morris {sensitivity}R Documentation

Morris's Elementary Effects Screening Method

Description

morris implements the Morris's elementary effects screening method (Morris 1992). This method, based on design of experiments, allows to identify the few important factors at a cost of r * (p + 1) simulations (where p is the number of factors). This implementation includes some improvements of the original method: space-filling optimization of the design (Campolongo et al. 2007) and simplex-based design (Pujol 2008).

Usage

morris(model = NULL, factors, r, design, binf = 0, bsup = 1,
       scale = TRUE, ...)
## S3 method for class 'morris':
tell(x, y = NULL, ...)
## S3 method for class 'morris':
print(x, ...)
## S3 method for class 'morris':
plot(x, identify = FALSE, ...)
plot3d.morris(x, alpha = c(0.2, 0), sphere.size = 1)

Arguments

model a function, or a model with a predict method, defining the model to analyze.
factors an integer giving the number of factors, or a vector of character strings giving their names.
r either an integer giving the number of repetitions of the design, i.e. the number of elementary effect computed per factor, or a vector of two integers c(r1, r2) for the space-filling improvement (Campolongo et al.). In this case, r1 is the wanted design size, and r2 (> r1) is the size of the (bigger) population in which is extracted the design (this can throw a warning, see below).
design a list specifying the design type and its parameters:
  • type = "oat" for Morris's OAT design (Morris 1992), with the parameters:
    • levels : either an integer specifying the number of levels of the design, or a vector of integers for different values for each factor.
    • grid.jump : either an integer specifying the number of levels that are increased/decreased for computing the elementary effects, or a vector of integers for different values for each factor. If not given, it is set to grid.jump = 1. Notice that this default value of one does not follow Morris's recommendation of levels / 2.
  • type = "simplex" for simplex-based design (Pujol 2008), with the parameter:
    • scale.factor : a numeric value, the homothety factor of the (isometric) simplexes. Edges equal one with a scale factor of one.
binf either an integer, specifying the minimum value for the factors, or a vector for different values for each factor.
bsup either an integer, specifying the maximum value for the factors, or a vector for different values for each factor.
scale logical. If TRUE, the input and output data are scaled before computing the elementary effects.
x a list of class "morris" storing the state of the screening study (parameters, data, estimates).
y a vector of model responses.
identify logical. If TRUE, the user selects with the mouse the factors to label on the (mu*, sigma) graph (see identify).
... any other arguments for model which are passed unchanged each time it is called.
alpha a vector of three values between 0.0 (fully transparent) and 1.0 (opaque) (see rgl.material). The first value is for the cone, the second for the planes.
sphere.size a numeric value, the scale factor for displaying the spheres.

Details

plot2d draws the (mu*, sigma) graph.

plot3d.morris draws the (mu, mu*, sigma) graph (requires the rgl package). On this graph, the points are in a domain bounded by a cone and two planes (application of the Cauchy-Schwarz inequality).

Value

morris returns a list of class "morris", containing all the input argument detailed before, plus the following components:

call the matched call.
X a data.frame containing the design of experiments.
y a vector of model responses.
ee a r * p matrix of elementary effects for all the factors.


Notice that the statitics of interest (mu, mu* and sigma) are not stored. They can be printed by the print method, but to extract numerical values, one has to compute them with the following instructions:

mu <- apply(x$ee, 2, mean)
mu.star <- apply(x$ee, 2, function(x) mean(abs(x)))
sigma <- apply(x$ee, 2, sd)

Warning messages

"keeping r' repetitions out of r"
when generating the design of experiments, identical repetitions are removed, leading to a lower number than requested.

References

M. D. Morris, 1991, Factorial sampling plans for preliminary computational experiments, Technometrics, 33, 161–174.

F. Campolongo, J. Cariboni and A. Saltelli, 2007, An effective screening design for sensitivity, Environmental Modelling & Software, 22, 1509–1518.

G. Pujol (2008), Simplex-based screening designs for estimating metamodels, submited to Reliability Engineering and System Safety.

See Also

decoupling

Examples

# Test case : the non-monotonic function of Morris
x <- morris(model = morris.fun, factors = 20, r = 4,
            design = list(type = "oat", levels = 5, grid.jump = 3))
print(x)
plot(x)
## Not run: morris.plot3d(x)  # (requires the package 'rgl')

[Package sensitivity version 1.4-0 Index]