cusp (version 2.3.8)

oliva: Synthetic cusp data set

Description

Synthetic ‘multivariate’ data from the cusp catastrophe as generated from the equations specified by Oliva et al. (1987).

Usage

data(oliva)

Format

A data frame with 50 observations on the following 12 variables.

x1

splitting factor predictor

x2

splitting factor predictor

x3

splitting factor predictor

y1

the bifurcation factor predictor

y2

the bifurcation factor predictor

y3

the bifurcation factor predictor

y4

the bifurcation factor predictor

z1

the state factor predictor

z2

the state factor predictor

alpha

the true \(alpha\)'s

beta

the true \(beta\)'s

y

the true state variable values

Details

The data in Oliva et al. (1987) are obtained from the equations $$\alpha_i = X_{i1} - .969\,X_{i2} - .201\,X_{i3}, $$ $$\beta_i = .44\,Y_{i1} + 0.08\,Y_{i2} + .67\,Y_{i3} + .19\,Y_{i4}, $$ $$y_i = -0.52\,Z_{i1} - 1.60\,Z_{i2}.$$ Here the \(X_{ij}\)'s are uniformly distributed on (-2,2), and the \(Y_{ij}\)'s and \(Z_{i1}\) are uniform on (-3,3). The states \(y_i\) were then generated from the cusp density, using rcusp, with their respective \(\alpha_i\)'s and \(\beta_i\)'s as normal and splitting factors, and then \(Z_2\) was computed as $$Z_{i2} = (y_i + 0.52 Z_{i1} )/( 1.60).$$

References

Oliva T, Desarbo W, Day D, Jedidi K (1987). GEMCAT: A general multivariate methodology for estimating catastrophe models. Behavioral Science, 32(2), 121137.

Examples

data(oliva)
set.seed(121)
fit <- cusp(y ~ z1 + z2 - 1, 
	alpha ~ x1 + x2 + x3 - 1, ~ y1 + y2 + y3 + y4 - 1, 
	data = oliva, start = rnorm(9))
summary(fit)
if (FALSE) {
cusp3d(fit, B=5.25, n.surf=50, theta=150) 
# B modifies the range of beta (is set here to 5.25 to make 
# sure all points lie on the surface)
}