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

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`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 |

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.

`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 |

Sunbok Lee

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.

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# 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)
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