# Modelling the Influence of Regional Identity on Human Migration

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodologies

#### 2.1. Used Migration Data

#### 2.2. Model Specification

#### 2.3. Fitting a Standard Gravity Model for Human Migration

#### 2.4. Expansion of the Gravity Model

#### 2.4.1. Specification of Regional Identities

#### 2.4.2. Introduction of the Different Sets of Identity Regions

#### 2.5. Comparison of the Importance of Identity in Different Sets of Regions

#### 2.6. Creation of Randomly Generated Identity Regions

#### Optimisation of a Set of Identity Regions

## 3. Results

#### 3.1. Influence of the Embedding of Identity Regions on the Expected Number of Migrants

#### 3.2. Comparison of Median $ICM$ Value Distributions

## 4. Discussion

#### 4.1. Effect on the Influence of the Distance Parameter

#### 4.2. Model Limitations

#### 4.2.1. Strong Geographical Identities Require Little Displacement

#### 4.2.2. Identity Regions

#### 4.3. Development of Identity Influence over Time

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

GLM | Generalised Linear Model |

ICM | Identity Comparison Measure |

NUTS | Nomenclature of Territorial Units for Statistics |

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**Figure 1.**Visual representation of the steps taken to assign municipalities to spatially clustered regions using the k-means algorithm. This algorithm can be applied to generate different numbers of regions. This number of regions is controlled by the variable k. To be able to compare the generated regions with a certain set of identity regions, this k is set equal to the number of regions present in this set of identity regions.

**Figure 2.**Difference between the expected number of migrants found in Equations (3) and (6)–(8). When two municipalities are located in the same identity region, the number of migrants in the basic gravity model is much lower than expected in the extended models, whereas this is the other way around for municipalities that are not located within the same region. The maximum distance travelled by migrants within the same region is cut to the reflect the size of the regions within each of the sets of regions.

**Figure 3.**Indexed changes in the predicted number of migrants between two municipalities with 50,000 residents that are located 50 km apart and the indexed changes in the exp($\iota $) value inside the model for each of the three sets of identity regions between 1996 and 2016. For every year, all municipalities were merged to form the municipalities that existed in 2016 to prevent the different numbers of municipalities from having any influences.

Intra-Municipal Migration | Inter-Municipal Migration | |
---|---|---|

Migration data | One CBS dataset [32] | Multiple CBS datasets [32] |

Distance data | Estimate: Distance between the centres of both municipalities | Estimate: $\sqrt{\frac{1}{2}|\varnothing |}$ |

Parameter | Description |
---|---|

$\alpha $ | Influence of ${p}_{a}$ on the number of migrants |

$\beta $ | Influence of ${p}_{b}$ on the number of migrants |

$\delta $ | Influence of ${\Delta}_{a\to b}$ on the number of migrants |

$\gamma =\mathrm{log}\left(G\right)$ | Normalisation constant of the regression function |

$\iota =\mathrm{log}\left(I\right)$ | Increase in the number of migrants when both municipalities are located in the same identity region |

${\Delta}_{a\to b}$ | Distance between municipality a and municipality b in kilometres |

${M}_{a\to b}$ | Number of migrants between municipality a and municipality b |

${p}_{a}$ | Population of municipality a |

${p}_{b}$ | Population of municipality b |

Data Set | Regions | Specification |
---|---|---|

NUTS 2 (Provinces) | 12 | [36] |

NUTS 3 (COROP regions) | 40 | [36] |

Historic regions | 70 | [38] |

**Table 4.**A comparison between the median $ICM$ values of the three different identity region configurations and the median $ICM$ value distributions of the same number of randomly generated spatially clustered regions, both optimised and non-optimised. Fifty samples were taken for distributions that involve the optimisation algorithm and 250 samples were taken for each of the non-optimised distributions that consist of randomly spatially clustered regions.

Predefined | Spatially Clustered | ||||
---|---|---|---|---|---|

95% CI | Max. | 95% CI | Max. | ||

NUTS 2 | Default | 12.34 | [12.60, 13.39] | 13.79 | |

Optimised | [13.02, 13.75] | 13.75 | [13.43, 14.24] | 14.38 | |

NUTS 3 | Default | 33.03 | [28.23, 33.33] | 34.23 | |

Optimised | [37.49, 39.12] | 39.12 | [36.88, 40.54] | 40.59 | |

Historic | Default | 42.34 | [40.11, 47.26] | 49.73 | |

Optimised | [54.48, 59.51] | 59.94 | [53.96, 61.83] | 62.05 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Vermeulen, W.R.J.; Roy, D.; Quax, R. Modelling the Influence of Regional Identity on Human Migration. *Urban Sci.* **2019**, *3*, 78.
https://doi.org/10.3390/urbansci3030078

**AMA Style**

Vermeulen WRJ, Roy D, Quax R. Modelling the Influence of Regional Identity on Human Migration. *Urban Science*. 2019; 3(3):78.
https://doi.org/10.3390/urbansci3030078

**Chicago/Turabian Style**

Vermeulen, Willem R. J., Debraj Roy, and Rick Quax. 2019. "Modelling the Influence of Regional Identity on Human Migration" *Urban Science* 3, no. 3: 78.
https://doi.org/10.3390/urbansci3030078