#> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 Rater Variance 1.05 0.811 1.63 0.330
#> 2 Target Variance 0.680 0.471 1.26 0.214
#> 3 Residual Variance 1.45 1.38 1.54 0.457
#>
#> # Intercept Estimates
#> # A tibble: 108 × 6
#> component id term estimate lower upper
#> <chr> <int> <chr> <dbl> <dbl> <dbl>
#> 1 Rater 1 Intercept 0.883 0.454 1.35
#> 2 Rater 2 Intercept 1.70 1.23 2.14
#> 3 Rater 3 Intercept 0.568 0.101 1.02
#> 4 Rater 4 Intercept -1.19 -1.63 -0.725
#> 5 Rater 5 Intercept 0.487 0.0521 0.963
#> 6 Rater 6 Intercept 1.32 0.856 1.76
#> 7 Rater 7 Intercept 0.288 -0.221 0.684
#> 8 Rater 8 Intercept -0.143 -0.616 0.288
#> 9 Rater 9 Intercept -0.695 -1.18 -0.280
#> 10 Rater 10 Intercept -1.74 -2.23 -1.32
#> # … with 98 more rows# Create river plot of variance percentages
plot(res_1, type = "river")
# Create density plot of variance posteriors
plot(res_1, type = "variances")
# Create jitter plot of random intercepts
plot(res_1, type = "intercepts")
# Calculate variance components and ICCs
res_2 <- calc_icc(
.data = ppa_type1,
subject = "Target",
rater = "Rater",
scores = "Score",
k = 12,
file = "m2"
)
res_2
#> # ICC Estimates
#> # A tibble: 6 × 7
#> score term estimate lower upper raters error
#> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr>
#> 1 Score ICC(A,1) 0.220 0.154 0.337 1 Absolute
#> 2 Score ICC(A,k) 0.782 0.686 0.859 12 Absolute
#> 3 Score ICC(A,khat) 0.956 0.929 0.973 72 Absolute
#> 4 Score ICC(C,1) 0.336 0.246 0.470 1 Relative
#> 5 Score ICC(C,k) 0.862 0.797 0.914 12 Relative
#> 6 Score ICC(Q,khat) 0.974 0.959 0.985 72 Relative
#>
#> # Variance Estimates
#> # A tibble: 3 × 6
#> component term estimate lower upper percent
#> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 Rater Variance 1.07 0.800 1.58 0.332
#> 2 Target Variance 0.703 0.480 1.28 0.218
#> 3 Residual Variance 1.45 1.38 1.54 0.450
#>
#> # Intercept Estimates
#> # A tibble: 108 × 6
#> component id term estimate lower upper
#> <chr> <int> <chr> <dbl> <dbl> <dbl>
#> 1 Rater 1 Intercept 0.875 0.442 1.37
#> 2 Rater 2 Intercept 1.66 1.23 2.14
#> 3 Rater 3 Intercept 0.579 0.108 1.02
#> 4 Rater 4 Intercept -1.17 -1.64 -0.731
#> 5 Rater 5 Intercept 0.522 0.0609 0.962
#> 6 Rater 6 Intercept 1.34 0.840 1.78
#> 7 Rater 7 Intercept 0.248 -0.213 0.694
#> 8 Rater 8 Intercept -0.190 -0.613 0.288
#> 9 Rater 9 Intercept -0.684 -1.19 -0.264
#> 10 Rater 10 Intercept -1.80 -2.23 -1.31
#> # … with 98 more rows# Create density plot of all posteriors
plot(res_2)
# Create density plot of specific posteriors
plot(res_2, parameters = c("ICC(A,k)", "ICC(C,k)"))
In posneg, 110 images were rated by between 2 and 5 raters on how
“Negative” and “Positive” they appeared.
# Calculate variance components and ICCs
res_3 <- calc_icc(
.data = posneg,
subject = "Image",
rater = "Rater",
scores = c("Negative", "Positive"),
file = "m3",
control = list(adapt_delta = 0.999)
)
res_3
#> # ICC Estimates
#> # A tibble: 12 × 7
#> score term estimate lower upper raters error
#> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <chr>
#> 1 Negative ICC(A,1) 0.266 0.126 0.417 1 Absolute
#> 2 Negative ICC(A,khat) 0.470 0.234 0.602 2.12 Absolute
#> 3 Negative ICC(A,k) 0.684 0.419 0.781 5 Absolute
#> 4 Negative ICC(C,1) 0.270 0.132 0.423 1 Relative
#> 5 Negative ICC(Q,khat) 0.473 0.238 0.604 2.12 Relative
#> 6 Negative ICC(C,k) 0.691 0.433 0.785 5 Relative
#> 7 Positive ICC(A,1) 0.453 0.308 0.578 1 Absolute
#> 8 Positive ICC(A,khat) 0.640 0.485 0.743 2.12 Absolute
#> 9 Positive ICC(A,k) 0.809 0.690 0.872 5 Absolute
#> 10 Positive ICC(C,1) 0.461 0.316 0.583 1 Relative
#> 11 Positive ICC(Q,khat) 0.643 0.489 0.744 2.12 Relative
#> 12 Positive ICC(C,k) 0.814 0.698 0.875 5 Relative
#>
#> # Variance Estimates
#> # A tibble: 6 × 7
#> score component term estimate lower upper percent
#> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 Negative Image Variance 2.61e- 1 0.128 0.478 2.72e- 1
#> 2 Negative Rater Variance 2.98e-11 0.0000141 0.184 3.11e-11
#> 3 Negative Residual Variance 6.96e- 1 0.578 0.918 7.28e- 1
#> 4 Positive Image Variance 1.22e+ 0 0.797 1.89 4.51e- 1
#> 5 Positive Rater Variance 1.59e-11 0.0000218 0.322 5.88e-12
#> 6 Positive Residual Variance 1.48e+ 0 1.19 1.93 5.49e- 1
#>
#> # Intercept Estimates
#> # A tibble: 230 × 7
#> score component id term estimate lower upper
#> <chr> <chr> <int> <chr> <dbl> <dbl> <dbl>
#> 1 Negative Image 1 Intercept -0.396 -1.01 0.231
#> 2 Negative Image 2 Intercept -0.0588 -0.729 0.493
#> 3 Negative Image 3 Intercept 0.0343 -0.605 0.633
#> 4 Negative Image 4 Intercept 1.03 0.373 1.74
#> 5 Negative Image 5 Intercept -0.374 -1.00 0.239
#> 6 Negative Image 6 Intercept -0.226 -0.863 0.368
#> 7 Negative Image 7 Intercept -0.121 -0.711 0.492
#> 8 Negative Image 8 Intercept 1.24 0.457 1.87
#> 9 Negative Image 9 Intercept -0.368 -0.978 0.226
#> 10 Negative Image 10 Intercept -0.363 -0.999 0.239
#> # … with 220 more rows