Morris Elementary Effects Screening

A decision model can have many inputs that could affect the result: criterion weights, threshold values, expert scores. Trying all of them at once, in every combination, is a heavy undertaking. The Morris screening method perturbs each input (factor) in turn by small steps and measures how much the result changes, repeating this a few times. Its output is not a ranking but three numbers for every factor: the average direction of its effect, the average size of its effect, and how irregular (interactive, non-linear) that effect is. It was introduced by Morris in 1991; its purpose is to separate "which factor matters, which does not" with a small number of model runs, not to perform a full variance decomposition.

The idea behind Morris is "examine roughly first" rather than "examine everything in detail." With many factors present, examining all of them in detail, for instance with Sobol indices, carries both a computational and an interpretive burden. Morris performs a cheap screening first, eliminates the unimportant factors, and leaves only the genuinely influential ones for detailed examination. This is a form of elimination, but it eliminates factors, not alternatives: it does not rank alternatives, it says which input deserves attention. The philosophical consequence is this: the method answers not "the exact answer" but "where should I look"; it determines which factors get carried forward to a more detailed method (such as Sobol) at the next step.

The method proceeds through four steps.

First, setting up the grid. The factors to be examined (for example, criterion weights) are scaled to between 0 and 1, and a few evenly spaced levels are set for each (for example, four levels: 0, one third, two thirds, one). The step size is fixed according to this number of levels.

Second, trajectories. Starting from a random point, the factors are perturbed one by one, in a random order, by the set step. Once every factor has been perturbed once, a trajectory is complete; this trajectory consists of the number of factors plus one point. This is repeated a few times, for a few separate trajectories.

Third, elementary effects. For every trajectory, how much the decision model's output changes when a factor is perturbed is recorded; this amount of change is that factor's "elementary effect" for that trajectory. Several elementary effects from several trajectories are gathered for the same factor.

Fourth, three summary numbers. All of a factor's elementary effects are combined to calculate three numbers: the signed mean (large if the effect's direction is always the same, small if the direction reverses), the absolute mean (the size of the effect, independent of direction), and the standard deviation (how irregular the effect is, how much it varies from trajectory to trajectory). A factor with a large absolute mean is important; a factor whose standard deviation is close to or larger than its absolute mean acts not alone but together with other factors, or affects the result non-linearly, and should be examined separately.

The formulas behind each step are given on the DecisionMind method page; this card carries no formulas.

Each of the three numbers says something different. A large absolute mean means that factor changes the result substantially; a small one means it can safely be set aside at the screening stage. If the standard deviation is markedly smaller than the absolute mean, the effect is regular and one-directional; if it is close to or larger than the absolute mean, the factor is interacting with other factors or acting non-linearly. If the signed mean and the absolute mean are close to each other, the effect always runs in the same direction (the result always rises or always falls as the factor increases); if there is a difference between them, the factor sometimes increases and sometimes decreases the result. No number says "this factor is this many per cent important"; Morris gives only ranking and rough size, an exact share requires Sobol indices. Thus:

"The Morris analysis proved that the C1 weight is the most important factor"

should read instead:

"The C1 weight has the largest average effect among the factors screened; confirming its exact contribution share requires validation with Sobol indices"

Morris screening works with crisp data and needs no decision table of its own; it needs a host decision model (for example a weighted sum, TOPSIS or VIKOR). Required inputs are a list of the factors to be screened (such as criterion weights or threshold values), each factor's lower and upper bound, the number of levels, and the number of trajectories. DecisionMind holds no extension of this method; where the result is uncertain and interaction needs to be measured in detail, it is complemented with Sobol sensitivity indices.

Where many factors are present and you want to see with a small number of trials which of them genuinely matter, Morris is exactly the right tool. It is also used to decide which factors should be carried into a more detailed sensitivity analysis (such as Sobol) at the next step.

The cases where it should not be used are as follows. If the number of factors is already small (two or three) and examining all of them in detail is feasible, skipping the screening and going straight to Sobol is more informative. If exact contribution percentages (variance shares) for the factors are required, Morris falls short; it gives only a rough order of importance. If the number of trajectories is very low (below ten), the results are unreliable; in that case the screening should be repeated, or work should proceed directly with fewer factors.

Many factors are present, a rough first elimination is wanted → Morris screening

Few factors remain, exact contribution share is needed → Sobol sensitivity indices

Only whether a single weight overturns the winner is being asked → Weight Sensitivity Analysis

Two different analyses' rankings are being compared → Spearman rank correlation

Morris's greatest strength is that it works with a small number of model runs even when many factors are present; as the number of factors grows, the computational load grows linearly, not exponentially. By giving three separate numbers (direction, size, irregularity), it answers not just "is it important or not" but also "how is it important," distinguishing whether a factor is regular or interactive. It can be applied directly to different decision models (weighted sum, TOPSIS, VIKOR, whichever), because it does not look inside the model, it only observes the input-output relationship.

Its limitations stem from its screening purpose. Morris does not show which two factors interact with each other; it only flags, through the standard deviation, whether a single factor is interactive (Campolongo, Cariboni and Saltelli, 2007). It gives no exact variance share; it makes only a rough distinction between "important" and "unimportant." If the number of trajectories is low (below ten), the estimates become unstable, and screening with different random seeds can give different orderings. Finally, the method assumes the factors can be perturbed independently of one another; where a mandatory link exists among factors, for instance where weights must sum to one, this link must be built into the model separately.

The most common mistake is using the signed (directional) mean in place of the absolute mean; if a factor sometimes acts to increase and sometimes to decrease the result, the signed mean cancels these effects against one another and makes an important factor look unimportant. A second mistake is keeping the number of trajectories very low (below ten) and presenting the results as though they were definitive. A third mistake is ignoring the standard deviation and looking only at the absolute mean; a large standard deviation shows that factor is interactive and cannot be interpreted on its own. A fourth mistake is reporting a Morris result as though it were an exact variance share; Morris gives only rough ranking and a sign of irregularity.

The governing principle is this:

Morris is a first elimination that shows, among many factors, which ones deserve attention; for an exact contribution share it must be carried forward to a detailed method (Sobol).