This function simplifies calculating p-values from linear models in which there are many outcome variables, such as in voxel-wise regressions. To perform such an analysis in R, you can concatenate the outcome variables column-wise into an n by p matrix y, where there are n subjects and p outcomes (see Examples). Calling lm(y~x) calculates the coefficients, but statistical inference is not provided. This function provides basic statistical inference efficiently.

bigLMStats(mylm, lambda = 0, includeIntercept = FALSE)

Arguments

mylm

Object of class lm.

lambda

Value of ridge penalty for inverting ill-conditioned matrices.

includeIntercept

Whether or not to include p-values for intercept term in result.

Value

A list containing objects:

fstat

F-statistic of whole model (one value per outcome).

pval.model

p-value of model (one value per outcome).

beta

Values of coefficients (one value per predictor per outcome).

beta.std

Standard error of coefficients.

beta.t

T-statistic of coefficients.

beta.pval

p-value of coefficients.

Examples

nsub <- 100 set.seed(1500) x <- 1:nsub y <- matrix(c(x + rnorm(nsub), sin(x)), nrow=nsub) x <- cbind(x, x^2) y1 <- y[, 1] y2 <- y[, 2] lm1 <- lm(y1~x) lm2 <- lm(y2~x) mylm <- lm(y ~ x) myest <- bigLMStats(mylm) print(paste("R beta estimates for first outcome is", summary(lm1)$coefficients[-1,1], "and for second outcome is", summary(lm2)$coefficients[-1,1]))
#> [1] "R beta estimates for first outcome is 0.996800064361502 and for second outcome is -0.000873326597445242" #> [2] "R beta estimates for first outcome is 3.96575611836199e-05 and for second outcome is -3.04190877512371e-06"
print(paste("and our estimate is", as.numeric(myest$beta[,1]), as.numeric(myest$beta[,2])))
#> [1] "and our estimate is 0.996800064361502 -0.000873326597445242" #> [2] "and our estimate is 3.96575611836199e-05 -3.04190877512371e-06"
print(paste("R std error estimate for first outcome is", summary(lm1)$coefficients[-1,2], "and for second outcome is", summary(lm2)$coefficients[-1,2], "and our estimate is", myest$beta.std[,1], myest$beta.std[,2]))
#> [1] "R std error estimate for first outcome is 0.0145452856084367 and for second outcome is 0.0100592155571058 and our estimate is 0.0145452856084366 0.0100592155571058" #> [2] "R std error estimate for first outcome is 0.000139527376091849 and for second outcome is 9.64942174398549e-05 and our estimate is 0.000139527376091849 9.64942174398548e-05"
print(paste("R t value estimate for first outcome is", summary(lm1)$coefficients[-1,3], "and for second outcome is", summary(lm2)$coefficients[-1,3], "and our estimate is", myest$beta.t[,1], myest$beta.t[,2]))
#> [1] "R t value estimate for first outcome is 68.5308003703503 and for second outcome is -0.0868185588118081 and our estimate is 68.5308003703504 -0.0868185588118082" #> [2] "R t value estimate for first outcome is 0.284227814601156 and for second outcome is -0.0315242597518317 and our estimate is 0.284227814601156 -0.0315242597518317"
print(paste("R pval for first outcome is", summary(lm1)$coefficients[-1,4], "and for second outcome is", summary(lm2)$coefficients[-1,4], "and our estimate is", myest$beta.pval[,1], myest$beta.pval[,2]))
#> [1] "R pval for first outcome is 5.73699385771323e-84 and for second outcome is 0.930994703501836 and our estimate is 5.73699385771274e-84 0.930994703501836" #> [2] "R pval for first outcome is 0.776841657572364 and for second outcome is 0.974916219349365 and our estimate is 0.776841657572364 0.974916219349365"