### 2.2 Summated Ratings

Summated ratings are obtained by adding the values of the relevant items of a latent variable for each object and then computing the average value, taking due account of the missing data. For example, let X1, X2, …, Xp be the values (observations, ratings or measurements) on the p items of a latent variable. Then the index would be equal to S (X I)/p. Such indices can be constructed using IDAMS module TRANS.

Sometimes, it is illogical to construct an index by simply adding the values of different items. For example, it would be absurd to construct an index of research output by simply adding the numbers of books, articles in national and foreign journals, original research reports, patents, experimental materials, algorithms and designs, etc. In such cases, IDAMS module TRANS is a very useful and novel procedure for construction of indices.

##### 2.3 Partial Order Scoring (POSCOR)

The problem of ranking objects is relatively simple if it is based on a property, which can be expressed on an ordinal or interval scale. In this case we can say that an object (A) precedes an object (B) if the values corresponding to it on the scale is less than that of the other one. The necessary and sufficient condition for the rank ordering is that the variable examined should be measured at least on an ordinal scale. In the case of nominal scale no rank ordering can be performed. But the problem is not so simple if the property is expressed by more than one variable, which have to be considered simultaneously in rank ordering. In this case, the ordinal measurability of the variables is not a sufficient condition for rank ordering.

Consider the case when two variables V1 and V2 are used in measuring the objects. Then we have the following alternatives:

(a)   The values equal in both the variable.
(b)   Object A precedes B at least on one of the variables; on the other variable, A and B may be equal.
(c)   B precedes A at least on one of the variables; on the other variable A and B may be equal.
(d)   A precedes B on V1 and B precedes A on V2.
(e)   B precedes A on V1 and A precedes B on V2.

Obviously, definite rank order can be given only in the case of (b) and (c). In the case of (d) and (e) rank ordering of A and B is controversial. In such cases, additional restrictions or other procedures are required to achieve a definite rank order. The situation is also the same in the case of more than two variables.

Alternatives (a) – (e) allow us to define a binary partial order relation:

(a) Þ A = B

(b) Þ A precedes B

(c) Þ B precedes A

(d), (e) Þ A and B are not related

The internal structure of a partially ordered set allows us to define a 'dominated' and a 'dominating' subset for each element of it. The cardinal numbers (or the measures) of these subsets and their relations characterize the relative position of the element in the hierarchy implied by the partial order. A composite measure can be derived in this way, which shows the relative position of the elements within the data set and therefore a ranking of the elements can be based on it.

IDAMS module Poscor calculates (ordinal scale) scores using a procedure based on the hierarchical position of the elements in a partially ordered set according to a number of properties (or characteristics).