1 Introduction

Following the end of the Cold War, a number of political geographical transformations took place in Europe, including the disintegration of Yugoslavia, which, in some respects, is still an ongoing process if one considers the status of Kosovo or Bosnia and Herzegovina (hereafter Bosnia or BiH). Several armed conflicts erupted during the break-up process, of which the war in Bosnia was the longest (lasting for more than three years), in which the fault lines between the opposing factions were essentially (though not always) ethnic (Keil and Perry 2016). Only international intervention could stop the war, which meant that the opposing parties remained in the same territorial state, and the political conflict behind the war remained unresolved (Dahlman and Ó Tuathail 2005). Ethnic confrontations persisted and many considered the peace a war with other means (Bildt 2021). Therefore the Dayton Peace Agreement (DPA), which formally ended the war in 1995, had to create an extremely complex political system and power has been largely shared along ethnic divisions ever since (Keil and Perry 2016). The DPA decentralised the state along ethnic lines (some pre-war, but many a consequence of the large scale ethnic-based forced migrations), and it also granted territorial political rights to ethnic groups (Keil and Perry 2016; Zdeb 2019). The deal also created the framework for ethnic-based political activities, where a system of ethnic quotas, political parties based on ethnic affiliation and ethnic vetoes codifies the political role of ethnicity, so much so that some authors consider them ethnocratic structures (Reményi 2011; Hulsey and Stjepanović 2017). Territorial decentralisation of the state was a precondition for peace, but today the two parts of the country (the entity of Republika Srpska—RS, and the entity of the Federation of Bosnia and Herzegovina—FBiH), are on divergent paths in many respects. In the RS (48% of BiH territory, 35% of BiH population), approximately 83% of the population is of Serb ethnicity, 12.7% are Bosniaks and 2.3% are Croats. In the Brčko District (1% of BiH territory, 2.5% of BiH population) 42.4% of the population is Bosniak, 34.6% is Serb and 20.7% is of Croat origin. In the Federation (51% of BiH territory, 62.5% of BiH population), Bosniaks are the largest ethnic group with 70.4%, Croats account for 22.4% and Serbs for 2.6%, while the Bosniak population in the country as a whole has now reached an absolute majority (50.1%). (Census of the population of Bosnia and Herzegovina 2013).

1.1 Political context of Bosnia

The political system of the state is very complex, which is on one hand a legacy of the armed conflict and the agreement ending that (the 4th annex of which is the constitution of the state), and on the other a consequence of the ethnic composition. The legislature is bicameral, with the three constitutional ethnic groups sending an equal number of representatives to the upper house (15). Every four years, a total of 42 representatives are elected to the lower house from the two entities, 28 from the FBiH and 14 from the RS according to a party-list proportional open list system. In addition, the two entities have their own legislature, and the territory of the Federation has been cantonised partly on an ethnic (Bosniak–Croat) basis, and the individual cantons also have their own cantonal Assembly. At each of these electoral scales, the effect of ethnicity is different depending on the relative proportion of the ethnic group (Hulsey 2016).

Bosnia has a segmented multi-party system dominated by ethnic parties, but both declarative multi-ethnic and non-nationalist parties (Mujkić and Hulsey 2010) as well as competition between parties within the ethnic subsystems (Serb, Bosniak and Croat) have been present from the beginning (Hulsey and Keil 2019). Furthermore, the party system is very fragmented, making it difficult for voters to choose between competing ideological programmes (Hulsey 2016). Because certain ethnicities are almost completely absent from parts of the country, ethnic parties do not necessarily nominate candidates throughout the country, therefore both at different scales and in different constituencies different parties may compete for the voters (Hulsey and Keil 2019). The most supported parties in the Federation are the Stranka demokratske akcije, [SDA] (Muslim-Bosniak national, center-right party), the Hrvatska demokratska zajednica Bosne i Hercegovine, [HDZ] (Catholic-Croat, national, center-right party) and the Socijaldemokratska partija Bosne i Hercegovine [SDP] (officially multi-ethnic Social Democratic Party, but majority of the voters are Bosniaks (Mujkić and Hulsey 2010)). Alongside them are newer urban parties, such as the Savez za bolju budućnost BiH [SBB] (seceded from the SDA) and the Demokratska fronta [DF] (seceded from the SDP) that demand change. The Savez nezavisnih socijaldemokrata [SNSD]—which is a national populist Serb party despite the fact its name suggests that it is a Social Democratic party—has now become the dominant party in the RS, and its biggest opponent is the Srpska demokratska stranka [SDS] (right-wing Serb national party). The third largest Serb Party, Partija demokratskog progresa–Party of Democratic Progress (PDP) can be characterized by centre-right politics, while the fourth largest, the Demokratski narodni savez–Democratic People’s Alliance (DNS) adopted Serb nationalist and conservative stance. The spatial pattern of the main parties is shown in the Fig. 1.

Fig. 1
figure 1

Source Gekić et al. (2022)

Political parties with most votes for House of representatives in general elections 2018. See the annex for the abbreviations.

Since ethnicity is the primary compositional factor of party performance (Hulsey 2010) it is also the most influential in determining the spatiality of party support, ethnic parties perform better in the areas inhabited by their ethnic groups. There are also significant regional differences within the different parties of the same ethnic groups (Hulsey 2016). This suggests that, in addition to ethnicity, other factors also influence the spatiality of party support. The best example of this is the traditional support for multiculturalism, left-wing values and non-ethnic voting in and around the Tuzla Basin. The historical background to this, as Calori (2015) points out, dates back to the Austro-Hungarian Empire’s rule in the nineteenth century, when industrial developments increased population and diversity. The turbulent twentieth century history of the area is also accompanied by a more tolerant Bosnian society, one that was not organized around ethnic lines. Urbanity and related compositional factors (level of education, employment structure, etc.) also plays an important role in influencing party performances (Reményi et al. 2021). Elections to date (the last in 2018) at the state level have been won in almost all cases by ethnic parties, but in varying proportions and with different territorial outcomes (Gekić et al. 2022).

1.2 Electoral geography

With the development of (electoral) geographical research, we are starting to achieve a more thorough understanding of the influence of geographical location and spatial context on various processes. One of the key theoretical issues of electoral geography is whether only demographic characteristics (age, education…) can be found to lie behind election results, or whether geographical location and context (place-related historical traditions, neighborhood effect…) also have an “independent” influencing role. This so-called compositional-contextual debate takes place primarily between representatives of political science and political geography. As Agnew (1996) pointed out, not everything can be explained by social variables, local characteristics also play a role in the development of results. In opposition to this, representatives of political science (e.g., King 1996) argue that the role of location is not significant in itself, only through the distribution of social variables. Examination of election results in the Netherlands, e.g., by Gent, Jansen and Smits (2014), concluded that the nature of the settlement (suburban) has a demonstrable contextual effect on the election results of the right-wing populist party. The work of Johnston and Pattie (2006) presents the contextual nature of the British election. Several researchers, e.g., Walks (2006), believe that both contextual and compositional data have their own relevance; and should be examined together. The present study also seeks to support this proposition. Although the available data focus primarily on compositional components, it also covers the role of contextual factors where relevant.

For contextual factors, however, it is not sufficient to analyze the contextual role of the unit of analysis alone, it is necessary to cross the boundary and examine the role of surrounding units (Jensen et al. 2013). Lacombe and Shaughnessy (2007) found that studies of voter behavior based mainly on linear regression do not take into account autocorrelation from spatial processes and are therefore biased. Furthermore, these studies typically omit important variables that are based on spatial processes. The importance of spatiality is also highlighted in a study by Jensen and colleagues (2013), whose final conclusion is that the inclusion of the role of spatial dependence should be a vital component of any geographic research on electoral outcomes. Jensen and colleagues (2013) also draw attention to the regional dependence on geography, which may be particularly relevant in the case of our present research given the history of the country and the higher territorial level we are analyzing.

The contextual and spillover effects of adjacent areas have been analyzed in several electoral geography studies from all over the world using different spatial modelling techniques. In Tunisia, poverty levels (Amara and El Lahga 2016) and in the UK, the proportion of whites and incumbent MPs (Jensen et al. 2013) show indirect neighborhood effects. Spatial analysis can be useful even when indirect effects are not significant on their own, but it can still provide a more accurate picture of the true direct and total (direct+indirect) effects (Burnett and Lacombe 2012). For example, the introduction of the Austrian FPÖ's performance in the 2013 elections as an independent variable improved the fit of the model to the party's 2017 performance (Essletzbichler et al. 2021). The role of the spillover was found to be significant and its introduction removed significance from variables (e.g. the increase in the unemployment rate) that were predicted to be significant in the linear model. To further improve the estimation of the models, the authors also included a spatial error variable, which was also found to be significant. The role of spatial lag is shown in the models of Wuhs and McLaughin (2019), for the German CDU, SDP and AfD election results, while the spatial error model is relevant for the Left Party.

The role of spatial environment on party performance was also confirmed by Harbers' research (2017) in Mexico. The performance of individual parties was also affected by their performance in neighboring districts. Robinson and Noriega's (2010) study similarly demonstrates the role of the spatial lag variable. Increased support for Democrats in the Rocky Mountains is also felt in surrounding areas and generated extra votes. Moving closer to the unit of analysis of our present research, the only study that examines the electoral geography of the Balkan countries using spatial modelling is the work of Grdešić (2013). The author highlights the spillover effect of political preferences from neighboring areas, which creates regional party strongholds.

There are several political science explanations of the spillover effect of a party's performance in one electoral unit on neighboring areas. Johnston and colleagues (2004) argue for the political contagion of social interactions, i.e. the role of talking to others in shaping political opinion. When the spillover effect is coupled with a positive migration rate, the possibility of self-reinforced political contagion through migration patterns arises (Robinson and Noriega 2010). As the US example shows, supporters of certain parties are more inclined to migrate to areas where their own party's strength is growing. Finally, spatial dependence can also be caused by the campaigning strategy of individual parties, depending on how much they target the problems of particular spatial units and how much resources they spend on them (Johnston et al. 2004; Gimpel et al. 2007).

Spatial analyses have also been used in other subfields of political science and political geography, e.g. to analyze electoral turnout (Lacombe et al. 2014) to examine the degree of partisanship (Amlani and Algara 2021) or to justify yardstick theory (Elhorst and Fréret 2009). In spatial analysis, the evidence for the existence of spatial processes is indirect and we usually do not know the trigger or the exact direction and speed of the spreading effect. Thus, spatial diagnostics only serves to identify the existence and nature of the spatial process (Harbers 2017).

The source of the data is very important when it comes to measuring and analyzing contextual effects. Initial surveys used election results, but polling data now provide much more accurate information. However, producing and procuring such data is not possible everywhere and in all circumstances. In such cases, academia continues to use aggregate data on election results (Clem and Craumer 2004, 2005; Clem 2006), although we need to be aware of the disadvantages of such data (Agnew 1996; Forest 2018). For this research, we had no recourse to use any other data source than the election results, as high-quality polling data is not available on an appropriate territorial scale for Bosnia and Herzegovina.

Our objective is to look beyond the mainstream social factors influencing electoral results in BiH and try to uncover its spatial contextuality. We also seek to contribute to the better understanding of highly ethnicized electoral systems in general and Bosnia’s in particular. The political decentralisation of the state, the regional embeddedness of the parties and the geographical isolation of the ethnic groups lead us to use quantitative methods that are suitable for detecting the geographical dependencies that influence the results of the different parties. These represent spillover contextual effects that are typically ignored in studies of Bosnia so far.

2 Methodology

The spatial units of the analysis were the Osnovna izborna jedinica (“basic constituencies”), of which 80 are in the FBiH and 64 are in the RS. These correspond to municipalities with the exception of the Brčko District, which is divided into two constituencies, one for parties running on the FBiH list and the other for parties running on the RS list. However, due to this split into two constituencies, we do not have census data matching the constituencies in the Brčko District, so this area is excludedFootnote 1 from our analysis (leaving 79 constituencies in the FBiH and 63 in the RS). Johnston and Pattie (2006) also use the constituency as a unit on their “special scale of contextual effects” diagram, commenting as follows: “many voters identify with them, in that they provide their national political representation; they are also major units within which political parties are organized and develop their election strategies” (Johnston and Pattie 2006, p. 45) This unit of analysis has been frequently used in the past (e.g., Cox 1968; Jessop 1974) and has retained its importance to this day (e.g., Mattes and Milazzo 2014, Johnston et al. 2019).

The dependent and independent variables in the study are taken from Reményi and colleagues' (2021) study, which provides a comprehensive picture of the country's electoral geography based on aggregate data. Thus, the results of the SDA, SDP, HDZ, SBB and DF from the Federation were analyzed, while SNSD, SDS, DNS, PDP and SDA from the RS were included in the study (top five-five parties). The results for each five-five parties were examined based on the 2018 House of Representatives of BiH election.

Independent variables at the municipal level were surveyed during the 2013Footnote 2 census and we used the data from this survey. As several examples of the aforementioned research already highlighted the importance of ethnic voting in Bosnia, the percentage of the main ethnic groups targeted by each party (SDA, SDP, DF, SBB: Bosniak; HDZ: Croat; SNSD, SDS, PDP, DNS: Serb) was taken as the main compositional factor.Footnote 3 However, the ethnic spatial structure also appears as a contextual factor, and, to illustrate this, we chose the ethnic polarization index (MRQ), which has already been used in other electoral geography studies (eg. Németh and Dövényi 2019) and is an excellent alternative to describe societies characterized by ethnic tensions. As Montalvo and Reynal-Querol (2003) have argued, conflict is more likely to evolve the more polarized a population is into two large groups. The value of the index is zero in a homogenous population and reaches its maximum at one when exactly two equally distributed groups form the population in a given unit.

$$MRQ = 4\mathop \sum \limits_{i = 1}^{N} p_{i}^{2} \left( {1 - p_{i} } \right)$$

pi: Proportion of the i ethnic group in relation to the total population, N: Number of ethnic groups.

To help with interpretation we multiplied the index score by 100. In RS, we obtained a high Variance Inflation Factor (VIF) value between the proportion of Serbs and the polarization index, indicating multicollinearity, so only the ethnic ratio is included of the two variables in the models of SNSD, SDS, PDP and DNS.

Additional variables include the urbanization and migration rates of municipalities, the proportion of people with tertiary education, the level of unemployment, and the amount of people working in the primary and secondary sectorsFootnote 4 (Table 1.). However, some of these variables can also be contextual factors at the same time, especially unemployment, which can be an influencing factor when taken relative to levels in neighboring locations (Johnston and Pattie 2006; Sümeghy 2022). Compared to the study by Reményi and colleagues (2021), the interaction between the proportion of workers in the secondary sector and the unemployment rate is introduced as a new variable. As noted by Brambor and colleagues (2006), it is typically necessary to examine interactions in political analyses, even if they carry the risk of multicollinearity. The authors argue that the problems associated with multicollinearity are overrated and that centering or omitting main variables is rarely justified (Brambor et al. 2006).

Table 1 Descriptive statistics of the main independent variables included in the analysis (Descriptives were calculated prior to winsorisation).

We then ran the best-fit model for each party based on the study of Reményi and colleagues (2021) in RStudioFootnote 5 to examine “the importance that geographic space and location dependency may or may not have on election outcomes or voting patterns” (Lacombe and Shaughnessy 2007). We considered Moran's I index as the most important indicator of spatial dependence. Moran’s I (Anselin 1995) statistic indicates spatial autocorrelationFootnote 6 and warns about modeling errors.

$$I = \frac{n}{2A}\frac{{\mathop \sum \nolimits_{i = 1}^{n} \mathop \sum \nolimits_{j = 1}^{n} \delta_{ij} \left( {y_{i} - \overline{y}} \right)\left( {y_{j} - \overline{y}} \right)}}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {y_{i} - \overline{y}} \right)^{2} }}$$

n = Number of territorial units, yi = Value of the variable to be examined in each of the territorial units, \(\overline{y}\) = Arithmetic mean of the variable under investigation, A = number of neighbourhood links, δij = Moduli.

There can be several causes of spatial autocorrelation, such as a poorly chosen set of variables, a wrong model specification, or a misspecified spatial matrix (Kopczewska 2020). One of the most common source of error in these examples is the omission of one or more key variables from the model, resulting in a spatially concentrated pattern of the residuals (De Knegt et al. 2010). These variables can also be the result of spatial interactions, of which there are three main types: the spatial spillover effect of the dependent variable, the spatial correlation of errors and the neighborhood effect of independent variables (Durbin component) (Kopczewska 2020).

The most commonly used spatial modelling techniquesFootnote 7 to correct for errors arising from spatial autocorrelation are the spatial lag model (or spatial autoregressive model, SAR), the spatial error model (SEM), the spatial Durbin model (SDM), and the spatial Durbin error model (SDEM) the use of which is already shown in many electoral geographical studies (e.g., O'Loughlin et al. 1994; Robinson and Noriega 2010; Harbers 2017). The spatial lag model is used in cases where the dependent variable has a neighborhood effect (Rho) on areas close in space, in which case a spatially concentrated pattern is formed due to the interaction of neighboring municipalities (Anselin and Rey 2014). Jensen and colleagues (2013) see the electoral geographical manifestation of this phenomenon in the common electoral preference of the population of the area and in "copy-cat" behavior. In the spatial error model, the spatial pattern is caused by a variable (Lambda), often a local process with a strong contextual effect (Harbers 2017), which is not included in the model (Anselin and Bera 1998). This variable is often qualitative so quantitative analyses based on aggregate data are usually ignore it. The spatial Durbin model accounts for the spillover role of each independent variable in addition to the spillover effect of the dependent variable. Finally, the SDEM model includes the spillover effect of independent variables in addition to the interaction between the error terms (Elhorst 2014). Spatial models that include spatial spillovers of the dependent variable (spatial lag model and SDM in the case of this study) introduce an endogenous regressor on the right-hand side of the equation. For this reason, these models are global, contain endogenous feedback processes, that are spilling over to higher order neighbours. In contrast, spatial models with only exogenous variables are local and spatial spillovers only extend to neighbours defined by the spatial matrix (LeSage 2014). For models that include endogenous effects, the estimated values should also be interpreted differently. In models including the spatial lag effect of the dependent variable, the interpretation of the estimated parameters is limited, thus effects (direct,Footnote 8 indirect and total) need to be calculated to accurately determine the coefficients and the spillover factors (Kopczewska 2020). While in the case of SDEM, the Durbin component can be interpreted directly as the spillover effect (Kopczewska 2020).

For the spatial lag models, due to the endogenous effect, we also used the STSLS (spatial two stage least squares) approach, which uses the spatial lag of the independent variables as instruments (Kopczewska 2020). The eigenvalue vectors derived from the spatial weight matrix were used to calculate the impacts.

The Lagrange Multiplier (LM) diagnostics show which of the processes is present for each party and which method we should use.Footnote 9 In the LM test, the spatial weight matrix was determined based on the square root of the number of elements (Hassanat et al. 2014), which proved to be the ideal procedure for most parties in the country (Reményi et al. 2021). If the diagnostics reject the linear model with both robust error and robust lag, SDM or SDEM is the recommended solution. The diagnostic also displays a value for SARMA, which would suggest the use of the SAC model, but Anselin (1988) notes that this is never in fact the perfect specification.

SDM and SDEM can be reduced to both simpler spatial models (SAR, SLX and SEM), and if the fit does not deteriorate significantly (LR, log likelihood test), it is preferable to use the simpler solution. When the LM test inferred the use of either SDM or SDEM, both models were run and the better fitting one (compared to the linear model) was finally chosen. As the choice of spatial weight matrix has a significant impact on the outcome of the spatial analysis, the spatial models are run with the most commonly used weights (Knn5,Footnote 10 Knn square root of the number of elements, first order queen,Footnote 11 minimum distance, inverse distance) and the best fitting model (based on AIC values)Footnote 12 with a significant Wald testFootnote 13 is included in the analysis. In the analysis, the performance of each party is analyzed at the entity level. Thus, the spatial weight matrices are also interpreted at the entity level, so the nearest neighbours method only considers neighbors in the same entity. Similarly, the first order queen weight matrix of a municipality on the entity boundary only considers neighboring municipalities, which are in the same entity.

3 Results

The residuals from the linear regression analyses run in the study by Reményi and colleagues (2021) were subjected to Moran's I analysis to detect possible spatial autocorrelation, which may be an indicator of spatial dependence. The analysis suggests that, apart from the models for the results of the SDA (both in FBiH and RS entities) and the DF party, the spatial clustering of residuals persists for all other parties. Thus, the parameter estimates of linear models may be biased and the use of spatial modelling is recommended. The results of the Lagrange Multiplier (LM) tests are displayed in the table, showing that spatially correlated errors (SDP), spillover of the dependent variable (SBB, SDS) and these factors plus the neighborhood effect of the independent variables (SNSD, DNS, PDP) are all present. Although the Moran's I value for HDZ indicates spatial autocorrelation, the results of the Lagrange Multiplier tests suggest that spatial modelling is not warranted. Li and Hong (2019) note that generally in such cases Moran's I is biased and spatial modelling is not necessary. Kopczewska (2020) also points out that the existence of spatial autocorrelation does not always imply the need for spatial modelling (Table 2).

Table 2 Lagrange Multiplier tests for model type selection

For the SDP, a significant Wald test indicates a better fit of the spatial error model over the linear regression model.Footnote 14 The interaction between the proportion of workers in the secondary sector and the unemployment rate was found to be significant and replaced the role of the unemployment rate, which was significant in the study of Reményi and colleagues (2021). The spatial embeddedness of the party is indicated by the significant Lambda value, which refers to a variable that strongly defines and spatially delimits the party's stronghold.Footnote 15 Although the present study does not aim to explore the factor(s) behind spatial dependence, literature has already reported on the embeddedness of the SDP in the Tuzla basin. According to Calori (2015), this omitted variable could be the multicultural tradition of the Tuzla Basin, which causes a historically long-standing divergence in the political culture of the entity that has infiltrated the electoral pattern of the young country (Table 3).

Table 3 Results of SEM

The two parties whose spatial dependency is the result of the spillover effect of party results into neighboring areas are the Bosniak SBB and the Serb SDS. For both parties, the Wald test result is significant and the AIC values show a better fit compared to the linear models.Footnote 16 For SDS, this spatial effect is the only significant factor, while for SBB, the ethnic fault line and the supposed support of the Bosniak population are also present. The use of the STSLS model removed the significant indirect effect of the Bosnian ethnic proportion for SBB compared to the spatial lag model, while no change was observed for SDS (Table 4).

Table 4 Results of spatial lag models

Spatial spillovers have an impact not only on the support of the strongest Serb national party, the SNSD, but also on the support of smaller parties with a limited territorial base, such as the DNS or the PDP. In the case of the latter two parties, moreover, spatial modelling achieved a much better estimation and fit than linear regressionFootnote 17 (Reményi et al. 2021). For SNSD, the application of the Spatial Error Durbin Model produced a better fit, even though the lambda itself, which indicates the autocorrelation of spatial errors, did not become significant. The ethnic fault line and the share of Serbs explain and influence SNSD's and PDP’s support, although the other parties also prioritize Serb interests. The spillover effect of the independent variables is indicated by the fact that the lag effect of the share of Serbs was found to be stronger for SNSD than the direct effect. Compared to the results of the linear regression, the role of the sectoral factor increased, which is also explained by the significant spillover effect of this variable. The support for the two smaller Serb parties is indirectly influenced by the share of higher education, with a positive effect on the DNS result and a negative effect on the PDP result. The indirect effect of the education level of neighbouring areas is 4 times higher than the direct effect of the education of the central area for the DNS, and this is considered a remarkably strong spillover effect. The spatial embeddedness of the PDP is indicated by the significant neighbourhood effect of the party result (Table 5).

Table 5 Results of SDEM and SDM

4 Conclusion

Although spatial processes have been shown to influence electoral outcomes, electoral geography and political science analyses of the Balkan countries, with few exceptions, ignore them. As a result, biased and inconsistent estimates of the factors influencing the vote for individual parties are produced. Given the regional embeddedness of the country's parties and the typically stable spatial structure of their support (Reményi et al. 2021), these spatial effects may be even more important. This study examined the 2018 results for five-five parties of the FBiH and RS entities and finds that models that ignore spatial factors are characterized by clustering of poorly estimating residuals and that, with the exception of the SDA, HDZ and DF, the results of the other parties are influenced by some aspect of spatial dependence. Different spatial models have been used to resolve this dependence.

The causes underlying the spatial dependence of the parties include the spatial correlation of errors, the spillover effect of party results and the indirect neighborhood role of each independent variable. The spatial correlation of errors became significant for the SDP. It is indicating a local, typically qualitative cause that is not included in the models, but this spatial process largely delimits the main basis of the party's support. The present study confirmed the spatial dependence of the party in the Tuzla basin, which Calori (2015) explains by the historical tradition of multiculturalism. The impact of party performance on the results in neighbouring constituencies was shown for SBB, SDS and PDP. As in the Croatian study of Grdešić (2013), the spillover effect of party preferences is also evident in Bosnia, creating regional party strongholds. In the case of SDS and PDP, this effect is obvious in the election results. The SDS is strong in the south-eastern part of the RS and the PDP in the north-western part of the entity, while the parties have low support in the other party's territorial base, as shown by Reményi and colleagues' (2021) research based on local spatial autocorrelation.

The spillover effect is not only evident for the dependent variables but also for the independent variables. Such contextual effects were identified as the ethnic and the sectoral structure of neighbours for SNSD, and the educational profile of the neighbouring municipalities for PDP and DNS. For DNS, the negative indirect effects of unemployment, urbanity and migration rate were also present. SNSD performs better in extensive Serb areas, and the spatial lag effect of ethnicity has proved to be even stronger than the direct one. The same is true for the proportion of people working in the primary and secondary sectors, showing the important impact of those sectors on party support. The two smaller Serb parties' models show the opposite role of the indirect effect of education, with the DNS' performance boosted by proximity to neighbouring municipalities which have a highly educated population, while the PDP's high support in Lopare and around Srbac may benefit from the education levels of its neighbours, which is quite low even at the entity level. The authors point out that while spatial modelling is relevant for detecting these spatial spillover effects, it is not in itself suitable for explaining precisely why these effects occur. According to Jencks and Mayer (1990), many studies treat neighbourhood effects as a kind of “black box” and the exact effects are not explained. This is also a valid claim for models that include spillover effects based on aggregate data, which poses a limitation to our study. Therefore, further local qualitative research is needed, focusing on municipalities where spatial analysis has been used to show significant improvements in the model residuals.

In this study, we have analyzed each entity separately, but the location next to the entity boundary can also be a contextual effect. The influence of adjacent areas beyond the entity boundary and the spatial spillover is unlikely to be stopped by the boundary. After mapping the electoral results for the parties we found municipalities along the entity boundary but not in the main entity of the party, where some parties (SNSD and SDA) performed well. The spillover effect of the parties' results across the entity boundaries was analyzed using the spatial autoregressive tobit method.Footnote 18 The tobit method was chosen because these ethnic parties performed poorly in areas not populated by their own ethnicity, so that results around 0% were in the majority (positive skew). An extra variable representing entity (0 = RS, 1 = FBiH) was introduced in these models to reduce the problem of heteroskedasticity. Thus, for the whole country model, the spillover effect of the party result appeared for SNSD, while it was not significant for SDA. A proposal for further research is to investigate the effect of independent variables across entity boundaries. The results of the spatial tobit model augmented with Durbin components would presumably better reflect the results of our spatial Durbin error model for the SNSD entity result presented in this paper.