GLM influence measures {brainGraph}

Influence measures for a bg_GLM object

Description

These functions compute common (leave-one-out) diagnostics for the models in a bg_GLM object.

Usage

## S3 method for class 'bg_GLM'
rstandard(model, type = c("sd.1", "predictive"), ...)

## S3 method for class 'bg_GLM'
rstudent(model, ...)

## S3 method for class 'bg_GLM'
hatvalues(model, ...)

## S3 method for class 'bg_GLM'
cooks.distance(model, ...)

dffits.bg_GLM(model)

## S3 method for class 'bg_GLM'
dfbeta(model, ...)

## S3 method for class 'bg_GLM'
dfbetas(model, ...)

covratio.bg_GLM(model)

## S3 method for class 'bg_GLM'
influence(model, do.coef = TRUE, region = NULL, ...)

Arguments

model

A bg_GLM object

type

The type of standardized residuals. Default: 'sd.1'

...

Unused

do.coef

Logical indicating whether to calculate dfbeta

region

Character string of the region(s) to return results for. Default is to calculate for all regions

Details

The influence method calculates all diagnostics present in lm.influence and influence.measures, consisting of the following functions:

rstandard

Standardized residuals. Choosing type='predictive' returns leave-one-out cross validation residuals. The “PRESS” statistic can be calculated as colSums(resids.p^2)

rstudent

Studentized residuals

hatvalues

The leverage, or the diagonal of the hat/projection matrix

cooks.distance

Cook's distance

dffits.bg_GLM

The change in fitted values when deleting observations

dfbeta

The change in parameter estimates (coefficients) when deleting observations

dfbetas

The scaled change in parameter estimates

covratio.bg_GLM

The covariance ratios, or the change in the determinant of the covariance matrix of parameter estimates when deleting observations

Value

Most influence functions return a numeric matrix in which rownames are Study ID's and column names are regions. dfbeta and dfbetas return a numeric array in which each column is a parameter estimate and the 3rd dimension is for each region. influence returns a list with class infl.bg_GLM and elements:

infmat

Numeric array (like dfbeta) with DFBETAs, DFFITs, covratios, Cook's distance, and hat values

is.inf

Logical array of the same data as infmat; values of TRUE indicate the subject-variable-region combination is an outlier value

f

The model formula

sigma

The leave-one-out residual standard deviation

wt.res

Model residuals

Outlier values

Each variable has a different criterion for determining outliers. In the following: x is the influence variable (for DFBETA, the criterion applies to all DFBETAs); k is the number of columns of the design matrix; dfR is the residual degrees of freedom; and n is the number of observations.

DFBETAs

If |x| > 1

DFFITs

If |x| > 3 \sqrt{k / dfR}

covratio

If |1 - x| > (3k / dfR)

cook

If F_{k, dfR}(x) > 0.5

hat

If x > 3k / n

The return object of influence has a print method which will list the subjects/variables/regions for which an outlier was detected.

Author(s)

Christopher G. Watson, [e-mail]

See Also

GLM