Overview of Approaches to Incorporate Dynamics into the Measurement of Complex Phenomena with the Use of Composite Indices

Composite indices have substantially gained in popularity in recent years. Despite their alleged disadvantages, they appear to be very useful in measuring the level of certain phenomena that are too complex to express with a single indicator. Most rankings based on composite indicators are created at regular intervals, such as every month, every quarter or every year. A common approach is to base rankings solely on the most current values of single indicators, making no reference to previous results. The absence of dynamics from such measurements deprives studies of information on change in these phenomena and may limit the stability of classifications. This article presents the possibility of creating reliable, dynamic rankings of measured items and measuring the complex phenomena with the use of composite indices. Potential solutions are presented on the basis of a review of the international literature. Some advantages and disadvantages of the presented solutions are described and an example of a new approach is shown.


Introduction
Composite indices, understood as aggregated ordinal or cardinal measures of country performance and created through the manipulation of individual indicators (Saltelli, 2007), have substantially gained in popularity in recent years. Despite their alleged disadvantages, which mostly concern the simplified image of phenomena created by them, these indices represent a very convenient tool for comparing and classifying the results achieved by different countries in both social and economic domains. These indices appear to be particularly necessary for measuring the level of complex phenomena, which cannot be expressed with the use of a single indicator. A significant problem created with composite indices is that an objective measure assigned to a certain phenomenon cannot be found. This phenomenon has led to the creation of numerous rankings in terms of this phenomenon. Each of these rankings uses different indices, and, depending on the variables taken into account in creating the composite index, a certain country can be ranked differently, even if the measured phenomenon is the same. Such

The Notion of Dynamics
To clarify the considerations presented in the article, the explanation of a concept that is used often in the text is needed. Dynamics is a widely used concept and is mostly intuitively understood. For this reason, in the literature concerning dynamic phenomena, the definition of this concept is rarely ever explained in detail.
The most common explanation is derived from sociology. This term originates in the works of August Comte, the creator of positive philosophy. According his words: "The true general spirit of social dynamics then consists in conceiving of each of these consecutive social states as the necessary result of the preceding, and the indispensable mover of the following, according to the axiom of Leibnitz -the present is big with the future. In this view, the object of science is to discover the laws which govern this continuity, and the aggregate of which determines the course of human development" (Martineau, 1858).
In other words, dynamics, as it is currently understood, is a study of how things change over time, a pattern of change or growth of an object or the force or intensity of a phenomenon (Business Dictionary, 2011).
The dynamics of a phenomenon as its changes over time are often measured with the use of statistical tools. Statistics applies dynamics indicators or indices, which are relative numbers showing the ratio or difference between a phenomenon's level during a period under examination and the phenomenon's level during a base period. However, this may be an inadequate  compares only two periods and shows the change that has happened in the time between them. For example, this method is unable to capture information about dynamics in the longer term. The Nyquist-Shannon (Nyquist, 1928;Shannon, 1949)

The Essence of Complex Phenomena
In modern societies, researchers often must deal with phenomena that cannot be measured and expressed usefully with a single number. Socio-economic development, the quality of life, the level of satisfaction, the investment attractiveness of regions and the financial state of an enterprise all have many variables and span several domains. All phenomena that can be similarly described are called complex phenomena. In other words, these are all phenomena that must be described with more than one variable.
Socio-economic development is a prime example of the description above. As its name indicates, this concept is by definition connected to the sociological and economic domains. This duality is the strongest premise of the phenomenon's complexity.
Economic development cannot be explained by economic factors alone, and the concept of development includes more than mere changes in economic indicators (Szirmai, 2005, p. 15). Development, conceived of as economic growth, is a quantitative concept. Even if the understanding of development is limited to the economic sphere, it is clear that economic development encompasses more than economic growth alone. Economic development refers to growth accompanied by qualitative changes in the structure of production and employment, generally referred to as structural change (Kuznets, 1966). Development can then be defined as a movement in the direction of developmental goals, which include the reduction of poverty, increased economic welfare, improved health and education, and increased political and social freedom (Szirmai, 2005, p. 9). If any attempt to measure the overall development is to be made, these different domains must be taken into account. This statement is true not only for socioeconomic development but for all complex phenomena as well, provided the selection of relevant variables, adjusted to the measured phenomenon.

Measurement of Complex Phenomena with the Use of Composite Indices
The The coordinates of the pattern can be determined on the basis of expert opinions, generally accepted standards or empirical data (Sokołowski & Zając, 1987). Mosley and Mayer (1998) (Cherchye et al., 2007). to clean water, equal opportunities for both men and women, human rights and so forth (Szirmai, 2005, p. 15). A convenient way to combine this number of variables into readable results is composite indices, which can aggregate all of the above-mentioned aspects. Table 1 presents the most common examples of such composite indices, which are not limited to the context of socio-economic development. As it may be observed, for many of the phenomena, more than one index is used, which can lead to ambiguity in the results of measurement (Jones, 2004).
The multidimensionality of composite indicators is one of these measurements' major advantages. Such indices is that they usually do not provide any additional information that cannot be provided by a single index (Booysen, 2002) but do require much more data to introduce analysis (Saisana & Tarantola, 2002).
Existing indicators aggregating single indices are constantly improved to emphasise their advantages and to eliminate the drawbacks of their use. One direction of these improvements is to incorporate a phenomenon's dynamics into measurements, with composite indicators.

Approaches to Compliance of Dynamics in Measuring the Socio-economic Development
The most common application of composite indi-

Scope of the research Methodology Publication
Demand for electronic goods in Poland The composite indicator is based on a taxonomical measure of development proposed by Hellwig (1968). On the basis of collected data, the origin of a multidimensional coordinate system as the point of reference (pattern of development) is chosen (variables are standardised). Then, values of the composite index, calculated as the distance from the model object, are obtained. On their basis, variation coefficients for objects and growth rates in certain periods are calculated. In this case, variation coefficients express the phenomenon's dynamics. Ditmann & Pisz, 1975 Economic research and socio-economic development This idea is again similar to the method proposed by Hellwig (1968). On the basis of the collected data, a pattern of development is established (for each object, pattern should be individual). Then, the distance between each examined object and its pattern of development is calculated. The dynamics of development are estimated by incrementing between-distances to the pattern obtained in following periods. For each period, the pattern is calculated separately. Pluta, 1977 Dynamic and spatial comparative analysis of economical structures In this approach, structural changes in examined objects are measured. The value of the composite indicator is calculated for each adjacent pair of years. Doing so enables following the changes and detecting turning points occurring in objects' trends. For the index of structural changes, a coefficient of volatility of growth indicators for individual elements of the structure is used. Zeliaś, 1988 Comparative analysis of agricultural production's development The composite index is calculated as a mean of the variable's values describing the measured object. Knowledge about the indicator's values allows the estimation of the dynamics of the studied phenomenon. Dynamics in this context means the average increment of the phenomenon and the average pace of its growth, which are supplemented with the use of linear and exponential trending. Nowak, 1990 Indicators for social inclusion The value of a composite index is calculated as a weighted mean of single indicators. The dynamics of performance for each studied object are expressed as a percentage change between two periods under research.

Cherchye et al., 2004
Measurement of investment attractiveness of companies listed on stock exchange This study utilises a dynamic approach to assess the stability of classification. The mean value of differences in the composite indicator's value between two examined periods of time is calculated for all objects. The coefficient obtained reflects the dynamics of change occurring in the meantime. The dynamics in this case are aggregated for all studied objects. Tarczyński, 2004 10.5709/ce.1897-9254.42 DOI: CONTEMPORARY ECONOMICS Vol. 6 Issue 2 64-73 2012 be created. The values to be included in this database are then used to create a composite index. These values must be normalised, and suitable weights should be assigned to them. The following steps, which concern the exact rules and formulas for calculations, differ depending on the researchers' methodology. Table 2 lists some approaches that incorporate dynamics into the creation of composite indicators. All of the presented studies concern the taxonomy of ex- Assessment of the EU's internal market In this approach, the dynamics of each sub-indicator included in the composite index are calculated as the ratio between the value of an indicator in a certain period to its value in the base interval of time. After the dynamics of all sub-indicators are obtained, a weighted aggregation of the results is made. On this basis, the performance of examined countries is evaluated.

Regional development
The composite indicator is based on vector calculus. The chosen standard object (which can be described as pattern of development) is the one that has maximal values among stimulants and minimal among destimulants. This pattern can be constant and does not depend on the number of periods that are taken into account in the research. This approach allows other examined objects to be better than the standard one. Using the same pattern for the entire period under study, it is possible to compare objects' performances in subsequent intervals of time.