# testSlopes: Hypothesis tests for Simple Slopes Objects In rockchalk: Regression Estimation and Presentation

## Description

Conducts t-test of the hypothesis that the "simple slope" line for one predictor is statistically significantly different from zero for each value of a moderator variable. The user must first run `plotSlopes()`, and then give the output object to `plotSlopes()`. A plot method has been implemented for testSlopes objects. It will create an interesting display, but only when the moderator is a numeric variable.

## Usage

 `1` ```testSlopes(object) ```

## Arguments

 `object` Output from the plotSlopes function

## Details

This function scans the input object to detect the focal values of the moderator variable (the variable declared as `modx` in `plotSlopes`). Consider a regression with interactions

y <- b0 + b1*x1 + b2*x2 + b3*(x1*x2) + b4*x3 + ... + error

If `plotSlopes` has been run with the argument plotx="x1" and the argument modx="x2", then there will be several plotted lines, one for each of the chosen values of x2. The slope of each of these lines depends on x1's effect, b1, as well as the interactive part, b3*x2.

This function performs a test of the null hypothesis of the slope of each fitted line in a `plotSlopes` object is statistically significant from zero. A simple t-test for each line is offered. No correction for the conduct of multiple hypothesis tests (no Bonferroni correction).

When `modx` is a numeric variable, it is possible to conduct further analysis. We ask "for which values of `modx` would the effect of `plotx` be statistically significant?" This is called a Johnson-Neyman (Johnson-Neyman, 1936) approach in Preacher, Curran, and Bauer (2006). The interval is calculated here. A plot method is provided to illustrate the result.

## Value

A list including 1) the hypothesis test table, 2) a copy of the plotSlopes object, and, for numeric modx variables, 3) the Johnson-Neyman (J-N) interval boundaries.

## Author(s)

Paul E. Johnson <[email protected]>

## References

Preacher, Kristopher J, Curran, Patrick J.,and Bauer, Daniel J. (2006). Computational Tools for Probing Interactions in Multiple Linear Regression, Multilevel Modeling, and Latent Curve Analysis. Journal of Educational and Behavioral Statistics. 31,4, 437-448.

Johnson, P.O. and Neyman, J. (1936). "Tests of certain linear hypotheses and their applications to some educational problems. Statistical Research Memoirs, 1, 57-93.

plotSlopes

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45``` ```library(rockchalk) library(carData) m1 <- lm(statusquo ~ income * age + education + sex + age, data = Chile) m1ps <- plotSlopes(m1, modx = "income", plotx = "age") m1psts <- testSlopes(m1ps) plot(m1psts) dat2 <- genCorrelatedData(N = 400, rho = .1, means = c(50, -20), stde = 300, beta = c(2, 0, 0.1, -0.4)) m2 <- lm(y ~ x1*x2, data = dat2) m2ps <- plotSlopes(m2, plotx = "x1", modx = "x2") m2psts <- testSlopes(m2ps) plot(m2psts) m2ps <- plotSlopes(m2, plotx = "x1", modx = "x2", modxVals = "std.dev", n = 5) m2psts <- testSlopes(m2ps) plot(m2psts) ## Try again with longer variable names colnames(dat2) <- c("oxygen","hydrogen","species") m2a <- lm(species ~ oxygen*hydrogen, data = dat2) m2aps1 <- plotSlopes(m2a, plotx = "oxygen", modx = "hydrogen") m2aps1ts <- testSlopes(m2aps1) plot(m2aps1ts) m2aps2 <- plotSlopes(m2a, plotx = "oxygen", modx = "hydrogen", modxVals = "std.dev", n = 5) m2bps2ts <- testSlopes(m2aps2) plot(m2bps2ts) dat3 <- genCorrelatedData(N = 400, rho = .1, stde = 300, beta = c(2, 0, 0.3, 0.15), means = c(50,0), sds = c(10, 40)) m3 <- lm(y ~ x1*x2, data = dat3) m3ps <- plotSlopes(m3, plotx = "x1", modx = "x2") m3sts <- testSlopes(m3ps) plot(testSlopes(m3ps)) plot(testSlopes(m3ps), shade = FALSE) ## Finally, if model has no relevant interactions, testSlopes does nothing. m9 <- lm(statusquo ~ age + income * education + sex + age, data = Chile) m9ps <- plotSlopes(m9, modx = "education", plotx = "age", plotPoints = FALSE) m9psts <- testSlopes(m9ps) ```

### Example output              ```Values of income INSIDE this interval:
lo        hi
7413.29 214643.99
cause the slope of (b1 + b2*income)age to be statistically significant
Values of x2 INSIDE this interval:
lo          hi
-300.915232   -5.551897
cause the slope of (b1 + b2*x2)x1 to be statistically significant
Values of x2 INSIDE this interval:
lo          hi
-300.915232   -5.551897
cause the slope of (b1 + b2*x2)x1 to be statistically significant
Values of hydrogen INSIDE this interval:
lo          hi
-300.915232   -5.551897
cause the slope of (b1 + b2*hydrogen)oxygen to be statistically significant
Values of hydrogen INSIDE this interval:
lo          hi
-300.915232   -5.551897
cause the slope of (b1 + b2*hydrogen)oxygen to be statistically significant
Values of x2 OUTSIDE this interval:
lo        hi
-11.66052  57.50208
cause the slope of (b1 + b2*x2)x1 to be statistically significant
Values of x2 OUTSIDE this interval:
lo        hi
-11.66052  57.50208
cause the slope of (b1 + b2*x2)x1 to be statistically significant
Values of x2 OUTSIDE this interval:
lo        hi
-11.66052  57.50208
cause the slope of (b1 + b2*x2)x1 to be statistically significant
There were no interactions in the plotSlopes object, so testSlopes can't offer any advice.
```

rockchalk documentation built on May 2, 2019, 5:09 a.m.