pamm (version 1.121)

PAMM: Simulation function to assess power of mixed models

Description

Given a specific varaince-covariance structure for random effect, the function simulate different group size and assess p-values and power of random intercept and random slope

Usage

PAMM(numsim, group, repl, randompart, fixed, n.X, autocorr.X,
X.dist, intercept, heteroscedasticity = c("null"),
ftype="lmer", mer.sim=FALSE)

Value

data frame reporting estimated P-values and power with CI for random intercept and random slope

Arguments

numsim

number of simulation for each step

group

number of group. Could be specified as a vector

repl

number of replicates per group . Could be specified as a vector

randompart

vector of lenght 4 or 5, with 1: variance component of intercept, VI; 2: variance component of slope, VS; 3: residual variance, VR; 4: relation between random intercept and random slope; 5: "cor" or "cov" determine if the relation 4 between I ans S is a correlation or a covariance. Default: "cor"

fixed

vector with mean, variance and estimate of fixed effect to simulate. Default: c(0, 1, 0)

n.X

number of different values to simulate for the fixed effect (covariate). If NA, all values of X are independent between groups. If the value specified is equivalent to the number of replicates per group, repl, then all groups are observed for the same values of the covariate. Default: NA

autocorr.X

correlation between two successive covariate value for a group. Default: 0

X.dist

specify the distribution of the fixed effect. Only "gaussian" (normal distribution) and "unif" (uniform distribution) are accepted actually. Default: "gaussian"

intercept

a numeric value giving the expected intercept value. Default:0

heteroscedasticity

a vector specifying heterogeneity in residual variance across X. If c("null") residual variance is homogeneous across X. If c("power",t1,t2) models heterogeneity with a constant plus power variance function. Letting \(v\) denote the variance covariate and \(\sigma^2(v)\) denote the variance function evaluated at \(v\), the constant plus power variance function is defined as \(\sigma^2(v) = (\theta_1 + |v|^{\theta_2})^2\), where \(\theta_1,\theta_2\) are the variance function coefficients. If c("exp",t),models heterogeneity with an exponential variance function. Letting \(v\) denote the variance covariate and \(\sigma^2(v)\) denote the variance function evaluated at \(v\), the exponential variance function is defined as \(\sigma^2(v) = e^{2 * \theta * v}\), where \(\theta\) is the variance function coefficient.

ftype

character value "lmer", "lme" or "MCMCglmm" specifying the function to use to fit the model. Actually "lmer" only is accepted

mer.sim

simulate the data using simulate.merMod from lme4. Faster for large sample size but not as flexible.

Author

Julien Martin

Warning

the simulation is based on a balanced data set with unrelated group

Details

P-values for random effects are estimated using a log-likelihood ratio test between two models with and without the effect. Power represent the percentage of simulations providing a significant p-value for a given random structure

References

Martin, Nussey, Wilson and Reale Submitted Measuring between-individual variation in reaction norms in field and experimental studies: a power analysis of random regression models. Methods in Ecology and Evolution.

See Also

EAMM, SSF, plot.PAMM

Examples

if (FALSE) {
ours <- PAMM(numsim = 10, group = c(seq(10, 50, 10), 100),
             repl = c(3, 4, 6),
             randompart = c(0.4, 0.1, 0.5, 0.1), fixed = c(0, 1, 0.7))
plot(ours,"both")
   }