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The weighted product model (WPM) is a popular multi-criteria decision analysis (MCDA) / multi-criteria decision making (MCDM) method. It is similar to the weighted sum model (WSM) in that it produces a simple score, but has the very important advantage of overcoming the issue of 'adding apples and pears' i.e. adding together quantities measured in different units.
A basic decision matrix consists of establishing a set of criteria and a group of potential candidate designs. One of these is a reference candidate design. The other designs are then compared to this reference design and being ranked as better, worse, or same based on each criterion.
In decision theory, the weighted sum model (WSM), [1] [2] also called weighted linear combination (WLC) [3] or simple additive weighting (SAW), [4] is the best known and simplest multi-criteria decision analysis (MCDA) / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria.
The quadratic scoring rule is a strictly proper scoring rule (,) = = =where is the probability assigned to the correct answer and is the number of classes.. The Brier score, originally proposed by Glenn W. Brier in 1950, [4] can be obtained by an affine transform from the quadratic scoring rule.
A formula (typically a simple sum of all accumulated points) that calculates the score. A set of thresholds that helps to translate the calculated score into a level of risk, or an equivalent formula or set of rules to translate the calculated score back into probabilities (leaving the nominal evaluation of severity to the practitioner).
The individual's total number-correct score is not the actual score, but is rather based on the IRFs, leading to a weighted score when the model contains item discrimination parameters. It is actually obtained by multiplying the item response function for each item to obtain a likelihood function , the highest point of which is the maximum ...
The aim is to find non-negative weights such that for all examples, the sign of the weighted combination of the features matches its labels. That is, require that for all . Without loss of generality, assume the total weight is 1 so that they form a distribution.
The prediction is obtained by adding these products along with a constant. When the weights are chosen to give the best prediction by some criterion, the model referred to as a proper linear model. Therefore, multiple regression is a proper linear model. By contrast, unit-weighted regression is called an improper linear model.