# Investigating Contextual Effects on Burglary Risks: A Contextual Effects Model Built Based on Bayesian Spatial Modeling Strategy

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## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

#### 2.2. Dependent Variables

#### 2.3. Independent Variables

## 3. Methodology

#### 3.1. Modeling Strategy

#### 3.2. Prior Specification

#### 3.3. Model Implementation

#### 3.4. Model Assessment

## 4. Results

#### 4.1. Deviance Summaries of the Models

#### 4.2. Analysis of Independent Variables and Variance Parameters

#### 4.3. Mapping the Risks

#### 4.4. Identifying and Mapping the Relative Contribution

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Burglary risks given by (

**a**) the conventional Bayesian spatial model and (

**b**) the contextual effect model.

**Figure 4.**Burglary risks due to (

**a**) unstructured contextual effects and (

**b**) spatially structured contextual effects.

**Figure 5.**Posterior probabilities of (

**a**) unstructured contextual effects and (

**b**) spatially structured contextual effects having positive impacts on neighborhood burglary risks.

${\mathbf{X}}_{1}$ | ${\mathbf{X}}_{2}$ | ${\mathbf{X}}_{3}$ | ${\mathbf{X}}_{4}$ | ${\mathbf{X}}_{5}$ | ${\mathbf{X}}_{6}$ | ${\mathbf{X}}_{7}$ | |
---|---|---|---|---|---|---|---|

${\mathrm{X}}_{1}$ | 1.00 | ||||||

${\mathrm{X}}_{2}$ | −0.17 * | 1.00 | |||||

${\mathrm{X}}_{3}$ | −0.10 | 0.02 | 1.00 | ||||

${\mathrm{X}}_{4}$ | 0.42 *** | −0.20 ** | −0.27 *** | 1.00 | |||

${\mathrm{X}}_{5}$ | −0.26 *** | 0.26 *** | −0.19 ** | 0.18 * | 1.00 | ||

${\mathrm{X}}_{6}$ | −0.19 ** | −0.01 | −0.13 | −0.22 ** | −0.03 | 1.00 | |

${\mathrm{X}}_{7}$ | −0.05 | −0.15 | −0.15 | −0.05 | −0.10 | −0.08 | 1.00 |

^{1}Variables from top (left) to down (right) respectively are population density, young males, high education, unemployment, bar density, department store density, and policing. ***, ** and * represent significant at 0.01, 0.05 and 0.1 level, respectively.

Conventional Bayesian Spatial Model | Contextual Effects Model | |
---|---|---|

$\overline{D}$ | 733.509 | 733.606 |

${p}_{d}$ | 107.550 | 107.368 |

DIC | 841.059 | 840.974 |

**Table 3.**The intercept term, regression coefficients, and variance parameters estimated by the two models.

Variables | Conventional Bayesian Spatial Model | Contextual Effects Model |
---|---|---|

Mean (95% CI) | Mean (95% CI) | |

Intercept | −0.3981 (−0.5509, −0.2471) | −0.3927 (−0.5691, −0.2142) |

Population density | −0.3597 (−0.5749, −0.1393) | −0.3639 (−0.5783, −0.1490) |

% of young males | 0.0225 (−0.1616, 0.2050) | 0.0148 (−0.1747, 0.2038) |

High education | −0.0427 (−0.2325, 0.1483) | −0.0408 (−0.2300, 0.1453) |

Unemployment | 0.0380 (−0.1793, 0.2508) | 0.0353 (−0.1852, 0.2522) |

Bar density | 0.3617 (0.1613, 0.5651) | 0.3636 (0.1674, 0.5617) |

Department store density | 0.1858 (0.0152, 0.3561) | 0.1830 (0.0146, 0.3538) |

Policing | 0.0154 (−0.1657, 0.1968) | 0.0114 (−0.1689, 0.1896) |

${\sigma}_{u}^{2}$ | 0.6251 (0.1879, 0.9301) | 0.6501 (0.3363, 0.9219) |

${\sigma}_{s}^{2}$ | 0.3041 (0.0002, 2.0700) | 0.1422 (0.0002, 1.1950) |

${\sigma}_{v}^{2}$ | NA | 0.0208 (0.0002, 0.1560) |

${\sigma}_{h}^{2}$ | NA | 0.0271 (0.0002, 0.2464) |

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**MDPI and ACS Style**

Liu, H.; Zhu, X.; Zhang, D.; Liu, Z.
Investigating Contextual Effects on Burglary Risks: A Contextual Effects Model Built Based on Bayesian Spatial Modeling Strategy. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 488.
https://doi.org/10.3390/ijgi8110488

**AMA Style**

Liu H, Zhu X, Zhang D, Liu Z.
Investigating Contextual Effects on Burglary Risks: A Contextual Effects Model Built Based on Bayesian Spatial Modeling Strategy. *ISPRS International Journal of Geo-Information*. 2019; 8(11):488.
https://doi.org/10.3390/ijgi8110488

**Chicago/Turabian Style**

Liu, Hongqiang, Xinyan Zhu, Dongying Zhang, and Zhen Liu.
2019. "Investigating Contextual Effects on Burglary Risks: A Contextual Effects Model Built Based on Bayesian Spatial Modeling Strategy" *ISPRS International Journal of Geo-Information* 8, no. 11: 488.
https://doi.org/10.3390/ijgi8110488