# SSF

##### Simulation function to assess power of mixed models

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

- Keywords
- misc

##### Usage

```
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 \(\sigma^2(v)\) 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.

##### 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

##### 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

##### Examples

```
# NOT RUN {
oursSSF <- SSF(10,100,10,c(0.4,0.1,0.6,0))
plot(oursSSF)
# }
```

*Documentation reproduced from package pamm, version 1.121, License: GPL-2 | GPL-3*