oliva {cusp}R Documentation

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

α_i = X_{i1} - .969,X_{i2} - .201,X_{i3},

β_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 α_i's and β_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)

[Package cusp version 2.2 Index]