The Application Of Local Indicators For Categorical Data (LICD) In The Spatial Analysis Of Economic Development

Transcription

1 Comparatve Ecoomc Research, Volume 7, Number 4, /cer MICHAŁ B. PIETRZAK *, JUSTYNA WILK **, ROGER S. BIVAND ***, TOMASZ KOSSOWSKI **** The Applcato Of Local Idcators For Categorcal Data (LICD) I The Spatal Aalyss Of Ecoomc Developmet Abstract The paper makes a attempt to apply local dcators for categorcal data (LICD) the spatal aalyss of ecoomc developmet. The frst part dscusses the tests whch exame spatal autocorrelato for categorcal data. The secod part presets a two-stage emprcal study coverg 66 Polsh NUTS 3 regos. Frstly, we detfy classes of regos presetg dfferet ecoomc developmet levels usg taxoomc methods of multvarate data aalyss. Secodly, we apply a jo-cout test to exame spatal depedeces betwee regos. It exames the tedecy to form the spatal clusters. The global test dcates geeral spatal teractos betwee regos, whle local tests gve detaled results separately for each rego. The global test detects spatal clusterg of ecoomcally poor regos but s statstcally sgfcat as regards well-developed regos. Thus, the local tests are also appled. They dcate the occurrece of fve spatal clusters ad three outlers Polad. There are three clusters of wealth. Ther developmet s based o a dffuso mpact of regoal ecoomc cetres. The areas of easter * Ph.D., Ncolaus Copercus Uversty, Faculty of Ecoomc Sceces ad Maagemet, Departmet of Ecoometrcs ad Statstcs. ** Ph.D., Wrocław Uversty of Ecoomcs, Faculty of Ecoomcs, Maagemet ad Toursm, Departmet of Ecoometrcs ad Computer Scece. *** Professor, dr habl., Ph.D., Norwega School of Ecoomcs (NHH), Departmet of Ecoomcs ad Adam Mckewcz Uversty, Isttute of Soco-Ecoomc Geography ad Spatal Maagemet, Departmet of Spatal Ecoometrcs. **** Ph.D., Adam Mckewcz Uversty, Isttute of Soco-Ecoomc Geography ad Spatal Maagemet, Departmet of Spatal Ecoometrcs. Dowload Date /8/8 7:36 PM

2 04 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk ad orth wester Polad clude clusters of poverty. The frst oe s mpeded by the presese of three dvual growth cetres, whle the secod oe s out of rage of dffuso fluece of bgger agglomeratos. Keywords: jo-cout test, spatal depedece, local dcators of spatal assocato (LISA), exploratory spatal data aalyss (ESDA), ecoomc developmet, taxoomc aalyss. Itroducto The problem of spatal depedece s more ad more frequetly dscussed wth the framework of spatal ecoomc research. Ths partcular cocept s of hgh mportace sce t dcates the occurrece of the testy of certa pheomea depeds o ther spatal locato. I case of the majorty of socoecoomc pheomea the exstece of postve spatal depedece s ther atural property. Ths observato was preseted the form of Tobler s Frst Law of Geography accordg to whch Everythg s related to everythg else, but ear thgs are more related tha dstat thgs (Tobler 970). Falure to clude the exstece of spatal depedece ecoomc research ca lead to cogtve errors (Paelck ad Klaasse 979, Asel 988, Hag 003, Arba 006, LeSage ad Pace 009). The am of the paper s to detfy classes of regos presetg dversfed ecoomc developmet levels ad to apply a jo-cout test to exame spatal depedeces as regards these classes. The study covers the stuatos of 66 Polsh NUTS 3 regos (sub-regos) 0. The regos were dvded to two groups presetg relatvely low or relatvely hgh levels of ecoomc developmet. Groups were dstgushed usg taxoomc methods of multvarate data aalyss. The paper s dvded to two ma sectos. The frst secto dscusses statstcal tests of spatal autocorrelato, presets ther classfcato as regards a frame of referece ad also data type, ad t also explas tests for qualtatve data detal. The secod secto covers a emprcal study; t presets the dstgushed classes of regos ad dscusses the results of global ad local jo-cout tests. Dowload Date /8/8 7:36 PM

3 The Applcato Of Local Idcators For Categorcal 05. Tests of spatal autocorrelato for categorcal data The fucto of spatal autocorrelato s most ofte appled the detfcato of spatal depedece wth referece to soco-ecoomc pheomea. Statstcal tests, examg the statstcal sgfcace of spatal autocorrelato, are commoly cluded amog the tools of exploratory spatal data aalyss (ESDA). Asel dstgushed global ad local tests of spatal autocorrelato (Asel 995). Global tests exame total spatal autocorrelato betwee regos, whle local tests refer to the stuatos of dvdual regos; detfg spatal clusters ad also outler regos. The results of the studes ca support plag of the regoal developmet polcy ad spatal maagemet. The most frequetly appled global statstcal test of spatal autocorrelato s Mora s I test (Clff ad Ord 973, 98), whle Geary s C (954) ad Gets-Ord s G (Gets ad Ord 99) tests were also proposed. Some of these statstcs are also avalable as local dcators of spatal assocato (LISA). They exame quattatve data set, e.g. values of Gross Domestc Product (see Kopczewska 006, pp , Sucheck (Ed.) 00, pp. -5, Suchecka (Ed.) 04, p. 4). I the feld of ecoomc research, terrtoral uts are ofte classfed regard to ther socal ad ecoomc stuatos to exame regoal dversfcato. Multvarate data aalyss methods are frequetly used for these purposes. Revealed classes ca be equvalet (e.g. the ecoomc profles of regos) or raked (e.g. the good, moderate or poor stuatos of regoal labour markets). These classes as regards statstcal measuremet scales are realzatos of ometrc varables such as, accordgly, omal ad ordal varables (see Walesak 993). I ths stuato, a set of terrtoral uts s descrbed by qualtatve (categorcal) data. I terms of qualtatve data the measuremet of spatal depedece the global perspectve, t s possble to follow the jo-cout test applcato (Clff ad Ord 973, 98, see also Kopczewska 006, pp , Sucheck (Ed.) 00, pp. 0-, Petrzak et al. 04). A local varat of the measure represets a famly of local dcators for categorcal data (LICD) (Boots 003). The values of the global test are determed jotly for all regos ad the statstcal propertes of the test are well kow (Clff ad Ord 973, 98). Oe of the most mportat ssues whle usg a jo-cout test s to select the type of a adjacecy matrx. Ths sgfcatly affects the aalyss results. A cotguty matrx s most frequetly used, whle other approaches ca be, for example, based o applyg the k-earest eghbours method. Let assume that whte (W) meas a relatvely poor ecoomc stuato, whle black (B) a relatvely good ecoomc stuato of a rego. I the case Dowload Date /8/8 7:36 PM

4 06 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk of a two-colour map, the dea of jo-cout statstcs cossts coutg the whte-whte (WW), whte-black (WB) ad black-black (BB) types of eghbourhoods (Clff ad Ord 973, 98): BB WW BW j j j w x x j w ( x )( x ) j j w ( x x ) j j j () () (3) where: x, x j take the value of for a rego belogg to the black class (B) ad the value of 0 for a rego belogg to the whte class (W), w j a elemet of a adjacecy matrx. I case of postve spatal autocorrelato occurreces the eghbourhood of uts marked by the same colour should be the domatg oe over the eghbourhood of uts havg dfferet colours. Otherwse, a egatve correlato ca be adopted. If oe-colour eghbourhoods are ot domat over the two-colour oes, t dcates the radom dstrbuto of a varable. Whle examg statstcal propertes of jo-cout test, oe of two followg assumptos regardg a bary o-metrc varable s assumed. The frst oe assumes that each terrtoral ut s assged by realzatos of a radom varable of Beroull dstrbuto b( p), p ( 0,), where p s the probablty of occurrg, smlarly lke samplg wth replacemet. The secod oe assumes that the radom varable records each localzato, the value or zero wth equal probablty (smlarly lke samplg wthout replacemet). For both assumptos, t was proved that BB ad BW statstcs demostrate asymptotc ormal dstrbutos (Clff ad Ord 973, 98). I the test stadardzed BB ad BW statstcs are used: Z Z BB BW ( BB) BB E Var( BB) BW Var, E( BW ) ( BW ). (4) Dowload Date /8/8 7:36 PM

5 The Applcato Of Local Idcators For Categorcal 07 A determato of the values of Z BB ad Z BW statstcs requres kowledge of the momets of ther dstrbutos whch dffer accordg to the samplg method. I samplg wth replacemet, dstrbuto momets of BB statstcs are gve (5), whle for BW (6) (Clff, Ord 973). E( BB) p Var( BB) 4 S 0, 3 4 [ p S + p ( S S ) + p ( S S )]. (5) E( BB) p Var( BB) 4 ( p) S 0, [ p( p) S + 4 p ( p) ( S S )]. (6) where: S S S 0 j, ( wj + w j ) j w j w + j j j w j,. Whle samplg wthout replacemet, the procedure s much more complcated (see Clff ad Ord 973, pp. 5-6). The hypothess regardg the lack of statstcal sgfcace of spatal autocorrelato s rejected, f the value of the statstcs s located left-had rejected area or the value of rght-had rejected area. Z BW Z BB statstcs s located Dowload Date /8/8 7:36 PM

6 08 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk A dfferet way of testg thehypothess of the lack of spatal autocorrelato s proposed permuato approach. A a pror gve umber of colour permutatos o the map s performed. The for each permutato, the values of the BB ad BW statstcs are calculated. I the ext steps a emprcal dstrbuto of both statstcs s determed usg so-called pseudo-levels of sgfcace: p p BB BW # # ( BB BB ) perm k + ( BW BW ) perm k + obs obs,, where BB obs ad BW obs mea the values of statstcs for real spatal arragemet of colours, whle BB perm oraz BW perm mea the values for permutato arragemets (k the umber of permutatos). These three statstcs (BB, WW, BW) ca be also used for testg the local depedeces ( relato to each sgle ut). However, usg local tests s more dffcult tha usg a global test. The frst ssue s that the egbourhood matrx s determed separately for each rego, usg, for example, the cotguty matrx or k-earest eghbours matrx. The secod problem s that the statstcal propertes of the local test are ukow. Thus, the sgfcace of spatal depedeces ca ot be statstcally valdated. (7) 3. Classes of regos presetg dfferet levels of ecoomc developmet Comparatve studes examg stuatos of regos ad terrtoral dversfcato frequetly use taxoomc methods proposed the feld of multvarate data aalyss (see e.g Chojck ad Czyż 973, Grabńsk, Wydymus ad Zelaś 989, Strahl (Ed.) 006). The frst group of these methods teds to dstgush terally homogeous ad exterally separable classes of uts. Ths s the doma of cluster aalyss (Har et al. 006, Evertt ad Du 00, Florek et al. 95, Koleda 006, pp ). Ths approach s useful, amog others, the stuato whe the purpose of the study s to detfy clusters featurg, for example, a smlar job market structure, a smlar ecoomc profle, etc. (see e.g. Markowska 0, Strahl (Ed.) 006). Dowload Date /8/8 7:36 PM

7 The Applcato Of Local Idcators For Categorcal 09 Fgure. The 6 Polsh NUTS regos (dark bold le) dvded to 66 NUTS 3 regos (grey le) Gdańsk Trójmejsk Słupsk Suwalsk Starogardzk Ełck Szczecńsk Koszalńsk Olsztyńsk Elbląsk M. Szczec Grudządzk Stargardzk Bałostock Plsk Bydgosko-toruńsk Cechaowsko- Gorzowsk Włocławsk Ostrołęckosedleck Pozańsk płock Łomżyńsk M. Pozań M. Warszawa Końsk Warszawsk wschod Leszczyńsk Skerewck Zeloogórsk Łódzk Warszawsk zachod M. Łódź Kalsk Balsk Legcko-głogowsk Seradzk Wrocławsk Radomsk Puławsk Potrkowsk Lubelsk Jeleogórsk M. Wrocław Keleck Częstochowsk Chełmsko- Wałbrzysk Opolsk zamojsk Bytomsk Tarobrzesk Nysk Sosoweck Sadomersko- Glwck jędrzejowsk Krakowsk Rybck Rzeszowsk Tysk M. Kraków Tarowsk Przemysk Ośwęcmsk Belsk Nowosądeck Krośeńsk Source: The secod group covers methods used to arrage the uts accordace wth a superor crtero. These methods determe the postos of uts comparso to the other uts. Iteratoal lterature most frequetly dcates factor aalyss the feld (Har et al. 006, Evertt ad Du 00). Polsh lterature proposes a famly of lear arragemet methods (see e.g. Hellwg 968, Grabńsk 984, Pluta 976). Oe of the extesos of ths cocept s the TOPSIS method (Techque for Order of Preferece by Smlarty to Ideal Soluto) proposed by Hwag ad Yoo (98) wth further developmets by Yoo (987), Hwag, La ad Lu (993). The secod approach wll be appled the followg study. The purpose of the research s to exame regoal dversfcato of the ecoomc developmet level Polad 0. The study covers the stuato of 66 Polsh NUTS 3 regos, located 6 NUTS regos (Fgure ). Dowload Date /8/8 7:36 PM

8 0 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk Ecoomc developmet refers to the producto level, ecoomc growth, etrepreeurshp, as well as the wllgess to vest, ad also the stuato regoal job markets. The teto of the authors was to costruct a set of varables whch accout for all the ssues. I the frst step the statstcal data avalablty was examed. The set of varables also had to meet the followg applcato crtera: comparablty, clear defto of the research problem, measurablty ad usefuless the descrpto of pheomea for NUTS 3 regos, ad also formal crtera: relatvely hgh statstcal varato ad low statstcal correlato. Table presets the fal set of dagostc varables. Table. The set of dagostc varables No Name of varable Ut Per capta Gross Domestc Product PLN Natoal ecoomy ettes cluded the REGON regster per 0,000 habtats Etty 3 Per capta vestmet outlays eterprses PLN 4 Average mothly gross salares ad wages PLN 5 Regstered uemploymet rate % Source: Authors ow elaborato. I the ext step, the TOPSIS method was appled to exame the developmet levels of Polsh NUTS 3 regos. Oe of the ma advatages of ths method s comparg the stuatos of uts to a postve deal patter as well as a egatve deal patter (see Łuczak ad Wysock 0, Wysock 00). There were proposed a few ways of defg features of patter-object, depedg o the am of the research ad emprcal kowledge (see e.g. Hellwg 968, Pluta 976). I the preseted study the postve deal patter takes the form of a artfcal object whch represets the hghest real reached values of varables havg a postve mpact (stmulats) ad the lowest real reached values of varables havg a egatve mpact (destmulats). The egatve deal patter s calculated versely. The majorty of selected varables dcate stmulats of ecoomc developmet. Oly uemploymet depcts structural or ecoomc dffcultes wth regoal labour market. Next, the data was ormalzed usg utzato wth zero mmum. After ormalzato the varables take values the rage [0.0,.0]. The the values of varables wth egatve mpact (regstered uemploymet rate) were traslated to varables exertg a postve mpact by subtractg the value of. Dowload Date /8/8 7:36 PM

9 The Applcato Of Local Idcators For Categorcal Followg the above, Eucldea dstaces betwee each rego (th rego) ad the postve deal patter (PIP) ad also betwee each rego (th rego) ad the egatve deal patter (NIP), were calculated. The the values of the sythetc measure for each rego (SM ) were calculated (Hwag ad Yoo 98): NIP SM NIP + PIP (8) Fgure. Two classes of NUTS 3 Polsh regos presetg dfferet levels of ecoomc developmet Source: Authors ow elaborato o the bass of data provded by Local Data Bak of the Cetral Statstcal Offce of Polad (BDL GUS). The sythetc measure takes ts values the rage of [0.0,.0], where s determed for a rego presetg the most favourable values of varables, whle 0 s preseted by a rego wth the most ufavourable values. The hghest Dowload Date /8/8 7:36 PM

10 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk value (0.998) was recorded for the cty of Warsaw (the Mazowecke NUTS rego); the captal cty of Polad. The secod posto was take by the cty of Pozań (0.703) located the Welkopolske NUTS rego. The rest of regos took values the rage [0.654, 0.8]. The lowest value was recorded for Ełck rego, located the Warmńsko-Mazurske NUTS rego. I the ext step, o the bass of recorded values of the sythetc measure, regos were assged to classes presetg dfferet levels of ecoomc developmet. Dvso crtera were preseted Nowak (990, pp. 95-0). I the followg study, due to the occurrece of the outler value recorded by the cty of Warsaw, the meda value was used to dstgush classes of regos. Fgure presets the classfcato of NUTS 3 regos. The frst class detfes a relatvely low level (whte colour), whle the secod class refers to a relatvely hgh level of ecoomc developmet (black colour). There are vsble clusters characterzed by the low level of ecoomc developmet, e.g. the orther Polad (apart from Trójmejsk ad ts surroudg Gdańsk NUTS 3 rego). Clusters featurg a relatvely hgh level of ecoomc developmet, wester Polad, souther Polad ad also cetral Polad are also observed. Addtoally, we ca otce outler well-developed regos, e.g. Bałostock ad Lubelsk sub-regos easter Polad. 4. The global jo-cout test examg spatal depedece The applcato of the jo-cout test wll verfy coclusos made the prevous secto whch were based o the vsual aalyss of the regoal dversfcato of ecoomc developmet levels Polad. Table presets the aalyss results. Table. Global jo-cout test results Type of tested relato Statstcs Expected value Varace Z-value WW BB BW Source: Authors ow calculato usg spdep package (Bvad et al. 04) of R-CRAN. The results of jo-cout test are ot obvous both cases,.e. examg of black-to-black ad whte-to-whte relatos. The test proved the occurrece of a postve spatal depedece case of regos dsplayg a low level of socoecoomc developmet. Therefore, regos featurg a low developmet level show a tedecy towards spatal clusterg. Dowload Date /8/8 7:36 PM

11 The Applcato Of Local Idcators For Categorcal 3 Spatal clusterg of poor regos ca dcate that these regos preset a slow, however, ogog wthdrawal of resources such as eterprses, huma captal, etc. It results the advacg deterorato of the stuato the regos grouped such a spatal cluster. It also brgs about the expaso of spatal cluster boudares to more regos featurg a low developmet level. Ths stuato s dffcult to chage ad, addtoally, t wll probably keep advacg by further decrease the level of developmet compared to well developed regos. The results of the jo-cout test for black-to-black relato are ot obvous. Cotrary to vsual assessmet of the result of the taxoomc aalyss preseted Fgure, the jo-cout test results dcate sgfcat spatal depedece for regos characterzed by a relatvely hgh developmet level. The global test shows a overall stuato ad ca be affected by outler regos. The study eeds to be supplemeted by a detaled aalyss of spatal depedece. 5. The applcato of local jo-cout tests examg spatal clusters Specfyg the value of local dcators for categorcal data (LICD) seems to be a atural complemet of the results of the global jo-cout test. It ca become a tool for spatal cluster detfcato, especally the stuato whe the global jo-cout test dcates the statstcal sgfcace of spatal depedece. I the frst step the cotguty matrces were determed for each rego. Furthermore, 5% of regos showg the hghest values of BB ad WW statstcs (Equatos -) were selected. It was assumed that for these regos there s the hghest possblty of occurrece of local postve spatal depedeces. O the bass of local jo-cout test statstcs, fve types of regos were dstgushed. Fgure 3 shows the aalyss results. The A-type areas clude the NUTS 3 regos that had the hghest values of WW statstcs, whle the B-type areas recorded the lowest values of WW statstcs. The C-type areas cover the NUTS 3 regos wth the hghest values of BB statstcs, whle the D-type areas had the lowest values of BB statstcs. The E-type areas show hgh values of BW statstcs. The whte areas dsplay statstcal sgfcace of BB, WW ad BW statstcs. The test results revealed fve spatal clusters showg dfferet ecoomc ad spatal relatos betwee NUTS 3 regos. The largest cluster cossts of A-type NUTS 3 regos located the easter Polad ad B-type regos. Ths cluster cludes NUTS 3 regos of easter, south easter ad also orth easter Polad of A-type ad ther B-type eghbours. Ths cluster comprses almost Dowload Date /8/8 7:36 PM

12 4 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk 5% of the coutry s total area ad approxmately 0% of the total populato. It represets a area wth the hghest share of the agrcultural sector relato to other parts of Polad. The Podkarpacke, Lubelske, Podlaske ad Śwętokrzyske NUTS regos also belog to the poorest regos wth the Europea Uo. Ther per capta GDP s much below the atoal average, whle the uemploymet rate s much above the atoal average. The secod spatal cluster was formed orth wester Polad. The Koszalńsk NUTS 3 rego of A-type establshes the core of ths cluster ad ts surroudg regos of B-type determe the spatal borders of ths cluster. The ext three spatal clusters dsplay hgh ecoomc developmet. Each of them cossts of a well developed NUTS 3 rego (or regos) of C-type wth eghbourg D-type regos. The strogest ecoomcally s the spatal cluster located cetral Polad wth the core of the cty of Warsaw. Ths cluster cludes a greater part of the Mazowecke NTS rego. The secod spatal cluster covers the most dustralzed area of Polad. Ths cluster s formed by selected NUTS 3 regos of the Opolske ad Śląske NUTS regos. The thrd, ad also the bggest spatal cluster cludes NUTS 3 regos located the mddle of wester Polad. The cluster covers the area of the Lubuske ad also a part of the Welskopolske ad Dolośląske NUTS regos. The E-type areas such as the Bałostock, Lubelsk ad Rzeszowsk NUTS 3 regos show a relatvely good ecoomc developmet level. All of them are located the easter Polad, wth ecoomcally poor NUTS 3 regos. They ca be defed as outlers due to ther egatve spatal depedeces wth referece to ther eghbourg regos. They establsh local growth cetres ad are uable to form ecoomc clusters. They do ot costtute ecoomc support for ther eghbourg regos ad egatvely affect ther stuatos. Outlers cotrbute to drag eghbourg regos due to the fact that they are a place of cocetrato of vestmet outlays ad oe-way flows of well qualfed huma resources, etc. Ths leads to the deterorato of stuatos of the other regos formg the easter spatal cluster. Dowload Date /8/8 7:36 PM

13 The Applcato Of Local Idcators For Categorcal 5 Fgure 3. Local jo-cout tests results fve types of regos accordg to ecoomc developmet levels ad spatal depedeces Source: Authors ow elaborato. 6. Coclusos The paper made a attempt to apply a jo-cout test to the aalyss of spatal depedeces betwee classes of regos dsplayg dfferet ecoomc developmet levels. Two approaches were cluded the study. The frst oe examed the overall spatal teractos, whle the secod oe cocered the partcular stuatos of regos. Dowload Date /8/8 7:36 PM

14 6 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk The global jo-cout test dcated statstcally sgfcat spatal depedece exclusvely for NUTS 3 regos featurg a low level of ecoomc developmet. I case of NUTS 3 regos showg relatvely hgh developmet levels, the test dcated the statstcal sgfcace of spatal depedece. The results poted out the stregths ad weakesses of the global jocout test. It shows a overall stuato spatal clusterg. The presece of outlers,.e. extremely well or poorly developed regos whch dsplay statstcal sgfcace of spatal depedece of BW statstcs, ca sgfcatly fluece the test results. Local jo-cout test facltates more extesve aalyss of the studed ssue. The applcato of local dcators of spatal assocato (LISA) ca dcate covergece processes, regos exceptoally exposed to poverty, processes of formg metropolta areas etc. The results of local jo-cout tests dcated the occurrece of fve spatal clusters Polad. Two of them ca be see as areas of poverty, whle three of them ca be classfed as clusters of wealth. These clusters cover the dustralzed area of souther Polad ad also two areas presetg the best developed servce sector Polad. These clusters ca develop due to the dffuso of ovatos ad other support gve by regoal ecoomc cetres. The wdest area s covered by regos whch form clusters of poverty. The bggest oe s located the easter Polad ad spreads from the Elbląsk to Nowosądeck NUTS 3 rego. The majorty of ts regos have a poor ecoomc stuato whch s also mpeded by three local growth cetres whch take over the potetal ad curret sources of developmet. These cetres cotrbute to ecoomc dspartes easter Polad. The secod poverty cluster covers regos located orth wester Polad. Ths area s out of rage of dffuso fluece of the ctes of Szczec ad the Trójmejsk NUTS 3 rego. Ths prelmary study ca be a startg pot for further research. Oe of the dffcultes usg local jo-cout tests s that ther statstcal propertes are ukow ad ther results caot be valdated. The secod ssue s cosderg the stuatos of Polsh regos wthout referece to eghbourg foreg regos. There are macro-regos, e.g. Nysa Euro-rego cossted of eghbourg regos of Polad, Germay ad Czech Republc, whch cross-border cooperato exsts ad strog spatal relatos occur. The thrd problem s to determe the umber of related uts for whch the local jo-cout test s appled. I the study, the k-earest eghbour method was appled. But ths method ca pose problems whe cosderg regos located ear the coutry borders. The last problem cocers the level of terrtoral dvso, type of terrtoral uts ad ther teral structure. NUTS 3 regos were aalyzed the study due to statstcal data avalablty of the ma ecoomc statstcs, e.g. Dowload Date /8/8 7:36 PM

15 The Applcato Of Local Idcators For Categorcal 7 GDP, vestmet outlays etc. But NUTS 3 regos are terrtoral uts establshed for statstcal purposes, they are ot admstratve uts. I Polad, they usually cover a few eghbourg dstrcts located the terrtory of the same provce. Thus, a NUTS 3 rego s usually ot ecoomcally homogeeous because each of ts dstrcts realzes ts dvdual ecoomc developmet pla. The developmet levels ad drectos, ad progress rates ca sgfcatly dffer wth the NUTS 3 ut. The secod type of NUTS 3 regos covers admstratve uts whch fucto depedetly ad, Polad, clude the bggest agglomeratos. Comparg dfferet uts showg dfferet teral structures affects the aalyss results, a 5-to elephat s ot equal to 5 tos of ats. I all the stuatos, addtoal theoretcal, emprcal, ad smulato studes are recommeded. Ackowledgemet The authors would lke to thak the aoymous revewers for ther valuable commets ad suggestos to mprove the qualty of the paper. Refereces Asel L. (988), Spatal Ecoometrcs: Methods ad Models, Kluwer Academc, Dordrecht. Asel L. (995), Local dcators of spatal assocato LISA, Geographcal Aalyss, Oho State Uversty Press, vol. 7, ssue. Arba G. (006), Spatal Ecoometrcs: Statstcal Foudatos ad Applcatos to Regoal Covergece, Sprger-Verlag, Berl Hedelberg. Bvad R.S. et al. (04), The spdep package of R, Bvad R.S., Pebesma E.J., Gómez-Rubo V. (008), Appled Spatal Data Aalyses wth R, Sprger, New York. Boots B.( 003), Developg local measures of spatal assocato for categorcal data, Joural of Geographcal Systems, Sprger-Verlag, o. 5, Chojck Z., Czyż T. (973), Metody taksoom umeryczej w regoalzacj geografczej, PWN, Warszawa. Clff A.D., Ord J.K. (973), Spatal Autocorrelato, Po, Lodo. Clff A.D., Ord J.K. (98), Spatal Processes: Models ad Applcatos, Po, Lodo. Evertt B.S., Du G. (00), Appled Multvarate Data Aalyss, Arold, Lodo. Florek K., Łukaszewcz J., Perkal J., Stehaus H., Zubrzyck S. (95), Taksooma wrocławska, ʻPrzegląd Atropologczyʼ, Vol. XVII. Dowload Date /8/8 7:36 PM

16 8 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk Geary R. C. (954), The cotguty rato ad statstcal mappg, ʻThe corporated Statstcaʼ, Vol. 5(3), pp Gets A., Ord J. K. (99), The aalyss of spatal assocato by dstace statstcs, ʻGeographcal Aalyssʼ, Vol. 4, Issue 4, pp Grabńsk T. (984), Welowymarowa aalza porówawcza w badaach dyamk zjawsk ekoomczych, Akadema Ekoomcza w Krakowe, sera specjala: moografe, r 6, Kraków. Grabńsk T., Wydymus S., Zelaś A. (989), Metody taksoom umeryczej w modelowau zjawsk społeczo-gospodarczych, PWN, Warszawa. Hag R. (003), Spatal Data Aalyss: Theory ad Practce, Cambrdge Uversty Press, Cambrdge. Har J.F., Black W.C., Bab B.J, Aderso R.E., Tatham R.L. (006), Multvarate Data Aalyss, Pearso Pretce Hall, New Jersey. Hellwg Z. (968), Zastosowae metody taksoomczej do typologczego podzału krajów ze względu a pozom ch rozwoju oraz zasoby strukturę wykwalfkowaych kadr, ʻPrzegląd Statystyczyʼ, R. XV, zeszyt 4, s Hwag C. L., La Y. J., Lu T. Y. (993), A ew approach for multple objectve decso makg, Computers ad Operatoal Research, No0, pp Hwag C.L., Yoo K. (98), Multple Attrbute Decso Makg: Methods ad Applcatos, Sprger-Verlag, New York. Koleda M. (006), Taksooma umerycza. Klasyfkacja, porządkowae aalza obektów welocechowych, Akadema Ekoomcza m. Oskara Lagego we Wrocławu, Wrocław. Kopczewska K. (006), Ekoometra statystyka przestrzea z wykorzystaem programu R CRAN, Cedewu, Warszawa. LeSage J., Pace R.K. (009), Itroducto to Spatal Ecoometrcs, Chapma & Hall/CRC, Boca Rato. Łuczak A., Wysock F. (0), Porządkowae lowe obektów z wykorzystaem rozmytych metod AHP TOPSIS, ʻPrzegląd Statystyczyʼ, Vol. LVIII, Issue -. Markowska M. (0), Dyamcza taksooma owacyjośc regoów, Uwersytet Ekoomczy we Wrocławu, Wrocław. Nowak E. (990), Metody taksoomcze w klasyfkacj obektów społeczo-ekoomczych, PWE, Warszawa. Paelck J.H.P., Klaasse L.H. (979), Spatal Ecoometrcs, Saxo House, Farborough. Petrzak M.B, Wlk J,. Kossowsk T., Bvad R. (04), The detfcato of spatal depedece the aalyss of regoal ecoomc developmet - jo-cout test applcato, [:] Papeż M., Śmech S. (Ed.), Proceedgs of the 8 TH Professor Aleksader Zelas Iteratoal Coferece o Modellg ad Forecastg of Soco-Ecoomc Pheomea. Pluta W. (976), Welowymarowa aalza porówawcza w badaach ekoomczych, PWE, Warszawa. Dowload Date /8/8 7:36 PM

17 The Applcato Of Local Idcators For Categorcal 9 Strahl D. (ed.) (006), Metody ocey rozwoju regoalego, Wyd. Akadem Ekoomczej we Wrocławu, Wrocław. Suchecka J. (ed.) (04), Statystyka przestrzea. Metody aalz struktur przestrzeych, C.H. Beck., Warszawa. Sucheck B. (ed.) (00), Ekoometra przestrzea. Metody modele aalzy daych przestrzeych, Wydawctwo C.H. Beck, Warszawa. Tobler W. (970), A computer move smulatg urba growth the Detrot rego, ʻEcoomc Geographyʼ, Oxford Uversty Press, No 46(), pp Walesak M. (993), Stratege postępowaa w badaach statystyczych w przypadku zboru zmeych merzoych a skalach różego typu, ʻBadaa Operacyje Decyzjeʼ, No, pp Wysock F. (00), Metody taksoomcze w rozpozawau typów ekoomczych rolctwa obszarów wejskch, Uwersytet Przyrodczy w Pozau, Pozań. Yoo K. (987), A recoclato amog dscrete compromse stuatos,joural of Operatoal Research Socety, No 38, pp Streszczee ZASTOSOWANIE LOKALNYCH WSKAŹNIKÓW DLA DANYCH JAKOŚCIOWYCH (LICD) W PRZESTRZENNEJ ANALIZIE ROZWOJU GOSPODARCZEGO W artykule podjęto próbę zastosowaa lokalych wskaźków dla daych jakoścowych (LICD) w przestrzeej aalze rozwoju gospodarczego. W perwszej częśc omówoo testy służące do badaa autokorelacj przestrzeej a podstawe daych jakoścowych. W drugej częśc zaprezetowao dwu etapowe badae emprycze obejmujące 66 polskch regoów klasy NUTS 3. Najperw zdetyfkowao klasy regoów prezetujące róży pozom rozwoju gospodarczego, z wykorzystaem taksoomczych metod welowymarowej aalzy statystyczej. Następe zastosowao test jo-cout w celu określea przestrzeych zależośc mędzy regoam. Bada o tedecje do tworzea sę klastrow przestrzeych. Test globaly wskazuje ogóle terakcje przestrzee mędzy regoam, atomast testy lokale dają szczegółowe wyk w odeseu do poszczególych regoów. Globaly test jo-cout ujawł przestrzee grupowae sę regoów o skm pozome rozwoju gospodarczego, e potwerdzł jedak zależośc przestrzeych w odeseu do regoów dobrze rozwętych. Z tego względu badae uzupełoo o zastosowae lokalego testu jo-cout. Ujawł o występowae pęcu klastrów Dowload Date /8/8 7:36 PM

18 0 Mchał B. Petrzak, Justya Wlk, Roger S. Bvad, Tomasz Kossowsk przestrzeych trzech regoów odstających. Zdetyfkowae zostały trzy klastry bogactwa. Ich rozwój bazuje a dyfuzyjym oddzaływau regoalych cetrów wzrostu. Obszar Polsk wschodej oraz pólco-zachodej zajmują klastry bedy. Sytuacja perwszego z ch jest pogarszaa przez trzy dywduale cetra wzrostu, atomast drug klaster zajduje sę poza zasęgem dyfuzyjego wpływu wększych aglomeracj. Słowa kluczowe: test jo-cout, zależość przestrzea, lokale wskaźk zależośc przestrzeych (LISA), eksploracyja aalza daych przestrzeych (ESDA), rozwój gospodarczy, aalza taksoomcza Dowload Date /8/8 7:36 PM