Application of the PROperty FITting Method (PROFIT) to Classification of EU Countries Based on Their Innovation Level

Roszko-Wojtowicz, Elzbieta; Bialek, Jacek Working Paper Application of the PROperty FITting Method (PROFIT) to Classification of EU Countries Based on Their Innovation Level Institute of Economic Research Working Papers, No. 103/2017 Provided in Cooperation with: Institute of Economic Research (IER), Toruń (Poland) Suggested Citation: Roszko-Wojtowicz, Elzbieta; Bialek, Jacek (2017) : Application of the PROperty FITting Method (PROFIT) to Classification of EU Countries Based on Their Innovation Level, Institute of Economic Research Working Papers, No. 103/2017, Institute of Economic Research (IER), Toruń This Version is available at: https://hdl.handle.net/10419/219925 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/ Institute of Economic Research Working Papers No. 103/2017 Application of the PROperty FITting Method (PROFIT) to Classification of EU Countries Based on Their Innovation Level Elżbieta Roszko-Wójtowicz, Jacek Białek Article prepared and submitted for: 9th International Conference on Applied Economics Contemporary Issues in Economy, Institute of Economic Research, Polish Economic Society Branch in Toruń, Faculty of Economic Sciences and Management, Nicolaus Copernicus University, Toruń, Poland, 22-23 June 2017 Toruń, Poland 2017 © Copyright: Creative Commons Attribution 3.0 License Application of the PROperty FITting Method (PROFIT) to Classification of EU Countries Based on Their Innovation Level Elżbieta Roszko-Wójtowicz1, Jacek Białek2 Abstract Research background: As it is known, innovativeness can be measured by using many known indices, such as the Global Innovation Index, the Summary Innovation Index, etc. and often these indices are based on different methodologies and take into consideration different sets of diagnostic variables. As a consequence, the final evaluation of innovativeness may strongly depend on the innovation index used. Obviously, some groups of indices lead to similar ranks of the EU countries. Nevertheless, if there are at least two groups of indices which provide different ranks of these countries, a problem with the proper evaluation of their real innovativeness arises. One of the solutions is to select the most valuable indices by observing the impact of all indices on forming distances between innovativeness levels of the EU countries. Following this option, the main aim of this paper is classification of the EU countries with respect to their innovativeness and the evaluation of international index influences on the classification obtained. Purpose of the article: The aim of the paper is to conduct the research on differences in innovation intensity across the EU member countries. Methodology/methods: For the purpose of the article, the PROFIT (PROperty FITting) method, an extension of multidimensional scaling (MDS), was applied. The ultimate goal of MDS techniques is to produce a geometric map that illustrates the underlying structure of complex phenomena, for instance, innovativeness of the EU countries. It is a widely used method which collects attribute ratings for each object (country) and then finds the best correspondence of each attribute to the derived perceptual space. Applying the PROFIT method needs linear regression techniques and provides some additional information, i.e. the impact of the considered set of diagnostic variables on the shape of the perception map. Findings & Value added: The final result is a two-dimensional map of the EU countries which reflects distances among their innovativeness levels along with vectors presenting the influence of international indices of innovativeness on the structure of this map. The nature of the results and the ways in which they are 1 University of Łódź, Institute of Statistics and Demography 90-255 Łódź, 3/5 POW Street, e-mail: [email protected], 2 University of Łódź, Institute of Statistics and Demography 90-255 Łódź, 3/5 POW Street, e-mail: [email protected] interpreted are subsequently reviewed. The main conclusion drawn from the perception map created concerns the interpretation of the above-mentioned vectors, i.e. the information about the role of each international innovation index in clustering the EU countries with respect to their innovation intensity is obtained. JEL Classification: A11; A14; B16 Keywords: multidimensional scaling (MDS), property fitting method (PROFIT), innovation intensity, EU member countries, synthetic measures of innovativeness Introduction As it is known, innovativeness can be measured by using many known indices, such as the Global Innovation Index (Dutta et al., 2015), the Summary Innovation Index (European commission, 2015), and also the Innovation Output Indicator recently added by the European Commission (European Commission 2013; Vertesy & Deiss, 2016), as well as many others. Often these indices are based on different methodologies and take into consideration different sets of diagnostic variables. As a consequence, the final evaluation of innovativeness may strongly depend on the innovation index used. Sources of public statistical data play an important role in (1) the process of development of a proper national policy aimed at ensuring economic and social progress, and (2) the measurement and evaluation of phenomena occurring in the modern world. In the last few decades, the role and importance of statistics, especially indices of measurement, have significantly increased (Giovannini & Uysal, 2006). Public interest in information is based on current needs and is directly connected with people's active participation in various decision-making processes, both in the public and private domain (Hahn & Doganaksoy, 2008). This particular explosion of information often, instead of facilitating, becomes a considerable obstacle. Questions are raised about the quality and form of the information provided, its validity and reliability, thus further dilemmas are born (Goldsmith & Foxall, 2003, pp. 321-330; Hollanders, Van Cruysen, 2008). One of the solutions is to select the most valuable indices by observing the impact of all indices on forming distances between innovativeness levels of the EU countries. Following this option, the main aim of this paper is classification of the EU countries with respect to their innovativeness and the evaluation of international index influences on the classification obtained. In reference to the aim of the paper, a research hypothesis has been formulated stating that the degree of specialisation of an innovation index has a significant influence on the location/position of the EU Member States on a perceptual map. For the purpose of the analysis conducted, it has been assumed that the type and number of variables and the number of partial aggregates (sub-indices) included in the construction of the final innovation index determine the degree of index specialisation. For the purpose of the article, the PROFIT (PROperty FITting) method, an extension of multidimensional scaling (MDS), was applied. Multidimensional scaling is used in many different fields, including economics (e.g.: Black 1991), sociology (e.g: Beardsworth & Keil 1992) and political science, as well as many other disciplines. Multidimensional scaling is widely used to assess various socioeconomic events, ranging from social/human views (Wish, Deutsch, & Biener 1971) to perceptions of visual patterns (Hirschberg, Jones, & Haggerty, 1978). Methodology The Concept of the Analysis The research procedure was carried out according to the following steps: Step 1) Due to the varying range of variation of the innovation indices – SII, IOI and GII – selected for the analysis, first the standardisation of the variables according to the scheme corresponding to the zero unitarisation method was carried out. Step 2) Then multidimensional scaling was performed using the Euclidean distance, thus reducing the number of dimensions to two. Step 3) The last stage was the estimation of regression model parameters according to the PROFIT concept. As a result of activities carried out within the framework of the abovedescribed statistical procedure, a perceptual map was obtained illustrating similarities of the EU countries in terms their level of innovativeness and showing how individual innovation indices have contributed to the position of the individual countries on the map (Fig. 1). Research Method PROFIT (PROperty FITting) is a kind of external vector analysis of preference mapping. The standard reason for using this method is testing hypotheses about attributes that influence people’s judgement of similarities among a set of items. Nevertheless, there are no technical objections to using PROFIT for other cases, not related only to human preferences. The PROFIT method is a two-step procedure which is a combination of multidimensional scaling and multiple regression analysis. To understand the idea of PROFIT, it is advisable to start from the description of multidimensional scaling (MDS). Multidimensional scaling (MDS) is a means of visualising the level of similarity of individual cases of a dataset. It refers to a set of related ordination techniques used in information visualisation, in particular, to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction (Kruskal & Wish, 1978), Young & Hamer, 1987). An MDS algorithm aims to place each object in N-dimensional space so that the between-object distances are preserved as well as possible. Each object is then assigned coordinates in each of the N-dimensions. The number of dimensions of an MDS plot N can exceed 2 and is specified a priori. Choosing N=2 optimises the object locations for a twodimensional scatterplot. MDS can have a metric or non-metric form and, as a rule, the non-metric MDS is used before the PROFIT analysis (Kruskal, 1964, Takane et al., 1977). In such a case, the method finds both a nonparametric monotonic relationship between the dissimilarities in the itemitem matrix and the Euclidean distances between items, and the location of each item in the low-dimensional space. The relationship is typically found using isotonic regression: let denote the vector of proximities, – a monotonic transformation of and the point distances; then coordinates have to be found that minimise the so-called stress defined as follows (Kruskal, 1964): , (1) where lower indexes denote the i – th and the j – th point on MDS map. A PROFIT analysis evaluates the correspondence between one or more item attributes and the location of items in a multidimensional space. As it was above-mentioned, PROFIT, which is a combination of multidimensional scaling and multiple regression analysis, consists of two phases. After the first step (MDS), we obtain a configuration of n points x = (x1, x2, …, xn)T in r – dimensional space (r is usually 2 or 3). In the second phase, PROFIT takes as input both a configuration of points x and a set of attribute preferences data pk = (pk1, pk2, ..., pkn)T, where k = 1,2, ..., m, is a number of attributes (Zaborski & Pełka, 2013). Then a multiple regression analysis is performed using the coordinates of as independent variables and the attributes as dependent variables. The procedure provides a separate regression for each attribute with “classical” regression coefficients: . (2) Results and Discussion Research Data In this section, selected synthetic indices of innovativeness will be presented. The analysis conducted was limited to three major indices, i.e. the Global Innovation Index, the Summary Innovation Index and the Innovation Output Indicator. Differences in the approach to the measurement of innovativeness in each of these indices have a significant impact on the final results of the ranking of countries. One of the fundamental differences that can be observed is the degree of specialisation of the innovation indices selected for the analysis. The comparative summary of these three innovation indices presents the table below. Table 1. Comparative summary of selected indices No. Name of the indicator Source Number of variables Number of countries Data of publication 1. Global Innovation Index Business School of the World, the World Intellectual 79 141 Since 2007, annually 2. Innovation Output Indicator European Commission 5 38 Since 2010, 4-year time frame 3. Summary Innovaiton Index European Commission 25 34 Since 2001, annually Source: own elaboration based on: European Commission (2013), European Commission (2015), Vertesy & Deiss (2016), Dutta et al., (2015). The Global Innovation Index is characterised by the broadest coverage of variables. The eighth edition of the report presented 141 economies, the study covered 95.1% of the population living worldwide and 98.6% of global GDP (US $). In the construction of the ranking, 79 individual indicators that characterised innovativeness were included (Dutta et al., 2015). It is followed by the Summary Innovation Index. As with GII, subindices, made up of a specific number of variables, are also created for this index. Over the years, the methodology of calculating the SII has evolved, now 25 indicators, which have been assigned to one of the five categories, are used. The first three sets of indicators are variables from the input layer, and the last two from the output layer. The input layer is described by: a) factors stimulating innovativeness (enablers), b) firm activities which show innovative activities implemented at the company level. The output layer is described by effects which reflect the results of innovative activities carried out in the sphere of business (European Commission, 2015; Majerova, 2015, pp. 230-231). The Innovation Output Indicator is undoubtedly the index characterised by the narrowest specialisation among the ones chosen for the comparative analysis. Only five variables can be isolated in the index, and only in one case, at a lower level of analysis, an aggregate variable is generated. This applies to competitiveness of knowledge-intensive industries (with a high demand for specialist knowledge). The COMP component is defined as the arithmetic average (with equal weights) of two indicators: GOOD – the total value of exports of a country and SERV – the share of knowledgeintensive services in total services exports (European Commission, 2013, pp. 1-2). Research Results In the paper, the PROFIT analysis is used to show how an input set of attributes (the values of the individual innovation indices) of the objects (the EU Member States) is visualised on the multidimensional scaling axes. Coordinates assigned to the individual objects (countries) are considered as explanatory (independent) variables, while the values of individual attributes (innovation indices) of the objects are response (dependent) variables. In the presented example, three regression analyses were performed as three attributes (variables) – SII, GII, IOI – were included in multidimensional scaling. The coordinates of the individual attributes (variables) were determined with the use of standardised regression coefficients corresponding to each of the multidimensional scaling axes. After conducting the regression analyses for all the three innovation indices, the PROFIT analysis algorithm provides directional correlation coefficients determining the vector direction and sense that corresponds to each of the attributes selected to describe the dimensions. Thus three points with the following coordinates were determined on the MDS map: SII (Dim 1 – (0.978); Dim 2 – (0.036)), GII (Dim 1 – (0.959); Dim 2 – (-0.269)), and IOI (Dim 1 – (0.941); Dim 2 – (0.298)); detailed results are presented in Table 2. The determined coordinates for the individual attributes allow to show how the EU member countries are arranged according to the intensity of a given attribute. Figure 1. The perceptual map with vectors describing the individual dimensions of the plane. Note: The calculations were made with the use of Statistica 12.5 software Plus Suite – specialist analytical package. Source: own elaboration based on: European Commission (2013), European Commission (2015), Vertesy & Deiss (2016), Dutta et al., (2015). Figure 2. Shepard diagram illustrating the distances derived from the original data sources versus the distances reproduced in the MDS analysis. Note: The calculations were made with the use of Statistica 12.5 software Plus Suite – specialist analytical package.