construct_covmat_multi {LTFHPlus}

Constructing a covariance matrix for multiple phenotypes

Description

construct_covmat_multi returns the covariance matrix for an underlying target individual and a variable number of its family members for multiple phenotypes.

Usage

construct_covmat_multi(
  fam_vec = c("m", "f", "s1", "mgm", "mgf", "pgm", "pgf"),
  n_fam = NULL,
  add_ind = TRUE,
  genetic_corrmat,
  full_corrmat,
  h2_vec,
  phen_names = NULL
)

Arguments

fam_vec

A vector of strings holding the different family members. All family members must be represented by strings from the following list:

• m (Mother)

• f (Father)

• c[0-9]*.[0-9]* (Children)

• mgm (Maternal grandmother)

• mgf (Maternal grandfather)

• pgm (Paternal grandmother)

• pgf (Paternal grandfather)

• s[0-9]* (Full siblings)

• mhs[0-9]* (Half-siblings - maternal side)

• phs[0-9]* (Half-siblings - paternal side)

• mau[0-9]* (Aunts/Uncles - maternal side)

• pau[0-9]* (Aunts/Uncles - paternal side). Defaults to c("m","f","s1","mgm","mgf","pgm","pgf").

n_fam

A named vector holding the desired number of family members. See setNames. All names must be picked from the list mentioned above. Defaults to NULL.

add_ind

A logical scalar indicating whether the genetic component of the full liability as well as the full liability for the underlying individual should be included in the covariance matrix. Defaults to TRUE.

genetic_corrmat

A numeric matrix holding the genetic correlations between the desired phenotypes. All diagonal entries must be equal to one, while all off-diagonal entries must be between -1 and 1. In addition, the matrix must be symmetric.

full_corrmat

A numeric matrix holding the full correlations between the desired phenotypes. All diagonal entries must be equal to one, while all off-diagonal entries must be between -1 and 1. In addition, the matrix must be symmetric.

h2_vec

A numeric vector representing the liability-scale heritabilities for all phenotypes. All entries in h2_vec must be non-negative and at most 1.

phen_names

A character vector holding the phenotype names. These names will be used to create the row and column names for the covariance matrix. If it is not specified, the names will default to phenotype1, phenotype2, etc. Defaults to NULL.

Details

This function can be used to construct a covariance matrix for a given number of family members. Each entry in this covariance matrix equals either the percentage of shared DNA between the corresponding individuals times the liability-scale heritability h^2 or the percentage of shared DNA between the corresponding individuals times the correlation between the corresponding phenotypes. That is, for the same phenotype, the covariance between all combinations of the genetic component of the full liability and the full liability is given by

\text{Cov}\left( l_g, l_g \right) = h^2,

\text{Cov}\left( l_g, l_o \right) = h^2,

\text{Cov}\left( l_o, l_g \right) = h^2

and

\text{Cov}\left( l_o, l_o \right) = 1.

For two different phenotypes, the covariance is given by

\text{Cov}\left( l_g^1, l_g^2 \right) = \rho_g^{1,2},

\text{Cov}\left( l_g^1, l_o^2 \right) = \rho_g^{1,2},

\text{Cov}\left( l_o^1, l_g^2 \right) = \rho_g^{1,2}

and

\text{Cov}\left( l_o^1, l_o^2 \right) = \rho_g^{1,2} + \rho_e^{1,2},

where l_g^i and l_o^i are the genetic component of the full liability and the full liability for phenotype i, respectively, \rho_g^{i,j} is the genetic correlation between phenotype i and j and \rho_e^{1,2} is the environmental correlation between phenotype i and j. The family members can be specified using one of two possible formats.

Value

If either fam_vec or n_fam is used as the argument and if it is of the required format, if genetic_corrmat and full_corrmat are two numeric and symmetric matrices satisfying that all diagonal entries are one and that all off-diagonal entries are between -1 and 1, and if h2_vec is a numeric vector satisfying 0 \leq h2_i \leq 1 for all i \in \{1,...,n_pheno\}, then the output will be a named covariance matrix. The number of rows and columns corresponds to the number of phenotypes times the length of fam_vec or n_fam (+ 2 if add_ind=TRUE). If both fam_vec and n_fam are equal to c() or NULL, the function returns a (2 \times n_pheno) \times (2\times n_pheno) matrix holding only the correlation between the genetic component of the full liability and the full liability for the underlying individual for all phenotypes. If both fam_vec and n_fam are specified, the user is asked to decide on which of the two vectors to use. Note that the returned object has a number different attributes,namely fam_vec, n_fam, add_ind, genetic_corrmat, full_corrmat, h2 and phenotype_names.

See Also

get_relatedness, construct_covmat_single and construct_covmat.

Examples

construct_covmat_multi(fam_vec = NULL, 
                       genetic_corrmat = matrix(c(1, 0.5, 0.5, 1), nrow = 2),
                       full_corrmat = matrix(c(1, 0.55, 0.55, 1), nrow = 2),
                       h2_vec = c(0.37,0.44),
                       phen_names = c("p1","p2"))
construct_covmat_multi(fam_vec = c("m","mgm","mgf","mhs1","mhs2","mau1"), 
                       n_fam = NULL, 
                       add_ind = TRUE,
                       genetic_corrmat = diag(3),
                       full_corrmat = diag(3),
                       h2_vec = c(0.8, 0.65))
construct_covmat_multi(fam_vec = NULL, 
                       n_fam = stats::setNames(c(1,1,1,2,2), c("m","mgm","mgf","s","mhs")), 
                       add_ind = FALSE,
                       genetic_corrmat = diag(2),
                       full_corrmat = diag(2),
                       h2_vec = c(0.75,0.85))