qtl2 (version 0.24)

fit1: Fit single-QTL model at a single position

Description

Fit a single-QTL model at a single putative QTL position and get detailed results about estimated coefficients and individuals contributions to the LOD score.

Usage

fit1(
  genoprobs,
  pheno,
  kinship = NULL,
  addcovar = NULL,
  nullcovar = NULL,
  intcovar = NULL,
  weights = NULL,
  contrasts = NULL,
  model = c("normal", "binary"),
  zerosum = TRUE,
  se = TRUE,
  hsq = NULL,
  reml = TRUE,
  blup = FALSE,
  ...
)

Arguments

genoprobs

A matrix of genotype probabilities, individuals x genotypes. If NULL, we create a single intercept column, matching the individual IDs in pheno.

pheno

A numeric vector of phenotype values (just one phenotype, not a matrix of them)

kinship

Optional kinship matrix.

addcovar

An optional numeric matrix of additive covariates.

nullcovar

An optional numeric matrix of additional additive covariates that are used under the null hypothesis (of no QTL) but not under the alternative (with a QTL). This is needed for the X chromosome, where we might need sex as a additive covariate under the null hypothesis, but we wouldn't want to include it under the alternative as it would be collinear with the QTL effects.

intcovar

An optional numeric matrix of interactive covariates.

weights

An optional numeric vector of positive weights for the individuals. As with the other inputs, it must have names for individual identifiers.

contrasts

An optional numeric matrix of genotype contrasts, size genotypes x genotypes. For an intercross, you might use cbind(mu=c(1,1,1), a=c(-1, 0, 1), d=c(0, 1, 0)) to get mean, additive effect, and dominance effect. The default is the identity matrix.

model

Indicates whether to use a normal model (least squares) or binary model (logistic regression) for the phenotype. If model="binary", the phenotypes must have values in \([0, 1]\).

zerosum

If TRUE, force the genotype or allele coefficients sum to 0 by subtracting their mean and add another column with the mean. Ignored if contrasts is provided.

se

If TRUE, calculate the standard errors.

hsq

(Optional) residual heritability; used only if kinship provided.

reml

If kinship provided: if reml=TRUE, use REML; otherwise maximum likelihood.

blup

If TRUE, fit a model with QTL effects being random, as in scan1blup().

...

Additional control parameters; see Details;

Value

A list containing

• coef - Vector of estimated coefficients.

• SE - Vector of estimated standard errors (included if se=TRUE).

• lod - The overall lod score.

• ind_lod - Vector of individual contributions to the LOD score (not provided if kinship is used).

• fitted - Fitted values.

• resid - Residuals. If blup==TRUE, only coef and SE are included at present.

Details

For each of the inputs, the row names are used as individual identifiers, to align individuals.

If kinship is absent, Haley-Knott regression is performed. If kinship is provided, a linear mixed model is used, with a polygenic effect estimated under the null hypothesis of no (major) QTL, and then taken as fixed as known in the genome scan.

If contrasts is provided, the genotype probability matrix, \(P\), is post-multiplied by the contrasts matrix, \(A\), prior to fitting the model. So we use \(P \cdot A\) as the \(X\) matrix in the model. One might view the rows of

as the set of contrasts, as the estimated effects are the estimated genotype effects pre-multiplied by .

The ... argument can contain several additional control parameters; suspended for simplicity (or confusion, depending on your point of view). tol is used as a tolerance value for linear regression by QR decomposition (in determining whether columns are linearly dependent on others and should be omitted); default 1e-12. maxit is the maximum number of iterations for converence of the iterative algorithm used when model=binary. bintol is used as a tolerance for converence for the iterative algorithm used when model=binary. eta_max is the maximum value for the "linear predictor" in the case model="binary" (a bit of a technicality to avoid fitted values exactly at 0 or 1).

References

Haley CS, Knott SA (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69:315--324.

Kang HM, Zaitlen NA, Wade CM, Kirby A, Heckerman D, Daly MJ, Eskin E (2008) Efficient control of population structure in model organism association mapping. Genetics 178:1709--1723.

See Also

pull_genoprobpos(), find_marker()

Examples

# NOT RUN {
# read data
iron <- read_cross2(system.file("extdata", "iron.zip", package="qtl2"))
# }
# NOT RUN {
# insert pseudomarkers into map
map <- insert_pseudomarkers(iron$gmap, step=5)

# calculate genotype probabilities
probs <- calc_genoprob(iron, map, error_prob=0.002)

# grab phenotypes and covariates; ensure that covariates have names attribute
pheno <- iron$pheno[,1]
covar <- match(iron$covar$sex, c("f", "m")) # make numeric
names(covar) <- rownames(iron$covar)

# scan chromosome 7 to find peak
out <- scan1(probs[,"7"], pheno, addcovar=covar)

# find peak position
max_pos <- max(out, map)

# genoprobs at max position
pr_max <- pull_genoprobpos(probs, map, max_pos$chr, max_pos$pos)

# fit QTL model just at that position
out_fit1 <- fit1(pr_max, pheno, addcovar=covar)

# }