calculate_lm_combo {pcsstools}

Calculate a linear model for a linear combination of responses

Description

calculate_lm_combo describes the linear model for a linear combination of responses as a function of a set of predictors.

Usage

calculate_lm_combo(means, covs, n, phi, m = length(phi), add_intercept, ...)

Arguments

means

a vector of means of all model predictors and the response with the last m elements the response means (with order corresponding to the order of weights in phi).

covs

a matrix of the covariance of all model predictors and the responses with the order of rows/columns corresponding to the order of means.

n

sample size.

phi

vector of linear combination weights with one entry per response variable.

m

number of responses to combine. Defaults to length(weighs).

add_intercept

logical. If TRUE adds an intercept to the model.

...

additional arguments

Value

an object of class "pcsslm".

An object of class "pcsslm" is a list containing at least the following components:

call

the matched call

terms

the terms object used

coefficients

a p x 4 matrix with columns for the estimated coefficient, its standard error, t-statistic and corresponding (two-sided) p-value.

sigma

the square root of the estimated variance of the random error.

df

degrees of freedom, a 3-vector p, n-p, p*, the first being the number of non-aliased coefficients, the last being the total number of coefficients.

fstatistic

a 3-vector with the value of the F-statistic with its numerator and denominator degrees of freedom.

r.squared

R^2, the 'fraction of variance explained by the model'.

adj.r.squared

the above R^2 statistic 'adjusted', penalizing for higher p.

cov.unscaled

a p x p matrix of (unscaled) covariances of the coef[j], j=1,...p.

Sum Sq

a 3-vector with the model's Sum of Squares Regression (SSR), Sum of Squares Error (SSE), and Sum of Squares Total (SST).

References

Wolf JM, Barnard M, Xia X, Ryder N, Westra J, Tintle N (2020). “Computationally efficient, exact, covariate-adjusted genetic principal component analysis by leveraging individual marker summary statistics from large biobanks.” Pacific Symposium on Biocomputing, 25, 719–730. ISSN 2335-6928, doi:10.1142/9789811215636_0063, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6907735/.

Gasdaska A, Friend D, Chen R, Westra J, Zawistowski M, Lindsey W, Tintle N (2019). “Leveraging summary statistics to make inferences about complex phenotypes in large biobanks.” Pacific Symposium on Biocomputing, 24, 391–402. ISSN 2335-6928, doi:10.1142/9789813279827_0036, https://pubmed.ncbi.nlm.nih.gov/30963077/.