simDat102: Simulate data for Chapter 10.2: Linear mixed-effects model

Description

Simulate mass ~ length regressions in 56 populations of snakes with random population effects for intercepts and slopes. There is no correlation between the intercept and slope random variables.

Usage

simDat102(
  nPops = 56,
  nSample = 10,
  mu.alpha = 260,
  sigma.alpha = 20,
  mu.beta = 60,
  sigma.beta = 30,
  sigma = 30
)

Value

A list of simulated data and parameters.

nPops: Number of populations
nSample: Number of samples per population
mu.alpha: Mean of random intercepts
sigma.alpha: SD of random intercepts
mu.beta: Mean of random slopes
sigma.beta: SD of random slopes
sigma: Residual SD
pop: Indicator for population number
orig.length: Snake body length, not standardized
lengthN: Snake body length, standardized
alpha: Random intercepts
beta: Random slopes
eps: Residuals
mass: Simulated body mass for each snake

Arguments

nPops: Number of populations
nSample: Samples from each population
mu.alpha: Mean of random intercepts
sigma.alpha: SD of random intercepts
mu.beta: Mean of random slopes
sigma.beta: SD of random slopes
sigma: Residual standard deviation

Author

Marc Kéry

Examples

Run this code

library(lattice)
str(dat <- simDat102())      # Implicit default arguments
xyplot(dat$mass ~ dat$lengthN | dat$pop, xlab = 'Length', ylab = 'Mass', 
       main = 'Realized mass-length relationships', pch = 16, cex = 1.2, 
       col = rgb(0, 0, 0, 0.4))

# Fewer populations, more snakes (makes patterns perhaps easier to see ?)
str(dat <- simDat102(nPops = 16, nSample = 100))
xyplot(dat$mass ~ dat$lengthN | dat$pop, xlab = 'Length', ylab = 'Mass', 
       main = 'Realized mass-length relationships
       (default random-coefficients model)', 
       pch = 16, cex = 1.2, col = rgb(0, 0, 0, 0.4))

# Revert to random intercept model (and less residual variation), fewer pops 
# and more snakes. Increased sigma.alpha to emphasize the random intercepts part
str(dat <- simDat102(nPops = 16, nSample = 100, sigma.alpha = 50, sigma.beta = 0, sigma = 10))
xyplot(dat$mass ~ dat$lengthN | dat$pop, xlab = 'Length', ylab = 'Mass', 
       main = 'Realized mass-length relationships (random-intercepts model)', 
       pch = 16, cex = 1.2, col = rgb(0, 0, 0, 0.4))

# Revert to random-effects one-way ANOVA model, only random intercepts, but zero slopes
str(dat <- simDat102(nPops = 16, nSample = 100, sigma.alpha = 50, 
                     mu.beta = 0, sigma.beta = 0, sigma = 10))
xyplot(dat$mass ~ dat$lengthN | dat$pop, xlab = 'Length', ylab = 'Mass', 
       main = 'Realized mass-length relationships
       (one-way ANOVA model with random pop effects)', 
       pch = 16, cex = 1.2, col = rgb(0, 0, 0, 0.4))

# Revert to simple linear regression (= no effects of pop on either intercepts or slopes)
str(dat <- simDat102(nPops = 16, nSample = 100, sigma.alpha = 0, sigma.beta = 0, sigma = 10))
xyplot(dat$mass ~ dat$lengthN | dat$pop, xlab = 'Length', ylab = 'Mass', 
       main = 'Realized mass-length relationships
       (de-facto a simple linear regression now)', 
       pch = 16, cex = 1.2, col = rgb(0, 0, 0, 0.4))

# Revert to "model-of-the-mean": no effects of either population or body length
str(dat <- simDat102(nPops = 16, nSample = 100, sigma.alpha = 0, mu.beta = 0, 
                     sigma.beta = 0, sigma = 10))
xyplot(dat$mass ~ dat$lengthN | dat$pop, xlab = 'Length', ylab = 'Mass', 
       main = 'Realized mass-length relationships
       ("model-of-the-mean", no effects of pop or length)', 
       pch = 16, cex = 1.2, col = rgb(0, 0, 0, 0.4))

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