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06_mixed2/exercises-datsimlmm.md

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+Exercises: Data simulation for crossed random-effects models
+================
+
+- Change the data simulation by Baayen, Davidson, and Bates (2008) for
+  $N = 30$ subjects instead of only 3
+- You can use the following script and adjust it accordingly
+- You can choose if you want to use model matrices or create the vectors
+  “manually”
+
+``` r
+library(lattice)
+library(lme4)
+
+#--------------- (1) Create data frame ----------------------------------------
+datsim <- expand.grid(subject = factor(c("s1" , "s2" , "s3" )),
+                      item    = factor(c("w1" , "w2" , "w3" )),
+                      soa     = factor(c("long" , "short" ))) |>
+  sort_by(~ subject)
+
+#--------------- (2) Define parameters ----------------------------------------
+beta0 <- 522.22
+beta1 <- -19
+
+sw  <- 21
+sy0 <- 24
+sy1 <- 7
+ry  <- -0.7
+se  <- 9
+
+#--------------- (3) Create vectors and simulate data -------------------------
+# Fixed effects
+b0 <- rep(beta0, 18)
+b1 <- rep(rep(c(0, beta1), each = 3), 3)
+
+# Draw random effects
+w <- rep(rnorm(3, mean = 0, sd = sw), 6)
+e <- rnorm(18, mean = 0, sd = se)
+
+# Bivariate normal distribution
+sig <- matrix(c(sy0^2, ry * sy0 * sy1, ry * sy0 * sy1, sy1^2), 2, 2)
+y01 <- MASS::mvrnorm(3, mu = c(0, 0), Sigma = sig)
+y0 <- rep(y01[,1], each = 6)
+y1 <- rep(c(0, y01[1,2],
+            0, y01[2,2],
+            0, y01[3,2]), each = 3)
+
+datsim$rt <- b0 + b1 + w + y0 + y1 + e
+
+#--------------- (4) Simulate data using model matrices -----------------------
+X <- model.matrix( ~ soa, datsim)
+Z <- model.matrix( ~ 0 + item + subject + subject:soa, datsim,
+                  contrasts.arg = list(subject = contrasts(datsim$subject,
+                                                        contrasts = FALSE)))
+
+# Fixed effects
+beta <- c(beta0, beta1)
+# Random effects
+u <- c(w = unique(w),
+       y0 = y01[,1],
+       y1 = y01[,2])
+
+datsim$rt2 <- X %*% beta + Z %*% u + e
+
+#--------------- (5) Visualize simulated data ---------------------------------
+xyplot(rt ~ soa | subject, datsim, group = item, type = "b", layout = c(3, 1))
+```
+
+### Reference
+
+<div id="refs" class="references csl-bib-body hanging-indent">
+
+<div id="ref-Baayen08" class="csl-entry">
+
+Baayen, R. H., D. J. Davidson, and D. M. Bates. 2008. “Mixed-Effects
+Modeling with Crossed Random Effects for Subjects and Items.” *Journal
+of Memory and Language* 59 (4): 390–412.
+<https://doi.org/10.1016/j.jml.2007.12.005>.
+
+</div>
+
+</div>

06_mixed2/exercises.md

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+Exercise: Power simulation for LMM
+================
+
+## Physical healing as a function of perceived time
+
+Aungle and Langer (2023) investigate how perceived time influences
+physical healing
+
+- They used cupping to induce bruises on 33 subjects, then took a
+  picture, waited for 28 min and took another picture
+- Subjective time was manipulated to feel like 14, 28, or 56 min
+- The pre and post pictures were presented to 25 raters who rated the
+  amount of healing on a 10-point-scale with 0 = not at all healed, 5 =
+  somewhat healed, 10 = completely healed
+- Subjects participated in all three conditions over a two week period
+
+Data: [healing.RData](../data/healing.RData)
+
+``` r
+load("../data/healing.RData")
+
+str(dat)
+
+# Subject ID
+dat$Subject <- factor(dat$Subject)
+# Rater ID
+dat$ResponseId <- factor(dat$ResponseId)
+```
+
+1.  Visualize the data.
+
+    - Aggregate the data over Raters and plot the data for each subject
+      using `lattice::xyplot()`
+    - Aggregate the data over Subjects and plot one panel for each rater
+    - How would you choose the random effects for a model testing
+      healing over the three conditions
+
+2.  Fit the model you think fits the experimental design best
+
+3.  Test the effects of condition
+
+4.  Run a power simulation for a replication study:
+
+    - Set up a data frame containing the study design and sample size.
+
+    - Specify the minimum relevant effects.
+
+    - Set the fixed effects and variance components to plausible values.
+
+    - How many participants are required to detect the specified effect
+      with a power of 80%?
+
+    - Recover the parameters of the model for one simulated data set.
+
+### Reference
+
+<div id="refs" class="references csl-bib-body hanging-indent">
+
+<div id="ref-Aungle23" class="csl-entry">
+
+Aungle, P., and E. Langer. 2023. “Physical Healing as a Function of
+Perceived Time.” *Scientific Reports* 13 (1): 22432.
+<https://doi.org/10.1038/s41598-023-50009-3>.
+
+</div>
+
+</div>