EM.MIM {QTLEMM}

EM Algorithm for QTL MIM

Description

Expectation-maximization algorithm for QTL multiple interval mapping.

Usage

EM.MIM(
  D.matrix,
  cp.matrix,
  y,
  E.vector0 = NULL,
  X = NULL,
  beta0 = NULL,
  variance0 = NULL,
  crit = 10^-5,
  stop = 1000,
  conv = TRUE,
  console = TRUE
)

Arguments

D.matrix

matrix. The design matrix of QTL effects is a g*p matrix, where g is the number of possible QTL genotypes, and p is the number of effects considered in the MIM model. This design matrix can be conveniently generated using the function D.make().

cp.matrix

matrix. The conditional probability matrix is an n*g matrix, where n is the number of individuals, and g is the number of possible genotypes of QTLs. This conditional probability matrix can be easily generated using the function Q.make().

y

vector. A vector with n elements that contain the phenotype values of individuals.

E.vector0

vector. The initial value for QTL effects. The number of elements corresponds to the column dimension of the design matrix. If E.vector0=NULL, the initial value for all effects will be set to 0.

X

matrix. The design matrix of the fixed factors except for QTL effects. It is an n*k matrix, where n is the number of individuals, and k is the number of fixed factors. If X=NULL, the matrix will be an n*1 matrix where all elements are 1.

beta0

vector. The initial value for effects of the fixed factors. The number of elements corresponds to the column dimension of the fixed factor design matrix. If beta0=NULL, the initial value will be set to the average of y.

variance0

numeric. The initial value for variance. If variance0=NULL, the initial value will be set to the variance of phenotype values.

crit

numeric. The convergence criterion of EM algorithm. The E and M steps will iterate until a convergence criterion is met. It must be a value between 0 and 1.

stop

numeric. The stopping criterion of EM algorithm. The E and M steps will halt when the iteration number reaches the stopping criterion, treating the algorithm as having failed to converge.

conv

logical. If set to False, it will disregard the failure to converge and output the last result obtained during the EM algorithm before reaching the stopping criterion.

console

logical. Determines whether the process of the algorithm will be displayed in the R console or not.

Value

E.vector

The QTL effects are calculated by the EM algorithm.

beta

The effects of the fixed factors are calculated by the EM algorithm.

variance

The error variance is calculated by the EM algorithm.

PI.matrix

The posterior probabilities matrix after the process of the EM algorithm.

log.likelihood

The log-likelihood value of this model.

LRT

The LRT statistic of this model.

R2

The coefficient of determination of this model. This can be used as an estimate of heritability.

y.hat

The fitted values of trait values are calculated by the estimated values from the EM algorithm.

iteration.number

The iteration number of the EM algorithm.

References

KAO, C.-H. and Z.-B. ZENG 1997 General formulas for obtaining the maximum likelihood estimates and the asymptotic variance-covariance matrix in QTL mapping when using the EM algorithm. Biometrics 53, 653-665. <doi: 10.2307/2533965.>

KAO, C.-H., Z.-B. ZENG and R. D. TEASDALE 1999 Multiple interval mapping for Quantitative Trait Loci. Genetics 152: 1203-1216. <doi: 10.1093/genetics/152.3.1203>

See Also

D.make Q.make EM.MIM2 EM.MIMv

Examples

# load the example data
load(system.file("extdata", "exampledata.RDATA", package = "QTLEMM"))

# run and result
D.matrix <- D.make(3, type = "RI", aa = c(1, 3, 2, 3), dd = c(1, 2, 1, 3), ad = c(1, 2, 2, 3))
cp.matrix <- Q.make(QTL, marker, geno, type = "RI", ng = 2)$cp.matrix
result <- EM.MIM(D.matrix, cp.matrix, y)
result$E.vector