morris

Morris came up with an experimental plan that is composed of individually randomized OAT designs. The data analysis is then based on the so called *elementary effects*, the changes in an output due to changes in a particular input factor in the OAT design. The method is global in the sense that it does vary over the whole range of uncertainty of the input factors. The Morris method can determine if the effect of the input factor *x _{i}* on the output

According to Morris the input factor x* _{~i}* may be important if:

- f(
*x*+ Δ, x_{i}) − f(x) is nonzero, then x_{~i}affects the output._{~i} - f(
*x*+Δ, x_{i}) − f(x) varies as_{~i}*x*varies, then_{i}*x*affects the output nonlinearly._{i} - f(
*x*+Δ, x_{i}) − f(x) varies as x_{~i}varies, then_{~i}*x*affects the output with interactions._{i}

Δ is the variation size.

The input factor space is “discretized” and the possible input factor values will be restricted to be inside a regular *k*-dimensional *p*-level grid, where p is the number of “levels” of the design. The elementary effect of a given value *x _{i}* of input factor

*ee _{i}*(x) = [ f(x

for any *x _{i}* between 0 and 1 − Δ where x ∈ , and Δ is a predetermined multiple of 1/(

If all samples of the elementary effect of the *i*’th input factor are zero, then *x _{i}* doesn’t have any effect on the output

- a high mean indicates a factor with an important overall influence on the output and
- a high standard deviation indicates that either the factor is interacting with other factors or the factor has nonlinear effects on the output.

To compute *r* elementary effects of the *k* inputs we need to do 2*rk* model evaluations. With the use of Morris randomized OAT design the number of evaluations are reduced to *r*(*k* + 1).

The main advantage of the Morris design is the relatively low computational cost. The design requires only about one model evaluation per computed elementary effect.

One drawback with the Morris design is that it only gives an overall measure of the interactions, indicating whether interactions exists, but it does not say which are the most important. Also it can only be used with a set of orthogonal input factors, i.e. correlations cannot be induced on the input factors.

In an implementation, there is a need to think about the choice of the *p* levels among which each input factor is varied. In Ecolego these levels correspond to quantiles of the input factor distributions, if the distributions are not uniform. For uniform distributions, the levels are obtained by dividing the interval into equidistant parts. The choice of the sizes of the levels *p* and realizations *r* is also a problem; various experimenters have demonstrated that the choice of *p* = 4 and *r* = 10 produces good results.

- Max D. Morris. Factorial sampling plans for preliminary computational experiments.
*Technometrics*, 33(2):161–174, May 1991. - Saltelli, A. et al.
*Sensitivity analysis in practice. A Guide to Assessing Scientific Models*. John Wiley & Sons Ltd., Chichester, 2004.

morris.txt · Last modified: 2019/11/18 13:34 (external edit)