oliva {cusp}

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).

Source

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

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)
## Not run: 
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)

## End(Not run)