# SSF: Simulation function to assess power of mixed models In pamm: Power Analysis for Random Effects in Mixed Models

## Description

Given a specific total number of observations and variance-covariance structure for random effect, the function simulates different association of number of group and replicates, giving the specified sample size, and assess p-values and power of random intercept and random slope

## Usage

 ```1 2``` ``` SSF(numsim, tss, nbstep = 10, randompart, fixed = c(0, 1, 0), n.X, autocorr.X, X.dist, intercept = 0, exgr = NA, exrepl = NA, heteroscedasticity = c("null") ) ```

## Arguments

 `numsim` number of simulation for each step `tss` total sample size, nb group * nb replicates `nbstep` number of group*replicates associations to simulate `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 id the relation between I ans S is correlation or covariance, set to `"cor"` by default `fixed` vector of lenght 3 with mean, variance and estimate of fixed effect to simulate `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 `exgr` a vector specifying minimum and maximum value for number of group. Default:`c(2,tss/2)` `exrepl` a vector specifying minimum and maximum value for number of replicates. Default:`c(2,tss/2)` `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 s2(v) denote the variance function evaluated at v, the constant plus power variance function is defined as s2(v) = (t1 + |v|^t2)^2, where t1, t2 are the variance function coefficients. If `c("exp",t)`,models heterogeneity with an exponential variance function. Letting v denote the variance covariate and s2(v) denote the variance function evaluated at v, the exponential variance function is defined as s2(v) = exp(2* t * v), where t is the variance function coefficient.

## 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

## Value

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

## Warning

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

Julien Martin

## 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.

`PAMM`, `EAMM`, `plot.SSF`
 ```1 2 3 4 5``` ```## Not run: oursSSF <- SSF(,100,10,c(0.4,0.1,0.6,0)) plot(oursSSF) ## End(Not run) ```