glm_helpers: Helper functions to set-up for GLM analyses

In brainGraph: Graph Theory Analysis of Brain MRI Data

Description

setup_glm is used to setup the data/objects for any function that uses the main GLM functionality in brainGraph.

contrast_names checks the dimensions of contrasts, generates contrast names, and sets column names for GLM functions. For F-contrasts, if a matrix is given, it converts it to a list to simplify processing later.

add_nans adds rows/columns (or higher dimensions) to model fit data for regions which were skipped (due to having a singular design matrix, usually).

cxtxfun_3d returns a function that calculates the “CXtX” matrix/array, used to calculate the standard error of a contrast. The function signature will be f(contrast, xtx, rkC, ny).

glm_data_table is used in brainGraph_GLM and brainGraph_mediate to create a data.table with the subject IDs and column(s) for the graph- or vertex-level metric of interest.

matrix2list makes working with different contrast types (i.e., t or F) a little simpler.

Usage

setup_glm(g.list, level, covars, X, contrasts, con.type, con.name, measure,
  outcome, ...)

contrast_names(contrasts, con.type, con.name, X)

check_if_singular(QR)

add_nans(fits, dimX, namesX, runX = names(fits$qr))

cxtxfun_3d(con.type, transpose = TRUE)

glm_data_table(g.list, level, measure)

matrix2list(mat)

maxfun(alternative)

sortfun(alternative)

Arguments

g.list	A brainGraphList object
level	Character string; either vertex (default) or graph
covars	A data.table of covariates
X	Numeric matrix, if you wish to supply your own design matrix. Ignored if outcome != measure.
contrasts	Numeric matrix (for T statistics) or list of matrices (for F statistics) specifying the contrast(s) of interest; if only one contrast is desired, you can supply a vector (for T statistics)
con.type	Either 't' or 'f'
con.name	Character vector of the contrast name(s); if contrasts has row/list names, those will be used for reporting results
measure	Character string of the graph measure of interest
outcome	Character string specifying the name of the outcome variable, if it differs from the graph metric (measure)
...	Arguments passed to brainGraph_GLM_design
QR	List of QR decompositions for each design matrix
fits	List object output by one of the model fitting functions (e.g., fastLmBG)
dimX	Integer vector containing the dimensions of the original design matrix/array (including singular designs)
namesX	List of character vectors containing the dimension names from the original design matrix/array
runX	Character vector of regions for which models were fit
transpose	Logical indicating whether to transpose the output of the selected function. Ignored for F-contrasts. Should be FALSE for T-contrasts when the “Guttman” partition method is used. Default: TRUE
mat	Numeric matrix in which each row is a single contrast vector
alternative	Character string, whether to do a two- or one-sided test. Default: 'two.sided'

Details

This function: removes unused levels from covars and DT.y.m, removes subjects with incomplete data, creates a design matrix (if not supplied), and supplies names to the contrast matrix.

The “CXtX” matrix/array for T-contrasts is the diagonal of

C (X^T X)^{-1} C^T

For F-contrasts, it is the inverse of the matrix:

(C (X^T X)^{-1} C^T)^{-1}

where in both cases, C is the contrast matrix and X is the design matrix/array.

For T-contrasts, the function will return a numeric vector/matrix with dimensions k \times r where k is the number of contrasts (i.e., the number of rows in the contrast matrix) and r is the number of regions. For F-contrasts, the function would return a numeric array with dimensions k \times k \times r, where k is the rank of the contrast matrix and r is the number of regions. If there is a single design for all regions, it will be a k \times k matrix.

Value

contrast_names – list containing the contrasts (matrix or list), contrast names, and number of contrasts

add_nans – the original fits object with NaN or NA inserted

cxtxfun_3d – A function with arguments for the contrast (numeric matrix), the “unscaled covariance” array, the (row) rank of the contrast, and the number of regions in the analysis (only used for F-contrasts)

glm_data_table - A data.table with one column containing the subject ID's and 1 or more columns with the graph- or vertex-level measure of interest.

matrix2list – A list with length equal to the number of rows of C

brainGraph documentation built on Oct. 23, 2020, 6:37 p.m.