oliva {cusp} | R Documentation |
Synthetic ‘multivariate’ data from the cusp catastrophe as generated from the equations specified by Oliva et al. (1987).
data(oliva)
A data frame with 50 observations on the following 12 variables.
x1
x2
x3
y1
y2
y3
y4
z1
z2
alpha
beta
y
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).
Oliva T, Desarbo W, Day D, Jedidi K (1987). GEMCAT: A general multivariate methodology for estimating catastrophe models. Behavioral Science, 32(2), 121137.
Oliva T, Desarbo W, Day D, Jedidi K (1987). GEMCAT: A general multivariate methodology for estimating catastrophe models. Behavioral Science, 32(2), 121137.
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)