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

In ASMbook: Functions for the Book "Applied Statistical Modeling for Ecologists"

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
)

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

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

Author(s)

Marc Kéry

Examples

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))

ASMbook documentation built on Sept. 11, 2024, 5:38 p.m.