sensitivity (version 1.5)

morris: 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 $r \times (p+1)$ 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, \dots)
## S3 method for class 'morris':
print(x, \dots)
## S3 method for class 'morris':
plot(x, identify = FALSE, \dots)
## S3 method for class 'morris':
plot3d(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,

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,

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.

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 $r \times p$ 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)

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).

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)
morris.plot3d(x)  # (requires the package 'rgl')