R: EM Algorithm for QTL MIM with Selective Genotyping

EM.MIM2 {QTLEMM}

R Documentation

EM Algorithm for QTL MIM with Selective Genotyping

Description

Expectation-maximization algorithm for QTL multiple interval mapping. It can handle genotype data which is selective genotyping.

Usage

EM.MIM2(
  QTL,
  marker,
  geno,
  D.matrix,
  cp.matrix = NULL,
  y,
  yu = NULL,
  sele.g = "n",
  tL = NULL,
  tR = NULL,
  type = "RI",
  ng = 2,
  cM = TRUE,
  E.vector0 = NULL,
  X = NULL,
  beta0 = NULL,
  variance0 = NULL,
  crit = 10^-5,
  stop = 1000,
  conv = TRUE,
  console = TRUE
)

Arguments

`QTL`	matrix. A q*2 matrix contains the QTL information, where the row dimension 'q' represents the number of QTLs in the chromosomes. The first column labels the chromosomes where the QTLs are located, and the second column labels the positions of QTLs (in morgan (M) or centimorgan (cM)).
`marker`	matrix. A k*2 matrix contains the marker information, where the row dimension 'k' represents the number of markers in the chromosomes. The first column labels the chromosomes where the markers are located, and the second column labels the positions of markers (in morgan (M) or centimorgan (cM)). It's important to note that chromosomes and positions must be sorted in order.
`geno`	matrix. A n*k matrix contains the genotypes of k markers for n individuals. The marker genotypes of P1 homozygote (MM), heterozygote (Mm), and P2 homozygote (mm) are coded as 2, 1, and 0, respectively, with NA indicating missing values.
`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 genotyped individuals, and g is the number of possible genotypes of QTLs. If cp.matrix=NULL, the function will calculate the conditional probability matrix for selective genotyping.
`y`	vector. A vector that contains the phenotype values of individuals with genotypes.
`yu`	vector. A vector that contains the phenotype values of individuals without genotypes.
`sele.g`	character. Determines the type of data being analyzed: If sele.g="n", it considers the data as complete genotyping data. If sele.g="f", it treats the data as selective genotyping data and utilizes the proposed corrected frequency model (Lee 2014) for analysis; If sele.g="t", it considers the data as selective genotyping data and uses the truncated model (Lee 2014) for analysis; If sele.g="p", it treats the data as selective genotyping data and uses the population frequency-based model (Lee 2014) for analysis. Note that the 'yu' argument must be provided when sele.g="f" or "p".
`tL`	numeric. The lower truncation point of phenotype value when sele.g="t". When sele.g="t" and tL=NULL, the 'yu' argument must be provided. In this case, the function will consider the minimum of 'yu' as the lower truncation point.
`tR`	numeric. The upper truncation point of phenotype value when sele.g="t". When sele.g="t" and tR=NULL, the 'yu' argument must be provided. In this case, the function will consider the maximum of 'yu' as the upper truncation point.
`type`	character. The population type of the dataset. Includes backcross (type="BC"), advanced intercross population (type="AI"), and recombinant inbred population (type="RI"). The default value is "RI".
`ng`	integer. The generation number of the population type. For instance, in a BC1 population where type="BC", ng=1; in an AI F3 population where type="AI", ng=3.
`cM`	logical. Specify the unit of marker position. If cM=TRUE, it denotes centimorgan; if cM=FALSE, it denotes morgan.
`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 nk matrix, where n is the number of individuals, and k is the number of fixed factors. If X=NULL, the matrix will be an n1 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

`QTL`	The QTL imformation of this analysis.
`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 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 with genotyping are calculated by the estimated values from the EM algorithm.
`yu.hat`	The fitted values of trait values without genotyping are calculated by the estimated values from the EM algorithm.
`iteration.number`	The iteration number of the EM algorithm.
`model`	The model of this analysis, contains complete a genotyping model, a proposed model, a truncated model, and a frequency-based model.

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>

H.-I LEE, H.-A. HO and C.-H. KAO 2014 A new simple method for improving QTL mapping under selective genotyping. Genetics 198: 1685-1698. <doi: 10.1534/genetics.114.168385.>

Examples

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

# make the seletive genotyping data
ys <- y[y > quantile(y)[4] | y < quantile(y)[2]]
yu <- y[y >= quantile(y)[2] & y <= quantile(y)[4]]
geno.s <- geno[y > quantile(y)[4] | y < quantile(y)[2],]

# 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))
result <- EM.MIM2(QTL, marker, geno.s, D.matrix, y = ys, yu = yu, sele.g = "f")
result$E.vector

[Package QTLEMM version 2.1.0 Index]