# An R function for linear mixed model simulation.

### Description

An R function for linear mixed model simulation with generated data set and a given model.

### Usage

1 |

### Arguments

`formula` |
A linear mixed model formula. |

`method` |
The default linear mixed model approach is MINQUE. Users can choose both or one of two linear mixed model approaches, REML and MINQUE. |

`ALPHA` |
A preset nominal probability level. |

### Details

No data frame is needed when more than one response variables are analyzed

### Value

Return list of simulated results for variance components

### Author(s)

Jixiang Wu <qgtools@gmail.com>

### References

Miller, R. G. 1974. The jackknife - a review. Biometrika, 61:1- 15.

Rao, C.R. 1971. Estimation of variance and covariance components-MINQUE theory. J Multiva Ana 1:19

Rao, C. R. and Kleffe, J. 1980. Estimation of variance components. In Handbook of Statistics. Vol. l: 1-40. Krishnaiah, P. R. ed. New York. North-Holland.

Searle, S. R., Casella, G. and McCulloch, C. E. 1992. Variance Components. John Wiley & Sons, Inc. New York.

Wu J (2012) GenMod: An R package for various agricultural data analyses. ASA, CSSA, and SSSA 2012 International Annual Meetings, Cincinnati, OH, p 127

Wu J., Bondalapati K., Glover K., Berzonsky W., Jenkins J.N., McCarty J.C. 2013. Genetic analysis without replications: model evaluation and application in spring wheat. Euphytica. 190:447-458

Zhu J. 1989. Estimation of Genetic Variance Components in the General Mixed Model. Ph.D. Dissertation, NC State University, Raleigh, U.S.A

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
library(minque)
data(ncii)
lmm.inf=lmm.check(Yld~1|Female*Male+Rep,data=ncii)
lmm.inf ##there are five variance components
v=c(20,20,20,20,20) ##there are five variance components
b=as.vector(100) ##there is only population mean as fixed effect
Y=lmm.simudata(Yld~1|Female*Male+Rep,data=ncii,v=v,b=b,SimuNum=50)
Female=factor(ncii$Female)
Male=factor(ncii$Male)
Rep=factor(ncii$Rep)
res=lmm.simu(Y~1|Female*Male+Rep)
res[[1]]
#End
``` |