Package 'MM4LMM' reference manual

Title:	Inference of Linear Mixed Models Through MM Algorithm
Description:	The main function MMEst() performs (Restricted) Maximum Likelihood in a variance component mixed models using a Min-Max (MM) algorithm (Laporte, F., Charcosset, A. & Mary-Huard, T. (2022) <doi:10.1371/journal.pcbi.1009659>).
Authors:	Fabien Laporte [aut, cre], Tristan Mary-Huard [aut], GQMS CoreFunctions Team [aut]
Maintainer:	Fabien Laporte <[email protected]>
License:	GPL (>= 2)
Version:	3.0.3
Built:	2025-02-28 07:36:27 UTC
Source:	CRAN

Min-Max algorithms for Variance Component Mixed Model Inference.

Description

This package provides a function to perform either ML or ReML estimation in a Variance Component Mixed Model. The optimization of the (possibly Restricted) log-likelihood is perfomed using the Min-Max algorithm described in Hunter et al. (2004). Depending on the number of variance components, different computational tricks are used to speed up inference. Additionally, the AnovaTest function provides Type I, Type III and Type III Kenward Roger approximation test series for fixed effects. The nullity of a specific linear combination can also be tested.

Details

Variance Component Mixed Models are mixed models of the form

$Y = X \beta + \sum_{k=1}^K Z_k u_k$

where Y is the response vector, X and $\beta$ are respectively the incidence matrix and the coefficient vector associated with the fixed effects, $u_k$ is the kth vector of random effects and corresponds to its associated incidence matrix. All random effect are assumed to be Gaussian with mean 0 and covariance $\sigma_k^2 R_k$ , where $R_k$ is a known correlation matrix and $\sigma_k^2$ is an unknown variance parameter. All random effects are assumed to be independent. In many applications the last random component corresponds to the error and therefore both $Z_k$ and $R_k$ correspond to the identity matrix.

In such models the inference of both the unknown variance components $\sigma_k^2$ ,..., $\sigma_K^2$ and the fixed effect $\beta$ can be achieved through Maximum Likelihood (ML) or Restricted Maximum Likelihood (ReML) estimation. Neither ML nor ReML yield close form expressions of the estimates, consequently the maximization of the (restricted) log-likelihood has to be performed numerically. This package provides the user with Min-Max algorithms for the optimization. Efficient tricks such as profiling, MME trick and MM acceleration are implemented for computational efficiency (see Johnson et al. (1995), Varadhan et al. (2008) for details). The main function MMEst handles parallel inference of multiple models sharing the same set of correlation matrices - but possibly different fixed effects, an usual situation in GWAS analysis for instance.

Author(s)

Fabien Laporte and Tristan Mary-Huard

Maintainer: Fabien Laporte <[email protected]>

References

Laporte, F., Charcosset, A., & Mary-Huard, T. (2022). Efficient ReML inference in variance component mixed models using a Min-Max algorithm. PLOS Computational Biology, 18(1), e1009659.

Johnson, D. L., & Thompson, R. (1995). Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. Journal of dairy science, 78(2), 449-456.

Hunter, D. R., & Lange, K. (2004). A tutorial on MM algorithms. The American Statistician, 58(1), 30-37.

Kenward, M. G., & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 983-997.

Varadhan, R., & Roland, C. (2008). Simple and globally convergent methods for accelerating the convergence of any EM algorithm. Scandinavian Journal of Statistics, 35(2), 335-353.

Zhou, H., Hu, L., Zhou, J., & Lange, K. (2015). MM algorithms for variance components models. arXiv preprint arXiv:1509.07426.

Type I and Type III Tests for mixed models.

Description

This function computes Type I and Type III tests for each fixed effect of a model, as displayed by the MMEst function. Alternatively, a specific linear combination of the fixed parameters may be tested (at 0).

Usage

AnovaTest(ResMMEst , TestedCombination=NULL , Type = "TypeIII" ,
    Cofactor = NULL , X = NULL , formula = NULL , VarList = NULL ,
    NbCores=1)
AnovaTest(ResMMEst , TestedCombination=NULL , Type = "TypeIII" ,
    Cofactor = NULL , X = NULL , formula = NULL , VarList = NULL ,
    NbCores=1)

Arguments

`ResMMEst`	A list as displayed by the `MMEst` function.
`TestedCombination`	A contrast matrix or a list of contrast matrices $C_m$ . Each matrix corresponds to a (set of) linear combination to be (jointly) tested at 0.
`Type`	"TypeI", "TypeIII" or "KR" (default is "TypeIII"). AnovaTest will compute tests of the given type for each fixed effect in the model. The option is ignored if a `TestedCombination` is provided. If `Type` is "KR" then AnovaTest will compute Type III test using Kenward Roger approximation, see Kenward and Roger (1997) for details.
`Cofactor`	The incidence matrix corresponding to fixed effects common to all models used in `MMEst`. If `NULL`, a single intercept is used as cofactor. This entry is needed when `Type` is "KR".
`X`	The incidence matrix or a list of incidence matrices corresponding to fixed effects specific to each model used in `MMEst` (default is `NULL`). This entry is needed when `Type` is "KR".
`formula`	The formula object specifying the fixed effect part of all models separated by + operators used in `MMEst` (default is `NULL`). This entry is needed when `Type` is "KR".
`VarList`	The list of correlation matrices associated with random and residual effects used in `MMEst` (default is `NULL`). This entry is needed when `Type` is "KR".
`NbCores`	The number of cores to be used.

Details

If no TestedCombination is provided, the function performs either Type I or Type III tests for each fixed effect in the model (default is Type III). If TestedCombination is provided, each linear combination in TestedCombination is tested at 0 using a Wald test. No check is performed regarding the estimability of the linear combination to be tested. If the dimension of the combination does not match with the dimension of ResMMEst, a NA is returned.

Value

The output of the function is a list with as many items as in the original input list ResMMEst. For each item of ResMMEst, a table is provided that contains the Wald test statistics, p-values and degrees of freedom for all tested hypotheses.

Author(s)

F. Laporte and T. Mary-Huard

References

Kenward, M. G., & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 983-997.

Examples

  require('MM4LMM')
  data(QTLDetectionExample)
  Pheno <- QTLDetectionExample$Phenotype
  Geno <- QTLDetectionExample$Genotype
  Kinship <- QTLDetectionExample$Kinship

  ##Build the VarList object
  VL <- list(Additive = Kinship , Error = diag(1,length(Pheno)))
  
  ##Perform inference
  Result <- MMEst(Y=Pheno , X = Geno , VarList = VL)

  ##Compute tests
  AOV <- AnovaTest(Result,Type="TypeI")
  
  ##Test specific contrast matrix
  TC = matrix(c(0,1),nrow=1)
  AOV2 <- AnovaTest(Result, TestedCombination = TC)
  
  AOV3 <- AnovaTest(Result, TestedCombination = TC , Type="KR" , X = Geno , VarList = VL)

require('MM4LMM')
  data(QTLDetectionExample)
  Pheno <- QTLDetectionExample$Phenotype
  Geno <- QTLDetectionExample$Genotype
  Kinship <- QTLDetectionExample$Kinship

  ##Build the VarList object
  VL <- list(Additive = Kinship , Error = diag(1,length(Pheno)))
  
  ##Perform inference
  Result <- MMEst(Y=Pheno , X = Geno , VarList = VL)

  ##Compute tests
  AOV <- AnovaTest(Result,Type="TypeI")
  
  ##Test specific contrast matrix
  TC = matrix(c(0,1),nrow=1)
  AOV2 <- AnovaTest(Result, TestedCombination = TC)
  
  AOV3 <- AnovaTest(Result, TestedCombination = TC , Type="KR" , X = Geno , VarList = VL)

BLUP from MM4LMM results

Description

This function computes the BLUP for each random vector included in the MMEst output. Note that this function can be called only if the argument X of MMEst was set to NULL

Usage

  MMBlup(Y,Cofactor = NULL, X = NULL, fmla = NULL,ZList=NULL,VarList,ResMM)
MMBlup(Y,Cofactor = NULL, X = NULL, fmla = NULL,ZList=NULL,VarList,ResMM)

Arguments

`Y`	The vector of response values used in the function `MMEst`.
`Cofactor`	The incidence matrix corresponding to fixed effects common to all models to be adjusted used in the function `MMEst`. If `NULL`, a vector full of 1 is used.
`X`	Must be `NULL`.
`fmla`	The formula object specifying the fixed effect part of all models separated by + operators used in the function `MMEst` (default is `NULL`).
`ZList`	The list of incidence matrices associated with random and residual effects used in the function `MMEst` (default is `NULL`).
`VarList`	The list of covariance matrices associated with random and residual effects used in the function `MMEst`.
`ResMM`	A list as displayed by the `MMEst` function for a Variance Component Analysis.

Value

The function returns a list where each element corresponds to the Best Linear Unbiased Prediction of a random component of the model.

Author(s)

GQMS CoreFunctions Team

Examples

  require('MM4LMM')
  data(VarianceComponentExample)
  DataHybrid <- VarianceComponentExample$Data
  KinF <- VarianceComponentExample$KinshipF
  KinD <- VarianceComponentExample$KinshipD
  
  ##Build incidence matrix for each random effect
  Zf <- t(sapply(as.character(DataHybrid$CodeFlint), function(x)
    as.numeric(rownames(KinF)==x)))
  Zd <- t(sapply(as.character(DataHybrid$CodeDent), function(x)
    as.numeric(rownames(KinD)==x)))
  
  ##Build the VarList and ZList objects
  VL = list(Flint=KinF , Dent=KinD , Error = diag(1,nrow(DataHybrid)))
  ZL <- list(Flint=Zf , Dent=Zd , Error = diag(1,nrow(DataHybrid)))
  
  ##Perform inference
  #A first way to call MMEst
  ResultVA <- MMEst(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                    , ZList = ZL  ,  VarList = VL)
  BlupVA <- MMBlup(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                    , ZList = ZL  ,  VarList = VL , ResMM=ResultVA)
require('MM4LMM')
  data(VarianceComponentExample)
  DataHybrid <- VarianceComponentExample$Data
  KinF <- VarianceComponentExample$KinshipF
  KinD <- VarianceComponentExample$KinshipD
  
  ##Build incidence matrix for each random effect
  Zf <- t(sapply(as.character(DataHybrid$CodeFlint), function(x)
    as.numeric(rownames(KinF)==x)))
  Zd <- t(sapply(as.character(DataHybrid$CodeDent), function(x)
    as.numeric(rownames(KinD)==x)))
  
  ##Build the VarList and ZList objects
  VL = list(Flint=KinF , Dent=KinD , Error = diag(1,nrow(DataHybrid)))
  ZL <- list(Flint=Zf , Dent=Zd , Error = diag(1,nrow(DataHybrid)))
  
  ##Perform inference
  #A first way to call MMEst
  ResultVA <- MMEst(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                    , ZList = ZL  ,  VarList = VL)
  BlupVA <- MMBlup(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                    , ZList = ZL  ,  VarList = VL , ResMM=ResultVA)

MM inference method for variance component mixed models

Description

This is the main function of the MM4LMM package. It performs inference in a variance component mixed model using a Min-Max algorithm. Inference in multiple models (e.g. for GWAS analysis) can also be performed.

Usage

MMEst(Y, Cofactor = NULL, X = NULL, formula=NULL, VarList, ZList = NULL, Method = "Reml",
	Henderson=NULL, Init = NULL, CritVar = 0.001, CritLogLik = 0.001,
	MaxIter = 100, NbCores = 1, Verbose = TRUE)
MMEst(Y, Cofactor = NULL, X = NULL, formula=NULL, VarList, ZList = NULL, Method = "Reml",
	Henderson=NULL, Init = NULL, CritVar = 0.001, CritLogLik = 0.001,
	MaxIter = 100, NbCores = 1, Verbose = TRUE)

Arguments

`Y`	A vector of response values.
`Cofactor`	An incidence matrix corresponding to fixed effects common to all models to be adjusted. If `NULL`, a single intercept is used as cofactor.
`X`	An incidence matrix or a list of incidence matrices corresponding to fixed effects specific to each model. If `X` is a matrix, one model per column will be fitted. If `X` is a list, one model per element of the list will be fitted (default is `NULL`).
`formula`	A formula object specifying the fixed effect part of all models separated by + operators. To specify an interaction between `Cofactor` and `X` use the colnames of `X` when it is a list or use "Xeffect" when `X` is a matrix.
`VarList`	A list of covariance matrices associated with random and residual effects.
`ZList`	A list of incidence matrices associated with random and residual effects (default is `NULL`).
`Method`	The method used for inference. Available methods are "Reml" (Restricted Maximum Likelihood) and "ML" (Maximum Likelihood).
`Henderson`	If `TRUE` the Henderson trick is applied. If `FALSE` the Henderson trick is not applied. If `NULL` the algorithm chooses wether to use the trick or not.
`Init`	A vector of initial values for variance parameters (default is `NULL`)
`CritVar`	Value of the criterion for the variance components to stop iteration. (see Details)
`CritLogLik`	Value of the criterion for the log-likelihood to stop iteration. (see Details)
`MaxIter`	Maximum number of iterations per model.
`NbCores`	Number of cores to be used.
`Verbose`	A boolean describing if messages have to be printed (TRUE) or not (FALSE). Default is TRUE.

Details

If X is NULL, the following model is fitted:

$Y = X_C \beta_C + \sum_{k=1}^K Z_k u_k$

with $X_C$ the matrix provided in Cofactor, $\beta_C$ the unknown fixed effects, $Z_k$ the incidence matrix provided for the kth component of ZList and $u_k$ the kth vector of random effects. If ZList is unspecified, all incidence matrices are assumed to be the Identity matrix. Random effects are assumed to follow a Gaussian distribution with mean 0 and covariance matrix $R_k \sigma_k^2$ , where $R_k$ is the kth correlation matrix provided in VarList.

If X is not NULL, the following model is fitted for each i:

$Y = X_C \beta_C + X_{[i]} \beta_{[i]} + \sum_{k=1}^K Z_k u_k$

where $X_{[i]}$ is the incidence matrix corresponding to the ith component (i.e. column if $X$ is a matrix, element otherwise) of $X$ , and $\beta_{[i]}$ is the (unknow) fixed effect associated to $X_{[i]}$ .

All models are fitted using the MM algorithm. If Henderson=TRUE, at each step the quantities required for updating the variance components are computed using the Mixed Model Equation (MME) trick. See Johnson et al. (1995) for details.

Value

The result is a list where each element corresponds to a fitted model. Each element displays the following:

`Beta`	Estimated values of $\beta_C$ and $\beta_{i}$
`Sigma2`	Estimated values of $\sigma_1^2,...,\sigma_K^2$
`VarBeta`	Variance matrix of `Beta`
`LogLik (Method)`	The value of the (restricted, if `Method` is "Reml") log-likelihood
`NbIt`	The number of iterations required to reach the optimum
`Method`	The method used for the inference
`attr`	An integer vector with an entry for each element of `Beta` giving the term in `Factors` which gave rise to this element (for internal use in the function `AnovaTest`)
`Factors`	Names of each term in the formula

Author(s)

F. Laporte and T. Mary-Huard

References

Laporte, F., Charcosset, A., & Mary-Huard, T. (2022). Efficient ReML inference in variance component mixed models using a Min-Max algorithm. PLOS Computational Biology, 18(1), e1009659.

Hunter, D. R., & Lange, K. (2004). A tutorial on MM algorithms. The American Statistician, 58(1), 30-37.

Zhou, H., Hu, L., Zhou, J., & Lange, K. (2015). MM algorithms for variance components models. arXiv preprint arXiv:1509.07426.

Examples

require('MM4LMM')

#### Example 1: variance component analysis, 1 model
data(VarianceComponentExample)
DataHybrid <- VarianceComponentExample$Data
KinF <- VarianceComponentExample$KinshipF
KinD <- VarianceComponentExample$KinshipD

##Build incidence matrix for each random effect
Zf <- t(sapply(as.character(DataHybrid$CodeFlint), function(x)
  as.numeric(rownames(KinF)==x)))
Zd <- t(sapply(as.character(DataHybrid$CodeDent), function(x)
  as.numeric(rownames(KinD)==x)))

##Build the VarList and ZList objects
VL = list(Flint=KinF , Dent=KinD , Error = diag(1,nrow(DataHybrid)))
ZL <- list(Flint=Zf , Dent=Zd , Error = diag(1,nrow(DataHybrid)))

##Perform inference
#A first way to call MMEst
ResultVA <- MMEst(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                  , ZList = ZL  ,  VarList = VL)
length(ResultVA)
print(ResultVA)

#A second way to call MMEst (same result)
Formula <- as.formula('~ Trial')
ResultVA2 <- MMEst(Y=DataHybrid$Trait  , Cofactor = DataHybrid,
                   formula = Formula
                  , ZList = ZL  ,  VarList = VL)
length(ResultVA2)
print(ResultVA2)



#### Example 2: Marker Selection with interaction between Cofactor and X matrix
Formula <- as.formula('~ Trial+Xeffect+Xeffect:Trial')
ResultVA3 <- MMEst(Y=DataHybrid$Trait  , Cofactor = DataHybrid,
                  X = VarianceComponentExample$Markers,
                   formula = Formula
                  , ZList = ZL  ,  VarList = VL)
length(ResultVA3)
print(ResultVA3[[1]])


#### Example 3: QTL detection with two variance components
data(QTLDetectionExample)
Pheno <- QTLDetectionExample$Phenotype
Geno <- QTLDetectionExample$Genotype
Kinship <- QTLDetectionExample$Kinship

##Build the VarList object
VLgd <- list(Additive=Kinship , Error=diag(1,length(Pheno)))

##Perform inference
ResultGD <- MMEst(Y=Pheno , X=Geno
                  , VarList=VLgd , CritVar = 10e-5)

length(ResultGD)
print(ResultGD[[1]])
require('MM4LMM')

#### Example 1: variance component analysis, 1 model
data(VarianceComponentExample)
DataHybrid <- VarianceComponentExample$Data
KinF <- VarianceComponentExample$KinshipF
KinD <- VarianceComponentExample$KinshipD

##Build incidence matrix for each random effect
Zf <- t(sapply(as.character(DataHybrid$CodeFlint), function(x)
  as.numeric(rownames(KinF)==x)))
Zd <- t(sapply(as.character(DataHybrid$CodeDent), function(x)
  as.numeric(rownames(KinD)==x)))

##Build the VarList and ZList objects
VL = list(Flint=KinF , Dent=KinD , Error = diag(1,nrow(DataHybrid)))
ZL <- list(Flint=Zf , Dent=Zd , Error = diag(1,nrow(DataHybrid)))

##Perform inference
#A first way to call MMEst
ResultVA <- MMEst(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                  , ZList = ZL  ,  VarList = VL)
length(ResultVA)
print(ResultVA)

#A second way to call MMEst (same result)
Formula <- as.formula('~ Trial')
ResultVA2 <- MMEst(Y=DataHybrid$Trait  , Cofactor = DataHybrid,
                   formula = Formula
                  , ZList = ZL  ,  VarList = VL)
length(ResultVA2)
print(ResultVA2)



#### Example 2: Marker Selection with interaction between Cofactor and X matrix
Formula <- as.formula('~ Trial+Xeffect+Xeffect:Trial')
ResultVA3 <- MMEst(Y=DataHybrid$Trait  , Cofactor = DataHybrid,
                  X = VarianceComponentExample$Markers,
                   formula = Formula
                  , ZList = ZL  ,  VarList = VL)
length(ResultVA3)
print(ResultVA3[[1]])


#### Example 3: QTL detection with two variance components
data(QTLDetectionExample)
Pheno <- QTLDetectionExample$Phenotype
Geno <- QTLDetectionExample$Genotype
Kinship <- QTLDetectionExample$Kinship

##Build the VarList object
VLgd <- list(Additive=Kinship , Error=diag(1,length(Pheno)))

##Perform inference
ResultGD <- MMEst(Y=Pheno , X=Geno
                  , VarList=VLgd , CritVar = 10e-5)

length(ResultGD)
print(ResultGD[[1]])

Covariance Matrix for variance estimators.

Description

This function computes the covariance matrix of variance estimators using either the inverse of the Expected Hessian Matrix or the inverse of the Average Information Matrix.

Usage

MMVcov(ResMM , Y , Cofactor = NULL , formula = NULL,
    ZList = NULL , VarList , information="Expected")
MMVcov(ResMM , Y , Cofactor = NULL , formula = NULL,
    ZList = NULL , VarList , information="Expected")

Arguments

`ResMM`	A list as displayed by the `MMEst` function for a Variance Component Analysis (only the first element of the list will be analyzed).
`Y`	The vector of response values used in the function `MMEst`.
`Cofactor`	The incidence matrix corresponding to fixed effects common to all models to be adjusted used in the function `MMEst`. If `NULL`, a vector full of 1 is used.
`formula`	The formula object specifying the fixed effect part of all models separated by + operators used in the function `MMEst` (default is `NULL`).
`ZList`	The list of incidence matrices associated with random and residual effects used in the function `MMEst` (default is `NULL`).
`VarList`	The list of covariance matrices associated with random and residual effects used in the function `MMEst`.
`information`	A string specifying the method used to approximate the covariance matrix. It can be either "Expected" (default) to use the Expected Hessian Matrix or "AI" to use the Average Information Matrix. The AI matrix is always computed using Reml estimates whereas the expected hessian matrix could also be used for ML estimates.

Details

If information is not specified then the algorithm computes the covariance matrix using the Expected matrix based on the inference method (Reml or ML) used in the first item of ResMM. If information is equal to "AI" then it computes the AI matrix to calculate the covariance matrix. Only the first item of ResMM is analyzed.

Value

The output of the function is a list:

`vcov`	The covariance matrix of the variance estimators
`SE`	The standard errors of the variance estimators (the square root of the covariance matrix diagonal)

Author(s)

F. Laporte and T. Mary-Huard

Examples

  require('MM4LMM')
  data(VarianceComponentExample)
  DataHybrid <- VarianceComponentExample$Data
  KinF <- VarianceComponentExample$KinshipF
  KinD <- VarianceComponentExample$KinshipD

  ##Build incidence matrix for each random effect
  Zf <- t(sapply(as.character(DataHybrid$CodeFlint), function(x)
  as.numeric(rownames(KinF)==x)))
  Zd <- t(sapply(as.character(DataHybrid$CodeDent), function(x)
  as.numeric(rownames(KinD)==x)))

  ##Build the VarList and ZList objects
  VL = list(Flint=KinF , Dent=KinD , Error = diag(1,nrow(DataHybrid)))
  ZL <- list(Flint=Zf , Dent=Zd , Error = diag(1,nrow(DataHybrid)))

  ##Perform inference
  #A first way to call MMEst
  ResultVA <- MMEst(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                  , ZList = ZL  ,  VarList = VL)
  Expected_vcov <- MMVcov(ResMM=ResultVA,Y=DataHybrid$Trait,
                  Cofactor = matrix(DataHybrid$Trial),
                  , ZList = ZL  ,  VarList = VL)
  AI_vcov <- MMVcov(ResMM=ResultVA,Y=DataHybrid$Trait,
                  Cofactor = matrix(DataHybrid$Trial),
                  , ZList = ZL  ,  VarList = VL , information = "AI")
require('MM4LMM')
  data(VarianceComponentExample)
  DataHybrid <- VarianceComponentExample$Data
  KinF <- VarianceComponentExample$KinshipF
  KinD <- VarianceComponentExample$KinshipD

  ##Build incidence matrix for each random effect
  Zf <- t(sapply(as.character(DataHybrid$CodeFlint), function(x)
  as.numeric(rownames(KinF)==x)))
  Zd <- t(sapply(as.character(DataHybrid$CodeDent), function(x)
  as.numeric(rownames(KinD)==x)))

  ##Build the VarList and ZList objects
  VL = list(Flint=KinF , Dent=KinD , Error = diag(1,nrow(DataHybrid)))
  ZL <- list(Flint=Zf , Dent=Zd , Error = diag(1,nrow(DataHybrid)))

  ##Perform inference
  #A first way to call MMEst
  ResultVA <- MMEst(Y=DataHybrid$Trait  , Cofactor = matrix(DataHybrid$Trial)
                  , ZList = ZL  ,  VarList = VL)
  Expected_vcov <- MMVcov(ResMM=ResultVA,Y=DataHybrid$Trait,
                  Cofactor = matrix(DataHybrid$Trial),
                  , ZList = ZL  ,  VarList = VL)
  AI_vcov <- MMVcov(ResMM=ResultVA,Y=DataHybrid$Trait,
                  Cofactor = matrix(DataHybrid$Trial),
                  , ZList = ZL  ,  VarList = VL , information = "AI")

QTL Detection Example

Description

This corresponds to (a sample of) the dataset presented in Rincent et al. (2014).

Usage

data("QTLDetectionExample")data("QTLDetectionExample")

Format

The format is: List of 3

Phenotype: Named num [1:259]
Genotype: int [1:259,1:10]
Kinship: num [1:259,1:259]

Details

The list contains three elements:

Phenotype: a numeric vector containing phenotypes of individuals
Genotype: a matrix containing the genotypes of indviduals over 10 biallelic markers
Kinship: a matrix of simple relatedness coefficients between individuals

Source

https://link.springer.com/article/10.1007/s00122-014-2379-7

References

Rincent, R., Nicolas, S., Bouchet, S., Altmann, T., Brunel, D., Revilla, P., ... & Schipprack, W. (2014). Dent and Flint maize diversity panels reveal important genetic potential for increasing biomass production. Theoretical and applied genetics, 127(11), 2313-2331.

Examples

data(QTLDetectionExample)
names(QTLDetectionExample)
## maybe str(QTLDetectionExample) ; plot(QTLDetectionExample) ...
data(QTLDetectionExample)
names(QTLDetectionExample)
## maybe str(QTLDetectionExample) ; plot(QTLDetectionExample) ...

Variance Component Example

Description

This corresponds to (a sample of) the dataset presented in Giraud et al. (2017).

Usage

data("VarianceComponentExample")data("VarianceComponentExample")

Format

The format is: List of 3

Data

'data.frame': 432 obs. of 5 variables

Trial: a factor with 2 levels
CodeHybrid: a factor with 177 levels
CodeDent: a factor with 116 levels
CodeFlint: a factor with 122 levels
Trait: a numeric vector

KinshipD

num [1:116,1:116]

KinshipF

num [1:122,1:122]

Details

The list contains three elements:

Data: a data frame containing the information about hybrids (trials, hybrid names, dent parental lines, flint parental lines and phenotypes)
KinshipD: a matrix of simple relatedness coefficients between dent lines
KinshipF: a matrix of simple relatedness coefficients between flint lines

Source

doi:10.1534/genetics.117.300305

References

Giraud, H., Bauland, C., Falque, M., Madur, D., Combes, V., Jamin, P., ... & Blanchard, P. (2017). Reciprocal Genetics: Identifying QTL for General and Specific Combining Abilities in Hybrids Between Multiparental Populations from Two Maize (Zea mays L.) Heterotic Groups. Genetics, 207(3), 1167-1180.

Examples

data(VarianceComponentExample)
names(VarianceComponentExample)
## maybe str(VarianceComponentExample) ; plot(VarianceComponentExample) ...
data(VarianceComponentExample)
names(VarianceComponentExample)
## maybe str(VarianceComponentExample) ; plot(VarianceComponentExample) ...

Package 'MM4LMM'

Help Index

Min-Max algorithms for Variance Component Mixed Model Inference.

Description

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Type I and Type III Tests for mixed models.

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BLUP from MM4LMM results

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MM inference method for variance component mixed models

Description

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Covariance Matrix for variance estimators.

Description

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QTL Detection Example

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Examples

Variance Component Example

Description

Usage

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Examples