# powerLmer2: Power analysis for normal data 2 In fullfact: Full Factorial Breeding Analysis

## Description

Extracts the power values of dam, sire, and dam by sire variance components from a linear mixed-effect model using the lmer function of the lme4 package. Options to include one random position and/or one random block effect(s).

## Usage

 ```1 2``` ```powerLmer2(varcomp, nval, alpha = 0.05, nsim = 100, position = NULL, block = NULL, ml = F) ```

## Arguments

 `varcomp` Vector of known dam, sire, dam by sire, residual, and position and/or block variance components, i.e. c(dam, sire, dam x sire, residual, position/block). If there is a position and a block c(..., residual, position, block). `nval` Vector of known dam, sire, offspring per family, and offspring per position or number of blocks sample sizes, i.e. c(dam, sire, offspring, position/block). If there is a position and a block c(..., offspring, position, block). `alpha` Statistical significance value. Default is 0.05. `nsim` Number of simulations. Default is 100. `position` Optional number of positions. `block` Optional vector of dams and sires per block, e.g. c(2,2). `ml` Default is FALSE for restricted maximum likelihood. Change to TRUE for maximum likelihood.

## Details

Extracts the dam, sire, dam, dam by sire, and position and/or block power values. Power values are calculated by stochastically simulation data and then calculating the proportion of significance values less than alpha for each component (Bolker 2008). Significance values for the random effects are determined using likelihood ratio tests (Bolker et al. 2009).

## Value

Prints a data frame with the sample sizes, variance component inputs, variance component outputs, and power values.

## Note

Maximum likelihood (ML) estimates the parameters that maximize the likelihood of the observed data and has the advantage of using all the data and accounting for non-independence (Lynch and Walsh 1998, p. 779; Bolker et al. 2009). On the other hand, ML has the disadvantage of assuming that all fixed effects are known without error, producing a downward bias in the estimation of the residual variance component. This bias can be large if there are lots of fixed effects, especially if sample sizes are small. Restricted maximum likelihood (REML) has the advantage of not assuming the fixed effects are known and averages over the uncertainty, so there can be less bias in the estimation of the residual variance component. However, REML only maximizes a portion of the likelihood to estimate the effect parameters, but is the preferred method for analyzing large data sets with complex structure.

## References

Bolker BM. 2008. Ecological models and data in R. Princeton University Press, New Jersey.

Bolker BM, Brooks ME, Clark CJ, Geange SW, Poulsen JR, Stevens MHH, White J-SS. 2009. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology and Evolution 24(3): 127-135. DOI: 10.1016/j.tree.2008.10.008

Lynch M, Walsh B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer Associates, Massachusetts.

`powerLmer`, `powerLmer3`
 ```1 2 3 4 5 6 7 8 9``` ```#100 simulations #position only, e.g. 8 tanks ## Not run: powerLmer2(varcomp=c(0.2030,0,0.1798,0.5499,0.1077),nval=c(8,8,20,40),position=8) #block only, e.g. four 2 x 2 ## Not run: powerLmer2(varcomp=c(0.2030,0,0.1798,0.5499,0.1077),nval=c(8,8,20,4),block=c(2,2)) #position and block ## Not run: powerLmer2(varcomp=c(0.2030,0,0.1798,0.5499,0.1077,0.1077),nval=c(8,8,20,40,4), position=8,block=c(2,2)) ## End(Not run) ```