Package 'gemma2'

Calculate Omega matrices

Description

Calculate Omega matrices

Usage

calc_omega(eval, D_l)

Arguments

eval	vector of eigenvalues from decomposition of relatedness matrix
D_l	vector of length d_size

Value

list of length 2. First entry in the list is the symmetric matrix OmegaU. Second entry in the list is the symmetric matrix OmegaE.

Examples

calc_omega(eval = 50:1, D_l = runif(2))

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Calculate Qi (inverse of Q) and log determinant of Q

Description

Calculate Qi (inverse of Q) and log determinant of Q

Usage

calc_qi(eval, D_l, X)

Arguments

eval	vector of eigenvalues from decomposition of relatedness matrix
D_l	vector of length d_size
X	design matrix

Value

a list of length two. First entry in the list is a symmetric numeric matrix, Qi, the inverse of the Q matrix. The second entry in the outputted list is the log determinant of the matrix Q for use in likelihood calculations.

Examples

as.matrix(readr::read_tsv(system.file("extdata",
"mouse100.cXX.txt",
package = "gemma2"),
col_names = FALSE)[, 1:100]) -> kinship
eigen2(kinship) -> e2_out
e2_out$values -> eval
e2_out$vectors -> U
eigen_proc(V_g = diag(c(1.91352, 0.530827)),
V_e = diag(c(0.320028, 0.561589))) -> ep_out

calc_qi(eval = eval,
D_l = ep_out[[4]],
X = t(rep(1, 100)) %*% U)

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Calculate Sigma_ee and Sigma_uu matrices

Description

Calculate Sigma_ee and Sigma_uu matrices

Usage

calc_sigma(eval, D_l, X, OmegaU, OmegaE, UltVeh, Qi)

Arguments

eval	eigenvalues vector from decomposition of relatedness matrix
D_l	vector
X	design matrix
OmegaU	matrix
OmegaE	matrix
UltVeh	matrix
Qi	inverse of Q matrix

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Calculate XHiY

Description

Calculate XHiY

Usage

calc_XHiY(eval, D_l, X, UltVehiY)

Arguments

eval	vector of eigenvalues from the decomposition of the relatedness matrix
D_l	vector of length d_size
X	design matrix
UltVehiY	a matrix

Value

numeric vector

Examples

readr::read_tsv(system.file("extdata",
"mouse100.pheno.txt",
package = "gemma2"),
col_names = FALSE) -> pheno
phe16 <- as.matrix(pheno[, c(1, 6)])
as.matrix(readr::read_tsv(system.file("extdata",
"mouse100.cXX.txt",
package = "gemma2"),
col_names = FALSE)[, 1:100]) -> kinship
eigen2(kinship) -> eout
eout$values -> eval
eout$vectors -> U
UltVehi <- matrix(c(0, -1.76769, -1.334414, 0),
nrow = 2,
byrow = FALSE) # from output of eigen_proc()
calc_XHiY(eval = eval,
D_l = c(0.9452233, 5.9792268),
          X = rep(1, 100) %*% U,
          UltVehiY = UltVehi %*% t(phe16) %*% U
          )

---

Center a relatedness matrix, after Zhou's GEMMA function CenterMatrix

Description

Center a relatedness matrix, after Zhou's GEMMA function CenterMatrix

Usage

center_kinship(mat)

Arguments

mat	a relatedness matrix

Value

a centered relatedness matrix

Examples

readr::read_tsv(system.file("extdata",
"mouse100.cXX.txt",
package = "gemma2"),
col_names = FALSE)[, 1:100] -> kinship
e_out <- eigen2(as.matrix(kinship))
center_kinship(as.matrix(kinship)) -> kinship_centered

---

Eigendecomposition procedure for Vg and Ve

Description

Eigendecomposition procedure for Vg and Ve

Usage

eigen_proc(V_g, V_e, tol = 1/10000)

Arguments

V_g	a d_size by d_size covariance matrix
V_e	a d_size by d_size covariance matrix
tol	a positive number indicating the tolerance for isSymmetric

Value

a named list of length 4 containing the outputs of eigendecomposition procedure

Examples

eigen_proc(diag(2), diag(2))

---

Calculate eigendecomposition and return ordered eigenvalues and eigenvectors

Description

Calculate eigendecomposition and return ordered eigenvalues and eigenvectors

Usage

eigen2(spd, decreasing = FALSE)

Arguments

spd	a semi-positive definite matrix
decreasing	argument passed to order()

Value

a list with 2 components, the eigenvalues and the eigenvectors

Examples

readr::read_tsv(system.file("extdata",
"mouse100.cXX.txt",
package = "gemma2"),
col_names = FALSE)[, 1:100] -> kinship
e_out <- eigen2(as.matrix(kinship))

---

gemma2

Description

We implement an expectation-maximization algorithm for multivariate variance components after the GEMMA software's algorithm.

---

Calculate log likelihood

Description

Calculate log likelihood

Usage

MphCalcLogL(eval, D_l, Qi, UltVehiY, xHiy)

Arguments

eval	eigenvalues vector from decomposition of relatedness matrix
D_l	vector of eigenvalues from decomposition of Ve matrix
Qi	inverse of Q matrix
UltVehiY	matrix of (transformed) Y values
xHiy	vector

---

Perform expectation-maximization algorithm to infer Vg and Ve values for a pair of traits.

Description

Perform expectation-maximization algorithm to infer Vg and Ve values for a pair of traits.

Usage

MphEM(
  max_iter = 10000,
  max_prec = 1/1e+06,
  eval,
  X,
  Y,
  V_g,
  V_e,
  verbose_output = FALSE
)

Arguments

max_iter	maximum number of iterations for EM algorithm
max_prec	maximum precision for EM algorithm
eval	vector of eigenvalues from relatedness matrix decomposition
X	design matrix. Typically contains founder allele dosages.
Y	matrix of phenotype values
V_g	genetic covariance matrix
V_e	error covariance matrix
verbose_output	logical indicating whether to output entire collection of intermediate values for all iterations. Default is FALSE.

Value

a list of lists. Length of list corresponds to number of EM iterations

---

Stagger matrices within a larger, block-diagonal matrix

Description

Stagger matrices within a larger, block-diagonal matrix

Usage

stagger_mats(...)

Arguments

...	one or more matrices, separated by commas

Value

a block-diagonal matrix, with the inputted matrices as blocks on the diagonal.

Examples

foo <- matrix(rnorm(40000), ncol = 8)
block_diag <- stagger_mats(foo, foo)
dim(foo)
dim(block_diag)

---

Update E

Description

Update E

Usage

update_e(UltVehiY, UltVehiBX, UltVehiU)

Arguments

UltVehiY	matrix of transformed Y values
UltVehiBX	matrix of transformed BX values
UltVehiU	matrix of transformed U values

See Also

Other expectation-maximization functions: UpdateRL_B(), update_u(), update_v()

---

Update U matrix

Description

Update U matrix

Usage

update_u(OmegaE, UltVehiY, UltVehiBX)

Arguments

OmegaE	the OmegaE matrix, calculated in calc_omega
UltVehiY	matrix
UltVehiBX	matrix

See Also

Other expectation-maximization functions: UpdateRL_B(), update_e(), update_v()

Examples

readr::read_tsv(system.file("extdata",
"mouse100.pheno.txt",
package = "gemma2"),
col_names = FALSE) -> pheno
phe16 <- as.matrix(pheno[, c(1, 6)])
as.matrix(readr::read_tsv(system.file("extdata",
"mouse100.cXX.txt",
package = "gemma2"),
col_names = FALSE)[, 1:100]) -> kinship
eigen2(kinship) -> e2_out
e2_out$values -> eval
e2_out$vectors -> U
eigen_proc(V_g = diag(c(1.91352, 0.530827)),
V_e = diag(c(0.320028, 0.561589))) -> ep_out
UltVehi <- ep_out[[3]]
calc_omega(eval, ep_out$D_l) -> co_out
update_u(OmegaE = co_out[[2]],
        UltVehiY = UltVehi %*% t(phe16),
        UltVehiBX = matrix(c(-0.71342, -0.824482),
        ncol = 1) %*% t(rep(1, 100))
)

---

Update V_e and V_g

Description

Update V_e and V_g

Usage

update_v(eval, U, E, Sigma_uu, Sigma_ee, tol = 1/10000)

Arguments

eval	vector of eigenvalues from eigendecomposition of relatedness matrix
U	matrix
E	matrix
Sigma_uu	matrix
Sigma_ee	matrix
tol	a positive number indicating tolerance to be passed to isSymmetric()

See Also

Other expectation-maximization functions: UpdateRL_B(), update_e(), update_u()

---

Update B for restricted log likelihood

Description

Update B for restricted log likelihood

Usage

UpdateRL_B(xHiy, Qi, d_size)

Arguments

xHiy	vector
Qi	Q inverse matrix
d_size	number of traits

See Also

Other expectation-maximization functions: update_e(), update_u(), update_v()

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