RSA (version 0.5.1)

RSA.ST: Surface tests

Description

Calculates surface parameters a1 to a4, the stationary point, the principal axes, the eigenvectors and -values

Usage

RSA.ST(x, y = 0, x2 = 0, xy = 0, y2 = 0, b0 = 0,
    SE = NULL, COV = NULL, df = NULL, model = "full")

Arguments

x

Either an RSA object (returned by the RSA function), or the coefficient for the X predictor

y

Y coefficient

x2

X^2 coefficient

y2

Y^2 coefficient

xy

XY interaction coefficient

b0

The intercept

SE

In case that the coefficients are provided directly (as parameters x, y, x2, y2, xy), SE can provide the standard errors of these estimates. SE has to be a named vector, e.g.: SE=c(x=.1, y=.2, x2=.1, y2=.5, xy=.3). SEs of all paramete

COV

Covariances between parameters. COV has to be a named vector, e.g.: COV=c(x_y=.1, x2_y2 = .2, x2_xy = .3, y2_xy = .4), where x_y is the covariance between x and y, and so on. All these covariances have to provided with exactly these n

df

Degrees of freedom for the calculation of a1 to a4 confidence intervals. The df are the residual dfs of the model (df = n - estimated parameters). For the full polynomial model, this is n - 6 (folllowing parameters are estimated: Intercept, x, y,

model

If x is an RSA object, this parameter specifies the model from which to extract the coefficients

Value

• Returns surface parameters a1 to a4. If an RSA object or SE, COV and df are provided, also significance test and standard errors of a1 to a4 are reported. The stationary point (X0, Y0, and Z0). First principal axis (PA) relative to the X-Y plane (p10 = intercept, p11 = slope), second PA (p20 = intercept, p21 = slope). M = eigenvectors, l = eigenvalues, L = lambda matrix as1X to as4X: surface parameters of the PA, relative to X values as1Y to as4Y: surface parameters of the PA, relative to Y values PA1.curvature: quadratic component of the first PA (equivalent to the first eigenvalue) PA2.curvature: quadratic component of the second PA (equivalent to the second eigenvalue)

Details

No details so far.

References

Shanock, L. R., Baran, B. E., Gentry, W. A., Pattison, S. C., & Heggestad, E. D. (2010). Polynomial Regression with Response Surface Analysis: A Powerful Approach for Examining Moderation and Overcoming Limitations of Difference Scores. Journal of Business and Psychology, 25, 543–554. doi:10.1007/s10869-010-9183-4

See Also

RSA

Examples

# get surface parameters from known parameters
# example from Shanock et al. (2010), p. 548, Table 2
RSA.ST(x=-.23, y=.77, x2=-.07, y2=-.10, xy=.27)

# Get surface parameters from a computed RSA object
set.seed(0xBEEF)
n <- 300
err <- 2
x <- rnorm(n, 0, 5)
y <- rnorm(n, 0, 5)
df <- data.frame(x, y)
df <- within(df, {
	diff <- x-y
	absdiff <- abs(x-y)
	sqdiff <- (x-y)^2
	z.diff <- diff + rnorm(n, 0, err)
	z.abs <- absdiff + rnorm(n, 0, err)
	z.sq <- sqdiff + rnorm(n, 0, err)
	z.add <- diff + 0.4*x + rnorm(n, 0, err)
	z.complex <- 0.4*x + - 0.2*x*y + + 0.1*x^2 - 0.03*y^2 + rnorm(n, 0, err)
})

r1 <- RSA(z.sq~x*y, df)
RSA.ST(r1)