approx_and {pcsstools}

Approximate a linear model for a series of logical AND statements

Description

approx_and approximates the linear model for the a conjunction of m phenotypes as a function of a set of predictors.

Usage

approx_and(
  means,
  covs,
  n,
  predictors,
  add_intercept = TRUE,
  verbose = FALSE,
  response_assumption = "binary",
  ...
)

Arguments

means

vector of predictor and response means with the last m means being the means of m binary responses to combine in a logical and statement.

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.

predictors

list of objects of class predictor corresponding to the order of the predictors in means.

add_intercept

logical. Should the linear model add an intercept term?

verbose

should output be printed to console?

response_assumption

character. Either "binary" or "continuous". If "binary", specific calculations will be done to estimate product means and variances.

...

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, Westra J, Tintle N (2021). “Using Summary Statistics to Model Multiplicative Combinations of Initially Analyzed Phenotypes With a Flexible Choice of Covariates.” Frontiers in Genetics, 12, 1962. ISSN 1664-8021, doi:10.3389/fgene.2021.745901, https://www.frontiersin.org/articles/10.3389/fgene.2021.745901/full.