Determining of the degree of geographical marginality of settlements in Međimurje using GIS and exploratory factor analysis

is to develop a methodology for identifying, analyzing and determining marginal areas of Međimurje on the spatial level of settlement. Exploratory factor analysis was used in the research via GIS methods. The 30 selected variables were used for exploratory factor analysis. The suitability of the variables was tested using the Kaiser-Meyer-Olkin test and Bartlett’s test. Free, open source R, JASP and QGIS software were used. In the analysis, six factors were identified, by which the characteristic types of settlements in Međimurje were identified: 1) Spatial concentration and economic dynamics; 2) Demographic dynamics and population aging; 3) Education and economic diversification; 4) Availability of central functions; 5) Traditional extensive agricultural production; and 6) Stationary work contingent focused on primary activities. Based on the factor scores, a Međimurje index of marginalization of settlements (MIMaNa) was calculated. Based on this index, the degree of geographical marginality of settlements in Međimurje was determined.


Introduction
The phenomenon of marginality has been studied within the scope of various scientific disciplines in the last twenty years: geography, sociology, economics, agriculture, ecology, as well as at different spatial levels: local, territorial, regional and global.Additionally, various quantitative indicators have been used: demographic, spatial, socioeconomic, political, historical and ecological (Leimgruber, 1994;Pelc, 2006;Dery et al., 2012;Zsilincsar, 2014).Marginality is a multidimensional phenomenon and there is no universally agreed upon definition of marginality.Moreover, it is difficult to determine the boundaries of where, why and how marginality arises, or disappears, as well as how to predict it and prevent its emergence.Horvat and Toskić (2017) observed and identified that the pronounced complexity at the level of structural and systematic marginality were not sufficiently taken into account in previous research.According to the authors, two fundamental problems in research arise from the features of the phenomenon of marginality: 1) how to measure marginality due to its "partiality" (unclear boundaries, i.e. what is marginal and what is not); and 2) its multidimensionality, i.e. what is marginal in one system might not be in another.Therefore, the distinct complexity of marginality and marginalization and the aforementioned problems in approaching this process result in a methodologically very broad framework.This makes it difficult to define indicators of marginality and apply them consistently in research.Based on this, it can be concluded that marginality is a multi-dimensional, multi-layered, multi-sector and multi-level phenomenon.
More than three decades ago, Leimgruber (1994) defined marginal regions and concluded that the phenomenon of marginality is such a broad concept that it is very difficult to define it in a simple and clearly-defined way.Leimgruber points out four possible fundamental approaches: geometric, ecological, economic and social.Pelc (2017) explains Leimgruber's fundamental approaches in more detail below.
• Ecological.This approach is ambiguous: it can either be considered as the natural potential of an area for human survival, or as the state of the environment.
• Economic.Marginality in this case would be defined by production potential, accessibility, and infrastructure.
• Social.In this case the focus is on minorities and socially marginal groups, according to various criteria (ethnicity, language, religion etc.).
In contemporary research in Croatia, it is worth emphasizing research that is directly or indirectly related to research in marginal areas: at the local level (Nejašmić, 2005;Popović and Radeljak, 2011;Nejašmić and Toskić, 2013;Feletar, 2014;Nejašmić and Toskić, 2016); research focused on land use change and the determination of landscape degradation as a feature of marginal areas (Horvat, 2013;Cvitanović and Fuerst-Bjeliš, 2018); an overview of the basic concepts of geographic marginality (Horvat and Toskić, 2017); research on social exclusion in the sense of marginalization (Šućur, 1995; Šućur, 2004; Šporer, 2004); a look at the historical aspect of marginal groups in Croatian medieval societies (Karbić, 1991); and the impact of the traffic marginality on the everyday lives of secondary school students in Zagreb (Gašparović and Jakovčić, 2014).
Over the last few years, in addition to the usual conventional topics and areas dealing with marginality, there has been a significant increase in the amount of scientific research on marginality regarding completely new areas and topics, such as: the COVID-19 crisis, the migrant and refugee crisis, as well as climate change and globalization (Sevelius et al., 2020;Fuerst-Bjeliš, 2020;Sanfelici, 2021;Fuerst-Bjeliš and Šulc, 2022).Geographic Information Systems (GIS) can play a crucial role in understanding and addressing issues related to marginality.GIS is a technology that allows for the collection, analysis, and visualization of spatial data.By integrating geographic data • ekološki: ovo je gledište dvosmisleno, može se uzeti ili kao prirodni potencijal područja za ljudski opstanak ili kao stanje okoliša • ekonomski: marginalnost bi se u ovom slučaju definirala proizvodnim potencijalom, dostupnošću i postojećom infrastrukturom • društveni: u ovom bi slučaju fokus bio na manjinama i društveno marginalnim skupinama prema različitim kriterijima (nacionalnost, jezik, vjera itd.).
Posljednjih nekoliko godina, osim uobičajenih tema i područja koja se bave marginalnošću, znatno je porastao broj znanstvenih istraživanja marginalnosti na sasvim novim područjima i temama kao što su na primjer COVID-19 kriza, migrantska i izbjeglička kriza, klimatske promjene i globalizacija (Sanfelici, 2021;Sevelius i dr., 2020;Fuerst-Bjeliš, 2020;Fuerst-Bjeliš i Šulc, 2022).Geografski informacijski sustavi (GIS) mogu igrati ključnu ulogu u razumijevanju i rješavanju pitanja povezanih s marginalizacijom.GIS je tehnologija koja omogućuje prikupljanje, analizu i vizualizaciju prostornih podataka.Integrirajući geografske podatke s različitim socioekonomskim i demografskim informacijama, GIS može pružiti vrijedne uvide u obrasce marginalizacije i pomoći u identifikaciji područja ili populacija koje su najranjivije ili su zakinu-HRVATSKI GEOGRAFSKI GLASNIK 85/2, 5−45 (2023.)with selected socio-economic and demographic information, GIS can provide valuable insights into patterns of marginalization and help identify areas or populations that are the most vulnerable or disadvantaged.By employing exploratory factor analysis in the context of geographical marginality, researchers can uncover the latent dimensions that contribute to marginalization and gain a better understanding of the underlying factors shaping disparities across various geographic areas.This knowledge can inform policymakers, planners, and practitioners in developing targeted interventions and policies to address geographical marginality and promote more equitable development.In summary, GIS and factor analysis can be valuable tools in understanding and addressing marginality by providing spatial insights, supporting evidence-based decision-making, and empowering marginalized communities to participate in the mapping and planning processes.Lukić (2012) highlighted that in the last 30 years, factor analysis has been utilized in numerous research studies in geography and other social and natural sciences, thanks to the development of computers, specialized statistical software and GIS.In recent years, multivariate analysis methods and GIS have been increasingly used in geographical research within the context of physical and social geography.Rašić-Bakarić (2005) applied factor and cluster analysis to group selected units of local self-government in three counties based on similar characteristics.Kurnoga-Živadinović (2007) employed cluster and factor analysis, as well as discriminant analysis, to classify Croatian counties into larger groups with similar socio-economic indicators.Prelogović (2009) utilized factor analysis to examine the socio-spatial structure of Zagreb based on eighteen indicators.Bahovec et al. (2011) studied sustainable socio-economic development in selected countries by applying factor and cluster analysis to ten chosen indicators.Lukić (2012) created a detailed typology of rural and urban settlements in Croatia at the level of statistical settlements using principal component analysis and factor analysis.
For spatial analysis in territorial marginality mapping, Chieffallo et al. (2022) described a methodology that relies on geostatistical analysis techniques implemented within a GIS environment.Their approach involves measuring a system of quantitative indicators at the municipal level.The mapping process includes calculating the Moran correlation index and generating LISA cluster maps.These methods allow for the identification and visualization of spatial patterns and clusters of marginality across the studied area.To assess territorial marginality, Corrado and Scorza (2022) employed a machine learning-based approach.They utilized machine learning techniques to identify the typical characteristics of marginal areas in the Basilicata mountainous region.Subsequently, they applied the trained model to reclassify national territory.This approach enables the identification and classification of marginal areas based on their distinctive characteristics, offering valuable insights for targeted interventions and policy-making.The main aim of this research is to use GIS and exploratory factor analysis to create a methodology that would determine the degree of marginality of settlements in Međimurje based on the created marginality index (MIMaNa), which is itself based on specific indicators.The marginality index was obtained by combining six individual factors and assigning a weighted value to each of them based on the total variance of the individual factor in the total variance of the data set.

Study area
The research area is the County of Međimurje, and the spatial level of the research is settlement.According to the 2011 Census of Population, Households and Dwellings, a total of 113,804 inhabitants lived in Međimurje County, meaning 2.7% of the total population of Croatia.With its area of 729.22 km 2 , Međimurje is the smallest county and occupies only 1.3% of the total area of Croatia.However, it is the most densely populated county with 156.1 inhabitants per square kilometer.Data from the preliminary results of the 2021 Census show that in 10 years, Međimurje lost 7,941 inhabitants (almost 7%).The local self-government units of Čakovec and Orehovica are the only ones that recorded a slight increase in population (Croatian Bureau of Statistics, 2021).Two Roma settlements with an exclusively Roma population, Parag and Piškorovec, also recorded a significant increase in population.According to the natural-geographic features, two

Research methodology
In addition to the application of GIS, exploratory factor analysis was also used in the research.Using these analyses and selected variables, a methodology was created to identify and analyze geographic marginality.After the results were obtained, six factors were named and interpreted, which are shown on the thematic maps.Based on the obtained factors and factor scores, synthetic indices of the marginality of the settlements in Međimurje (MIMaNa) were created.The complete diagram of the methodology used in this research consists of 10 steps (Fig. 2).
The main aim of exploratory factor analysis is to obtain a relatively small number of latent variables that account for the largest amount of association in the set of observed variables.The method is used when there is no predefined idea regarding structure or dimension in the set of variables (Fulgosi, 1988;Tabachnick and Fidell, 2007;Hair et al., 2014).In addition to the general main goal, the research also has the following specific goals: • to create a complex image of the structure of variables, each of which represents a separate correlation with a specific significance.To show, analyze and identify the possible existence of geographical marginality of the settlements in Međimurje more clearly by grouping variables.
• to reduce the number of initial variables in order to interpret the results more clearly, so that the reduced results can be more easily put to use in further statistical analyses.
• to determine how many factors are needed for the best explanation of common characteristics among a set of variables, via factor analysis.
Free open source programs were used in the re-
A total of 60 potential variables were extracted from the collected data.After the statistical and cartographic analysis and assessment of the appropriateness of the data, the variables were divided into 5 dimensions.
After the exploratory factor analysis, 30 final variables were selected.A detailed description of the variables is described in Table 1.
Variables analyzed by factor analysis must be quantitative and form a suitable homogeneous set.The first step is to visually inspect the data correlations and identify those that are statistically significant.The presence of significant deviations can significantly affect the results of the exploratory factor analysis and the comprehensible interpretation of the obtained results.Deviations were checked using various procedures in JASP, such as: descriptive statistics, histogram and normal QQ-plot.Extreme values were observed for certain variables (vital index, number of inhabitants per km 2 , number of business entities, aging index), all of which refer to settlements with a majority Roma population (Parag and Piškorovec), so these settlements were omitted from further analysis as this would not affect the correlation of the data and the distortion of the factor values.The Keiser-Meyer-Olkin (KMO) measure of sampling adequacy (Kaiser and Rice, 1974) and Bartlett's test of sphericity (Bartlett, 1954) were used to detect multi-collinearity.All variables that had a KMO value of less than 0.5 were omitted from further analysis.The average KMO measure for all variables in this research is 0.730.Given that the KMO measure is greater than 0.7, the value is satisfactory to continue with the factor analysis.Bartlett's sphericity test showed that the p value is approximately equal to 0 (p<0.001),which means that a significant correlation was achieved between the selected variables.The results of the measures used show that the selected set of 30 variables is suitable for exploratory factor analysis.marginalnost nekoga područja jedan je od najvažnijih koraka pri kojem treba biti vrlo oprezan jer on usmjerava samo istraživanje i dobiveni rezultati uvelike ovise o njima.Međutim, kao što je već naznačeno, šarolikost i različitost varijabli i indikatora ne bi u istraživanjima trebalo sputavati i ograničavati, već otvoriti nove perspektive u istraživanju marginalnosti.Jedna je od specifičnost ovoga istraživanja da se u ovom radu koriste i mikropodatci za najnižu prostornu razinu, razinu naselja, od kojih su neki u ovakvim istraživanjima upotrijebljeni prvi put.Iz prikupljenih podataka izdvojeno je 60 potencijalnih varijabla.Nakon statističke i kartografske analize te procjene prikladnosti podataka varijable su podijeljene u pet dimenzija.Nakon eksplorativne faktorske analize izdvojeno je 30 konačnih varijabla.Detaljan opis varijabli opisan je u tablici 1.

F_NAD_VIS
The elevation of settlements / nadmorska visina naselja F_UDALJ Distance to the regional centre / udaljenost od regionalnoga središta F_CIJENA The price of travel to the regional centre / cijena putovanja do regionalnoga središta F_MIN Minutes of travel to the regional centre / minuta putovanja do regionalnoga središta F_GRADJ Share of construction area in the total area of the settlement / udio građevinskoga područja u ukupnoj površini naselja OB_VS_19+ Share of the population with higher education / udio visokoobrazovanoga stanovništva

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Factor extraction is a general term for the process of reducing the number of dimensions that are analyzed using variables in a data set to a smaller number of factors.Factor extraction involves determining the number of factors that can be used to best represent the interrelationships of a set of variables.In this research, the method of 0 (p<0.001),što znači da je postignuta značajna korelacija između odabranih varijabla.Rezultati korištenih mjera pokazuju da je odabrani skup od 30 varijabli prikladan za eksplorativnu faktorsku analizu.
The method of parallel analysis (Horn, 1965) in the JASP program suggested a solution with six factors (Fig. 3).Some authors believe that Horn's method is one of the most accurate and has the least variability and sensitivity for determining the number of factors (Humphreys and Montanelli, 1975;Glorfeld, 1995;Ledesma and Valero-Mora, 2007); with regard to the authors' subjective assessment, it was decided that such a solution would be kept for further analysis.Six isolated factors accounted for 66,0% of the total data variance, out of which the first factor accounted for 13,5%, the second for 12,8%, the third for 10,6%, the fourth for 10,3%, the fifth for 10,0%, and the sixth factor for 8,8% (Tab.2).
After selecting the number of factors and calculating the factor loading matrix, the unrotated factor matrix for significant factor loadings was examined.Unrotated solutions extract factors according to their order of importance (Tabachnick and Fidell, 2007;Hair et al., 2014).If the matrix does not have a completely clear set of factor loadings, meaning that the matrix has significant cross-loadings and the loadings are not maximized on only one factor, in order to improve the interpretation of the factor loadings, matrix rotation is used.The rotated factor matrix is crucial for understanding and interpreting the results of the analysis.Rotation is an attempt to reduce the number of basic indicators that have a high load on the same factor.Using rotation, the transformation of the factor axes is achieved.This makes it possible to simplify the structure, in which each indicator is loaded exclusively on one of the retained factors, which improves the comprehensibility of the factors.The ultimate effect of rotating the factor matrix, although the rotation cannot change the basic features of the analysis, is to redistribute the variance values to achieve a simpler, more theoretically meaningful factorial pattern, and to make the variables that are most useful in naming and interpreting each factor more easily identifiable.In this research, orthogonal Varimax rotation was used, which makes it so that the final factors are at right angles compared to each other.As a result of this rotation, it can be assumed that the information explained by one factor is independent of the information explained by other factors.The results of exploratory factor analysis with Varimax orthogonal rotation and the method of Zwick i Velicer, 1986;Glorfeld, 1995;Ledesma i Valero-Mora, 2007) i s obzirom na subjektivnu procjenu autora, odlučeno je da će se takvo rješenje zadržati u daljnjoj analizi.Šest izdvojenih faktora čini 66,0 % ukupne varijance podataka, od čega prvi faktor čini 13,5 %, drugi 12,8 %, treći 10,6 %, četvrti 10,3 %, peti 10,0 % i šesti faktor 8,8 % (tab.2).
Factor scores are composite scores calculated for each observation of each factor extracted via factor analysis (Thompson, 2004).Hair et al., (2014) concluded that factor scores are one of three ways to use obtained results in further analyses.In this research, from a conceptual point of view, the factor scores rep-izdvojenog u faktorskoj analizi (Thompson, 2004).Hair i dr. ( 2014) zaključuju da su faktorski bodovi jedan od triju načina za korištenje dobivenih rezultata u daljnjim analizama.U ovom istraživanju, konceptualno gledajući, faktorski bodovi predstavljaju stupanj u kojem svako međimursko naselje postiže svoju ocjenu prema opterećenjima faktora.Faktorski bodovi resent the degree to which each settlement in Međimurje achieves its rating according to factor loadings.Factor scores were calculated using the regression method.This method defines factor scores as the product of the factor matrix of variable loadings with the inverse of the covariance matrix of the variables and the data vector (Thomson, 1935;Thurstone, 1935).Before naming and interpreting the factors, the reliability coefficient was analyzed.This coefficient evaluates the internal consistency of each factor, with the most commonly-used method being Cronbach's alpha (Cronbach, 1951;Peter, 1979).In general, the agreed-upon lower limit for Cronbach's alpha values, which indicates sufficient internal consistency, is 0.70-although this can be reduced to 0.60 in exploratory analyses (Robinson et al., 1991).In this research, the Cronbach alpha value was determined for each factor separately.The fourth factor had the highest value (0.914), while the second factor had a value below the recommended level (0.502).It is difficult to determine the reason for the low value of the coefficient of this factor, but considering the significance of the variables used, the factor will be retained for further analysis.The other four factors are around the recommended value of 0.7.
In the process of naming and interpreting the factors, significant loads on the variables were analyzed.
Variables with higher loadings have a greater influence on the explanation of the factors.Of course, in such an interpretation and naming of factors, the sign of the load must also be considered.In this research, loads greater than 0.4 were selected.Based on the results of the exploratory factor analysis, names were determined for the six obtained factors.The process of naming and interpreting factors is largely based on the subjective opinion of the researcher conducting the factor analysis, so it is possible that different researchers would assign different names to the same factor and interpret the same results differently.In any case, the tendency is to assign as logical a name as possible, in accordance with the selected variables.Regarding the correlation diagram of factors and variables, we see positive and negative correlations of variables with the indicated values in relation to a certain factor.Positive correlations of factors with variables are shown in green, negative correlations in red, and the thickness of the line determines the size of the correlation.Positive and negative correlations between the factors themselves are shown in the same way (Fig. 4).

Result and discussion
The first factor that explained the largest share of the total variance (13.5%) had significant positive correlations with all six variables that the factor consists of.These are population density per km 2 , number of inhabitants, number of business entities and number of active trades (Tab.4).The number of inhabitants and population density can indicate the attractiveness and importance of a geographical area or specific settlement, while a lower number of inhabitants and a lower density suggest unattractiveness, the presence of poverty, and/or neglect in a given area.The number of active business entities and registered trades is an indicator of the development of entrepreneurship in a given area.There is also a positive correlation with the variables that indicate the share of the construction area in the total area of the settlement and road density.
The share of the construction area in relation to the total area of the settlement is an important indicator regarding the possible development and quality use of space.The variable representing road density is correlated with this spatial indicator, meaning the share of the area of certain types of roads (state, county, local and unclassified) in relation to the total area of the settlement.The development of the road network is closely related to the area's economic development.According to Malić (1971), the quality of transport connections has an influence on the formation of transformational characteristics of a settlement.Transport connections are related to the size of the settlement.Better transport connections contribute to changes in traditional settlements, and promote demographic and spatial expansion.All these indicators point to potential for dynamic development and quality use of space.Based on the six selected variables, the first factor was named Spatial concentration and economic dynamics.
If the geographical distribution of settlements of the first factor is considered, in addition to the settlements of Čakovec, Prelog and Mursko Središće, the area around the regional center (Čakovec) also stands out significantly.These are the settlements of Savska Ves, Strahoninec, Nedelišće, Dunjkovec, Šenkovec, Mihovljan, Pribislavec, and Ivanovec.These settlements have the largest number of registered trades and business entities, a larger number of in-
Ako razmotrimo geografski razmještaj naselja prvoga faktora, uz područja naselja Čakovca, Preloga i Murskog Središća, značajno odskače i područje oko regionalnoga središta -Čakovca.To su naselja Savska Ves, Strahoninec, Nedelišće, Dunjkovec, Šenkovec, Mihovljan, Pribislavec i Ivanovec.Ta naselja imaju najveći broj registriranih obrta i poslovnih subjekata, veći broj stanovnika i veći udio građevinskoga zemljišta s intenzivnom izgradnjom obiteljskih kuća i poslovnih zona.Na  habitants and a larger share of construction land with intensive construction of family houses and business zones.In the eastern part of Međimurje, the settlements of Donja Dubrava and Kotoriba in stand out, which have been known throughout their history for numerous trades.The lowest values of this factor were observed in the western part of Međimurje along the border with Slovenia, in the southwestern part along the border with Varaždin County, in the section from the settlement of Otok to the settlement of Pušćine, and in the northeastern part along the border with Hungary (Fig. 5).These are settlements with a small share of construction land, almost no registered trades and business entities, a small number of inhabitants and are therefore unattractive for the construction of both family houses and business zones.From the factor correlation diagram, it can be seen that this factor, quite understandably, has a positive correlation with the third factor, which is characterized by higher education and economic diversification, and a negative correlation with the fifth factor, which represents settlements with traditional extensive agricultural production.
The second factor explains 12.8% of the total variance, also via six variables, three of which are highly positively correlated with variables indicating population aging: the aging index, the share of retired persons in the total population, and the share of the population aged 60 years and older.Accordingly, this factor has negative correlations with variables that show the opposite meaning and are also related to population aging: the share of the population aged 0 to19 in the total population, the vital index and intercensal change in the number of inhabitants of the settlement in the 2001-2011 period.(Tab.5).The second factor, with regard to the aforementioned variables, is called Demographic dynamics and population aging.
This factor shows all the complexity of the phenomenon of marginality and corresponds with the research of Marić et al. (2020), in which the authors identified Štrigova itself as the most depressed settlement, and settlements with a significant Roma population as the most promising settlements in terms of demographics.Šlezak and Belić (2019) also observed a dichotomy formed by the intensive growth of the birth rate and the extremely young age structure of the Roma population and, on the other hand, negative natural change and the increasingly unfavorable age structure of the majority population.The authors concluded that the aforementioned changes will certainly significantly alter the ethnic structure of Međimurje County in the long term and consequently change the regional identity of the northernmost part of Croatia.
The data confirm the thesis that researchers must be familiar with the area of research because certain factors, when calculating the index, can significantly distort the results due to the extremely large values of certain variables.Considering the variables that determine this factor and with the change in the sign of the variable loading, we could easily name the second factor Settlements with extremely favorable demographic resources.Therefore, this factor was used in the construction of the Međimurje Index of marginalization of settlements (MIMaNa) in such a way that two indices were created: one with a positive sign (Index I) and the other with a negative sign (Index II) value of the factor, in accordance with the conclusion of Horvat and Toskić (2017) of how, due to the multidimensionality of the phenomenon of marginalization, such a situation can occur, i.e. something that is marginal in one system, but not in another.
The third factor with a share of 10.6% of the total variance contains five variables, two of which are highly correlated and indicate the existence of a highly educated population: the share of the population over the age of 15 enrolled in higher education institutions, and the share of the highly educated population over the age of 19; as well as two variables with slightly lower correlation values that also indicate a higher share of highly educated population: the share of households that use the Internet and the share of total employees in the quaternary sector (education, science, health and culture).The only negative correlation, which is quite understandable for this factor, is with the variable share of the population older than 15 without education and with incomplete primary school (Tab.6).With regard to the aforementioned variables, the factor was named Education and economic diversification.The spatial distribution of settlements included in this factor is a little more difficult to interpret.Čakovec, Prelog and Mursko Središće and the settlements of the Čakovec ring stand out, as well as several spatially-scattered settlements: Donji Kraljevec, Cirkovljan, Šenkovec, Vrhovljan (Fig. 7).The settlements of upper Međimurje, as well as settlements with a majority Roma population, have the lowest values.This factor differentiates set- Četvrti faktor objašnjava 10,3 % ukupne varijance.Faktor čine samo tri varijable s vrlo velikom pozitivnom korelacijom koje predstavljaju geografska obilježja naselja prema dostupnosti središnjih funkcija: udaljenosti od regionalnoga središta -Čakovca, cijeni putovanja do regionalnoga središta izračunatoj prema cijeni karte za autobus te potrebnom vremenu izraženom u minutama potrebnim za putovanje do regionalnoga središta (tab.7).S obzirom na navedene varijable ovaj smo faktor nazvali dostupnost središnjih funkcija.Pri ovom se faktoru pojavila dvojba koja je objašnjena u procjeni prikladnosti podataka, a s obzirom na to da je u pojedinim varijantama izrade faktorske matrice korištenjem različitih metoda i različitih metoda rotacije korelacija tih varijabla bila viša od 0.90, što upućuje na to da spomenute varijable mjere vrlo sličan fenomen.Upotreba suvišnih stavaka može pojačati korelacije pojmova pogrešaka pa se istraživačima savjetuje da minimaliziraju broj suvišnih pokazatelja (Rossiter, 2002;Drolet i Morrison, 2001;Hayduk i Littvay, 2012).Usprkos tomu odlučeno je da se ovaj faktor zadrži s obzirom na to da su varijable korištene u njemu karakterističan primjer prisutnosti geografske marginalnosti za naselja koja su najudaljenija od regionalnoga središta u kojem se nalaze sadržaji kojih nema u drugim dijelovima promatranoga područja.Prostorno gledajući, vrijednosti faktorskih bodova ovoga faktora sasvim zorno prikazuju centralni smještaj Čakovca kao regionalnoga središta Međimurja, potom slijedi koncentrični krug naselja koja su najbliža regionalnom središtu.Prostorno najudaljenija naselja na krajnjem istoč-tlements with a highly-educated and student population.It can be seen that some smaller settlements significantly stand out, which can easily be explained by the relatively small number of inhabitants of them, which then results in a relatively high proportion of highly-educated people, even though it is a smaller absolute number.The same can be said for the share of households that use the Internet.Thus, the village of Žabnik, with only 372 inhabitants, has 25 inhabitants enrolled in college.From the factor correlation diagram, it can be seen that this factor has a positive correlation with the first factor, and a negative correlation with the fourth, fifth and sixth factors.Individually, the settlements of Kuršanec, Gornji Kraljevec, Toplice Sveti Martin, Badličan and Celine have the lowest factor score values, while the settlements of Žabnik, Šenkovec, Vrhovljan, Donji Kraljevec and Cirkovljan have the highest.
The fourth factor explains 10.3% of the total variance.The factor consists of only three variables with a very high positive correlation, which represent the geographical features of the settlement according to the availability of central functions: the distance from the regional center (Čakovec), price of travel to the regional center calculated according to the price of a bus ticket, and the required time expressed in minutes that is needed to travel to the regional center (Tab.7).Considering the aforementioned variables, this factor was named Availability of central functions.A dilemma arose from this factor, one that was explained when assessing the appropriateness of the data; given that in some variants of creating the factor matrix using different methods and different methods of rotation, the correlation of these variables was higher than 0.90, it is indicated that these variables measure a very similar phenomenon.The use of redundant items can increase correlations of error terms, so it is advisable to minimize the number of non-essential and/or redundant indicators (Rossiter, 2002;Drolet and Morrison, 2001;Hayduk and Littvay, 2012).Despite this, it was decided to keep this factor considering that the variables used in it represent a characteristic example of the presence of geographical marginality for the settlements that are farthest from the regional center where there are facilities that are not found in other parts of the observed area.Spatially speaking, the factor score values for this factor clearly show the central location of Čakovec as the regional center of Međi-HRVATSKI GEOGRAFSKI GLASNIK 85/2, 5−45 (2023.)nom dijelu Međimurja i krajnjem sjeverozapadnom dijelu Gornjeg Međimurja očekivano imaju najmanje faktorske vrijednosti (sl.8).Pojedinačno gledajući, najmanju vrijednost faktorskih bodova imaju naselja Kotoriba, Donja Dubrava, Donji Vidovec, Sveta Marija i Čestijanec, dok najveće murje, followed by a concentric circle of settlements that are closest to the regional center.The spatially most distant settlements in the extreme eastern part of Međimurje and the extreme northwestern part of Upper Međimurje accordingly have the lowest factor values (Fig. 8).Looking at them individually, the set- Peti faktor objašnjava 10,0 % ukupne varijance.Faktor čini pet varijabli koje predstavljaju način korištenja zemljišta s obzirom na poljoprivrednu proizvodnju.Faktor ima pozitivnu korelaciju s većinom varijabli kojima se objašnjavaju reljefne osobine naselja te karakteristike poljoprivredne proizvodnje: nadmorska visina naselja, udio vinograda i voćnjaka u ukupnom poljoprivrednom zemljištu naselja te udio šumskoga zemljišta u ukupnom zemljištu naselja (tab.8).Sasvim razumljivo, jedina negativna korelacija jest varijabla koja upućuje na udio oranica u ukupnom poljoprivrednom zemljištu naselja pa ta varijabla značajno predstavlja naselja Donjeg Međimurja.S obzirom na reljefne osobine i izražen aspekt poljoprivredne proizvodnje kroz karakteristične kulture koje se uzgajaju na višim i nižim područjima, ovaj smo faktor nazvali tradicionalna ekstenzivna poljoprivredna proizvodnja.Gledajući prostorni obrazac ovoga faktora (sl.9), potpuno se očekivano vidi podjela na Gornje Međimurje (brežuljkasto područje s karakterističnom proizvodnjom vina, voćnjaci) i Donje Međimurje s karakterističnom poljoprivrednom proizvodnjom kultura karakterističnih za nizinska područja (krumpir, kukuruz, pšenica, ječam).Ovaj faktor s obzirom na prisutne varijable kod interpretacije rezultata i formiranja indeksa MIMaNa usko povezujemo sa šestim faktorom koji predstavlja poljoprivredu te smatramo da faktor ne utječe na marginalnost pa ostavljamo neutralan predznak.Peti faktor ima negativnu korelaciju s prvim i trećim faktorom.
The fifth factor explains 10.0% of the total variance.The factor consists of five variables that represent the way land is used with regard to agricultural production.The factor has a positive correlation with most of the variables that explain the terrain features of the settlement and the characteristics of agricultural production: the altitude of the settlement, the share of vineyards and orchards in the total agricultural land of the settlement, and the share of forest land in the total area of the settlement (Tab.8).Quite understandably, the only negative correlation is represented by the variable that indicates the share of arable land in the total agricultural land of the settlement, so this variable significantly represents the settlements of Lower Međimurje.Considering the terrain features and the pronounced aspect of agricultural production of characteristic crops grown in higher and lower areas, this factor was named Traditional extensive agricultural production.Looking at the spatial pattern of this factor (Fig. 9), the division into Upper Međimurje (a hilly area with characteristic production of wine and orchards) and Lower Međimurje with characteristic agricultural production of crops typical for lowland areas (potatoes, corn, wheat, barley) can be seen as expected.Considering the variables that are present, when interpreting the results and forming the MIMaNa index, this factor is closely associated with the sixth factor representing agriculture, and it does not seem to affect marginality, so it bears a neutral sign.Also, the factor has a negative correlation with the first and third factors.

Definiranje međimurskog indeksa marginalnosti naselja (MIMaNa)
Kao što je u teorijskom dijelu predstavljeno, faktorski bodovi kao rezultati eksplorativne faktorske analize koristit će se za grupiranje pojedinačnih pokazatelja da bi se formirao indeks koji sadrži što je više moguće zajedničkih podataka za pojedine pokazatelje.Dobiveni faktorski bodovi korišteni su za izradu međimurskog indeksa marginalnosti naselja (MIMaNa) kojim se prikazuju i objašnjavaju prostorni obrasci koji upućuju na moguće postojanje geografske marginalnosti te je na osnovi toga moguće izračunati stupnjevitost geografske marginalnosti.Konstruiranje indeksa MIMaNa izračunato portance of agriculture, which employs a significant share of the population in Međimurje.However, recently the question of economic profitability and productivity of traditional family farms has been raised.Negative correlations in this factor are shown by the following variables: the share of employed daily migrants out of the total employed in the settlement, the labor contingent, and the share of employees in the secondary sector (the share of employees in industry, construction, mining, energy and manufacturing trades).The labor contingent variable with a negative sign confirms and points to family farms that are still linked to the elderly population.All variables are related to agricultural activity; therefore, this factor was named Stationary work contingent focused on primary activities.
The factor is quite closely related to the previous factor, which divides the area of Međimurje with regard to traditional agricultural production conditioned by geographical features.According to the cartographic and statistical analysis, the settlements in the far eastern part of Međimurje and settlements with intensive agricultural production (Fig. 10) such as Belica, Orehovica, Goričan, Donji Kraljevec, Gardinovec (intensive production of potatoes, vegetables and fruit) stand out with positive factor scores.Individually, the settlements of Gornji Zebanec, Zaveščak, Lapšina, Marof and Celine have the lowest factor score values, while the settlements of Orehovica, Prhovec, Vugrišinec, Vukanovec, Čakovec and Tupkovec have the highest.
Udio varijance izračunava se na sljedeći način: Na primjer: Na osnovi dobivenih težina za svaki pojedinačni faktor i faktorskih bodova za svako pojedino naselje za svaki faktor indeks marginalnosti međimurskih naselja MIMaNa računa se prema sljedećoj formuli: plication of the approach explained in Nicoletti et al., 2000;OECD, 2008 andDharmaratne andAttygalle, 2018.Based on this approach and the obtained results, it was observed that there are six mutually complex indicators with weights for each factor.In Table 2, it can be seen how the share of the total variance explained by each of the factors is different.The six-factor model with Varimax rotation of the factor loading matrix explains 66.0% of the total variance, of which the first factor explains 13.5%, the second factor 12.8%, the third factor 10.6%, the fourth factor 10.3%, the fifth factor 10.0% and the last factor 8.8%.From this, it can be concluded that the importance of individual factors that measure the overall marginality of Međimurje settlements is not the same.Therefore, when combining these six indicators into one, each of them was weighted based on the share of the variance of an individual factor in the total variance (Tab.10).
The share of variance is calculated as follows: For j = 1, 2…6.
Također, u skladu s raspravom vezanom uz imenovanje i interpretaciju dobivenih faktora, a prije interpretiranja dobivenih sintetičkih indeksa marginalnosti, potrebno je naglasiti nekoliko važnih činjenica.Čakovec kao regionalno središte odskače vrijednošću faktorskih bodova u svih šest faktora i u obama konstruiranim indeksima geografske marginalizacije.Drugi faktor, demografska dinamika i starenje stanovništva, ima vrlo velik utjecaj na konačne rezultate indeksa marginalnosti.Naime, naselja sa značajnijim udjelom romske populacije, osim naselja Parag i Piškorovec koja smo izostavili iz analize, imaju karakteristike izrazito vitalnoga prostora.U stvarnosti je romska populacija u tim naseljima prostorno segregirana (Šlezak, 2010) i takva naselja nedvojbeno upućuju na marginalizirano područje.Četvrti faktor, dostupnost središnjih funkcija, ima vrlo velik utjecaj na rubna naselja, posebice rubna naselja istočnoga dijela Međimurja, upućujući na postojanje prometne marginalnosti pa je predznak faktora u obama indeksima promijenjen.Treći faktor s varijablama povezanim uz For settlement A (Badličan) = 0.2045x(result of factor scores of factor 1, settlement A) + 0.1939x(result of factor scores of factor 2, settlement A) + 0.1606x(result of factor scores of factor 3, settlement A) + 0.1561x(result of factor scores of factor 4, settlement A) + 0.1515x(result of factor scores of factor 5, settlement A) + 0.1333x(result of factor scores of factor 6, settlement A) = -0.2408 The direction of influence of each individual factor was not determined in advance in this research, considering the fact that a single factor can significantly increase or decrease the index of geographical marginality of the settlement, so it was necessary to adjust the sign.Here, in order to obtain a satisfactory and comprehensible structure, researchers should use their subjective judgment and have good familiarity with the subject in order to obtain answers to the research questions posed without losing too much data.Furthermore, in accordance with the discussion related to the naming and interpretation of the obtained factors, and before interpreting the obtained synthetic indexes of marginality, it is necessary to emphasize several important facts.Čakovec as a regional centre stands out with its factor score values in all six factors and in both constructed indexes of geographic marginalization.Another factor, demographic dynamics and population aging, has a very large influence on the final results of the marginality index.The settlements with a significant share of the Roma population (except for the settlements of Parag and Piškorovec, which we omitted from the analysis) have the characteristics of an extremely vital space.This is deceptive, however, as the Roma population is spatially segregated in these settlements (Šlezak, 2010), strongly indicating that these are marginalized areas.Furthermore, the fourth factor, the availability of central functions, has a very large influence on peripheral settlements, particularly those in the eastern part of Međimurje.The factor indicates the existence of traffic marginality, so the sign of the factor in both indices has been changed.obrazovanje ima velik utjecaj u izračunu faktorskih bodova za pojedina naselja s manjim brojem stanovnika, a većim brojem studenata.Vrijednosti petoga faktora koji dijeli međimurska naselja na osnovi reljefnih obilježja pri izračunu indeksa obračunat je kao apsolutna vrijednost bez predznaka s obzirom na to da prema mišljenju autora ovaj faktor ne govori o mogućoj marginalnosti naselja.
The third factor with variables related to education has a great influence in the calculation of factor scores for certain settlements with a smaller number of inhabitants and a larger number of students.
The values of the fifth factor that divides Međimurje settlements on the basis of terrain features were calculated as an absolute value without a sign when calculating the index, given that, according to the authors, this factor does not affect marginality.
The values of the factor scores1 from which the marginality indices were constructed were standardized and grouped into 5 classes using the Jenks optimization method (minimizing the variance within the class).A descriptive feature was added to each class obtained in this way to ensure easier interpretation and understanding.Two choropleth maps show two marginality indices of the settlements of Međimurje (MIMaNa), where the second factor (demographic dynamics and population aging) is interpreted differently--the sign of which has been changed, given that the demographic dynamics of some (predominantly Roma) settlements have been evaluated differently.
Pojedinačno gledajući, u naselja izrazite i umjerene marginalnosti spadaju: Toplice Sveti Martin na Muri, Marof, Lapšina, Jalšovec, Opo-as Parag and Piškorovec and settlements that represent ethnically homogeneous parts of larger administrative settlements with a Croatian population.As already stated, the settlements of Parag and Piškorovec were omitted from the factor analysis after data cleaning, and due to the observed extreme values of certain variables (for example, the vital index is an incredible 1586.7).In their research, Šućur (2000) pointed out the marginality of these two settlements in the spatial sense, in addition to the economic and sociocultural sphere of life of the Roma population.
• Settlements along the border with Hungary in a line from the settlement of Domašinec to the settlement of Čestijanec in the very north of the county.The only settlement with a higher value of the index is Mursko Središće and the settlements of Žabnik, Miklavec, Vrhovljan and Brezovec due to the aforementioned reason of higher values for the education factor, while the settlements of Domašinec and Podturen have a larger share of Roma population.
• A series of settlements in the south-southeast stretching from the Otok to Sveti Urban.Particularly, the settlements of Pušćine and Gornji Mihaljevec, which are located on important roads towards Varaždin and Čakovec, jump out with higher index values.
variability and range of results (from an extremely depressed to an extremely non-depressed area), which indicated the impossibility of adopting uniform measures and policies.

Conclusion
In this research, a quantitative approach with the application of GIS and exploratory factor analysis was applied to create a methodology that determined the degree of marginality of the settlements in Međimurje on the basis of a marginality index (MIMaNa) based on specific indicators.The MIMaNa index was obtained by combining six individual factors and assigning a weighted value to each of them, based on the share of the variance of the individual factor in the total variance of the data set.The multidimensional composite index gives a better picture of the economic, social, transport and related structural conditions in the settlements.The selection of included variables in the research for factor analysis can significantly affect the marginality index obtained.Moreover, the direction of influence of each individual factor can significantly increase or decrease the marginality index.From the obtained MIMaNA index, it is evident that geographical position is very important in the devel- Naselja koja su bliža regionalnom središtu spadaju u važnija razvojna i nemarginalna naselja.To su naselja s većim brojem poslovnih subjekata i aktivnih obrta, većim udjelom građevinskoga sektora i većom cestovnom gustoćom, što upućuje na potencijalni dinamičniji razvoj naselja i kvalitetnije korištenje prostora.S druge strane, manja, periferna naselja, posebice naselja Gornjeg Međimurja imaju manje vrijednosti indeksa marginalnosti, obilježava ih viši stupanj ostarjelosti, slabija prometna povezanost, slaba ekonomska aktivnost te nepostojanje ikakvih središnjih funkcija te spadaju u naselja izrazite ili umjerene marginalnosti.Iz perspektive Hrvatske danas Međimurje možda ne bi trebalo smatrati marginalnim područjem.Tijekom 20. stoljeća Međimurje je imalo obilježja marginalnoga područja zbog svoje periferne i granične lokacije, što je nepovoljno utjecalo na njegov društveni i gospodarski razvoj.Ulaskom Hrvatske u EU i zahvaljujući povezivanju regija unutar EU-a, geografski položaj Međimurja gubi ove negativne značajke i stječe značajke ulaznih vrata na glavnoj hrvatskoj transverzali prometne rute.Međutim, ovaj rad ističe kompleksnost teme marginalnosti.Čak i uz sofisticirane statističke analize izazovno je u potpunosti obuhvatiti sve nijanse marginalnosti.Iako kompleksni indeksi mogu pružiti neke uvide, oni ipak nude nepotpunu sliku.Marginalnost je složen koncept u kojem su različiti faktori međusobno povezani, ali i jedinstveni.Važno je napomenuti da je subjektivno iskustvo marginalnosti, uključujući samopredodžbu pojedinaca i način na koji ga drugi percipiraju, bitan aspekt koji često nije obuhvaćen mjerljivim podatcima.Marginalnost nije samo objektivna stvarnost, već i subjektivno iskustvo, posebno na mikroregionalnoj razini.U budućim istraživanjima marginalnosti preporučuje se uključivanje kvalitativnih metoda koje uzimaju u obzir percepciju marginalnosti uz kvantifikaciju širokoga spektra statističkih pokazatelja.Ova kombinacija omogućuje dublje razumijevanje fenomena marginalnosti i doprinosi sveobuhvatnijem pristupu proučavanju marginaliziranih područja.Kvalitativne metode poput intervjua ili fokusnih grupa omogućuju da se čuju glasovi marginaliziranih skupina i istraže njihove opment of the settlement.Settlements that are closer to the regional centre belong to more significantly developing and non-marginal settlements.These are settlements with a larger number of business entities and active trades, a larger share of construction area and a higher road density, which indicates more dynamic development of the settlement and better use of space.On the other hand, smaller peripheral settlements, especially the settlements of Upper Međimurje, have lower marginality index values, and are characterized by a higher aging degree, weaker traffic connections, weak economic activity and the absence of central functions.Therefore, they fall under settlements of extreme or moderate marginality.From the perspective of Croatia, Međimurje may not be considered a marginal region at the time of writing.During the 20 th century, Međimurje had the characteristics of a marginal region due to its peripheral and border location, which adversely affected its social and economic development.With the entry of Croatia into the EU and thanks to the interconnection of regions within the EU, the geographical position of Međumurje is losing these negative characteristics and acquiring the characteristics of an entrance gateway on the main Croatian transversal transit route.This paper highlights the complexity of the subject of marginality.Even with sophisticated statistical analyses, it is challenging to fully capture the intricacies of marginality.While complex indices can provide some insights, they offer an incomplete picture.Marginality is a multifaceted concept where various factors are interconnected yet unique.It is important to note that the subjective perception of marginality, including individuals' self-image and how others perceive it, is a significant aspect that is often not captured in measurable data.Marginality is not solely an objective reality but also a subjective experience, especially at the micro-regional level.In future research on marginality, qualitative methods that capture the perception of marginality should be used alongside the quantification of a wide range of statistical indicators.This combination allows for a deeper understanding of the phenomenon of marginality and contributes to a more comprehensive approach to studying marginalized populations.Qualitative methods, such as interviews or focus groups, enable the voices of marginalized groups to be heard and the exploration of perceptions, experiences, and contextual factors that percepcije, iskustva i kontekstualni čimbenici koji doprinose marginalizaciji.Ova dimenzija percepcije marginalnosti pruža dodatne uvide i informacije koje se ne mogu kvantitativno prikupiti, nadopunjujući kvantitativne podatke i pružajući sveobuhvatniju sliku marginalnosti.Rezultati istraživanja potvrđuju postojanje bitnih razlika u stupnju marginalnosti međimurskih naselja što upućuje na potrebu donošenja ravnomjernijih razvojnih mjera i politika pri planiranju budućega razvoja međimurskih naselja.Metodologija za identificiranje i analizu geografske marginalnosti i dobiveni rezultati iz ovoga istraživanja još jednom su pokazali i potvrdili svu slojevitost i multidisciplinarnost fenomena marginalnosti te otvorili neke nove spoznaje i dali povod za daljnja istraživanja.contribute to marginalization.This dimension of perceiving marginality provides additional insight and information that cannot be captured quantitatively, complementing the quantitative data and providing a more comprehensive picture of marginality.The results of the research confirm the existence of significant variations in the degree of marginality of the settlements in Međimurje, which indicates the need to adopt more balanced development measures and policies when planning the future development of settlements in Međimurje.The developed methodology for identifying and analysing geographic marginality and the results obtained from this research showed and confirmed all the layers and multidisciplinarity of the phenomenon of marginality and provided new insights, laying out a potential path for further research.