crossReg (version 1.0)

DeltaC: Confidence intervals for crossover points using the delta method

Description

Calculate confidence intervals for crossover points of two simple linear regression lines using the delta method.

Usage

DeltaC(Data, order)

Arguments

Data

a dataframe containing data values for y, x1, and x2

order

a scalar number representing the order of Delta method. 1=1st order delta method and 2=2nd order delta method

Value

• LowCI
  lower bound of confidence intervals for C based on the delta method
• UpperCI
  upper bound of confidence intervals for C based on the delta method

Details

Given a linear regression model y = b0 + b1*x1 + b2*x2 + b3*x1*x2, the crossover point of two simple regression lines can be directly calculated based on C=-b2/b3. The Delta method can be used to estimate the standard error of C = -b2/b3 based on the standard errors of b2 and b3 which can be obtained from a linear regression. The function DeltaC() calculates the confidence intervals for C based on the standard error of C obtained from the delta method.

References

Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, 185-227. Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology, 13, 290-312.

Examples

# example data
library(MASS)
out <- mvrnorm(1000, mu = c(0,0), Sigma = matrix(c(1,0.2,0.2,1), ncol = 2),empirical = TRUE)
x1 <- out[,1]
x2 <- out[,2]
epsilon <-rnorm(1000,0,1)
y <- 1 + 1*x1 + 0.5*x2 + 1*x1*x2 + epsilon  # true C = -0.5/1 = -0.5
simData <- data.frame(y=y,x1=x1,x2=x2)

# run DeltaC()
DeltaC(simData,2)