# A Modeling Framework: To Analyze the Relationship between Accessibility, Land Use and Densities in Urban Areas

^{*}

## Abstract

**:**

^{2}> 0.70) on a par with internationally accepted standards. The relationship was further elaborated through a decision tree analysis and 4D plot diagrams. Findings of the study can be utilized to model the density of a given land use and the correspondent accessibility scenarios. The proposed model is capable of quantifying the impact of the changes in the density correspondent to the accessibility and land use. Therefore, the study concludes that this will be an effective tool for decision-makers in the fields of land-use planning and transport planning for scenario building, impact analysis, and the formulation of land use zoning and urban development plans aiming at the overarching sustainability of future cities.

## 1. Introduction

## 2. Proposed Framework

#### 2.1. Conceptual Framework

#### 2.2. Quantifying Variable: Density, Accessibility, and Land Use

_{j}represents the ratio of the total sum of land area of the jth land-use type found in the analysis zone being analyzed and j is the number of land use types found in the zone.

_{i}represents CC values of the ith road-segment. d

_{ij}is the distance between “i” and “j” road-segments along the shortest-path. N is the sum of road-segments in a given road network. Additionally, the study utilized the road width to capture the mobility characteristics of accessibility [25].

_{i}represents the gross floor area (m

^{2}) of the ith building and A is the area of the urban block under computation.

_{i}represents the gross floor area (m

^{2}) of the building i, F

_{i}represents the number of floors of the ith building, and A represents the area of the zone under computation. Space matrix is a method to measure and present comprehensive ideas of the urban form density [26]. Space matrix utilizes 9 density categories based on the GSI, FAR, and L (refer Figure 3). The physical nature of these 9 categories is presented by google images on the right side of the Figure 3.

## 3. Materials and Methods

#### 3.1. Case Study Areas

#### 3.2. Data and Preparation

## 4. Results and Discussion

#### 4.1. Relationship among Accessibility, Land Use, and Density

#### 4.1.1. Result of the 4D Plot Diagram Analysis

#### 4.1.2. Result of the Decision Tree Analysis

#### 4.1.3. Regression Analysis

^{b}* RW

^{c}* LU

^{d}]

^{2}and mean absolute percent error (MAPE) to assess the goodness-of-fit when choosing the most appropriate model. Table 5 and Table 6 depict the statistics and specifications of the best model to estimate the density (D) for each case study. Models of all three case study areas recorded satisfactory level accuracy (i.e., R

^{2}> 0.70) which is an acceptable level of accuracy. Therefore, the study proposes that the developed models are suitable to model density in a given area based on land use and accessibility.

^{2}> 0.76) and out of the 750 zones, more than 78% recorded a very low level of error (low error = 10% difference). Figure 12a depicts the spatial distribution of actual density, modeled density, and error, and Figure 12b depicts the relationship between actual values and modeled values in a line plot.

^{2}> 0.72) in the Kurunegala case study area, and out of 148 zones, more than 81% recorded a very low level of error (Low error = 10% difference). Figure 13a depicts the spatial distribution of actual density, modeled density, and error, and Figure 13b depicts the relationship between actual values and modeled values in a line plot.

^{2}> 0.77) accuracy in the Mawanella case study area and out of 148 zones, more than 80% recorded a very low level of error (low error = 10% difference). Figure 14a depicts the spatial distribution of actual density, modeled density, and error, and Figure 14b depicts the relationship between actual values and modeled values in a line plot.

## 5. Conclusions and Recommendation

^{2}> 0.70) on a par with internationally accepted standards.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Batty, M. Urban analytics defined. Environ. Plan. B Urban Anal. City Sci.
**2019**, 46, 403–405. [Google Scholar] [CrossRef][Green Version] - Geurs, K.T.; Wee, V. Accessibility evaluation of landuse and transport strategies: Review and research directions. Transp. Geogr.
**2004**, 12, 127–140. [Google Scholar] [CrossRef] - Hellervik, A.; Nilsson, L.; Andersson, C. Preferential centrality a new measure unifying urban activity, attraction and accessibility. Urban Anal. City Sci.
**2019**, 46, 1331–1346. [Google Scholar] [CrossRef] - Bramley, G.; Kirk, K. Does planning make a difference in urban form? Recent evidence from Central Scotland. Environ. Plan. A
**2005**, 1–2. [Google Scholar] [CrossRef] - Marshall, A. Why Strategic Planning Fails to Produce Desired Results. In Proceedings of the Ninth International Space Syntax Symposium, Seoul, Korea, 31 October–3 November 2013; pp. 3–5. [Google Scholar]
- Jayasinghe, A.; Sano, K.; Rattanaporn, K. Application for developing countries: Estimating trip attraction in urban zones based on centrality. J. Traffic Transp. Eng.
**2017**, 4, 464–476. [Google Scholar] [CrossRef] - Lu, S.; Huang, Y.; Shi, C.; Yang, X. Exploring the Associations between Urban form and Neighborhood Vibrancy: A Case Study of Chengdu, China. Int. J. Geoinf.
**2019**, 8, 165. [Google Scholar] [CrossRef][Green Version] - Jang, M.; Kang, C. The effects of urban greenways on the geography of office sectors and employment density in Seoul, Korea. Urban Stud.
**2016**, 53, 1022–1041. [Google Scholar] [CrossRef] - Xiao, Y.; Webster, C. Urban Morphology and Housing Market; Springer Geography: Singapore, 2017. [Google Scholar]
- Batty, M. Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals; MIT Press: London, UK, 2017. [Google Scholar]
- Carlos, H.A. Density estimation and adaptive bandwidths: A primer for public health practitioners. Int. J. Health Geogr.
**2010**, 9, 9–39. [Google Scholar] [CrossRef] [PubMed][Green Version] - Jayasinghe, A.; Sano, K.; Abenayake, C.C.; Mahanama, P.K.S. A novel approach to model traffic on road segments of large-scale urban road networks. MethodsX
**2019**, 6, 1147–1163. [Google Scholar] [CrossRef] [PubMed] - Nes, A.V.; Pont, M.B.; Mashhoodi, B. Combination of space syntax with spacematrix and the mixed-use index. The Rotterdam south test case. In Proceedings of the Space Syntax Symposium, Santiago de Chile, Chile, 3–6 January 2012; pp. 1–29. [Google Scholar]
- Hillier, B.; Vaughan, L. The City as One Thing; UCL Discovery: London, UK, 2007. [Google Scholar]
- Paul, A. Understanding the influence of roadway configuration on traffic flows through a conventional traffic assignment model. J. Transp. Lit.
**2015**, 9, 40–44. [Google Scholar] [CrossRef] - Ratti, C. Urban texture and space syntax: Some inconsistencies. Environ. Plan. B Plan. Des.
**2004**, 31, 99–487. [Google Scholar] [CrossRef] - Talat, M. Accessibility, Infrastructure Provision and Residential Land Value: Modelling the Relation Using Geographic Weighted Regression in the City of Rajkot, India. Sustainability
**2020**, 12, 1–5. [Google Scholar] - Ye, Y.; Nes, A.V. Measuring urban maturation processes in Dutch and Chinese new towns: Combining street network configuration with building density and degree of landuse diversification through GIS. J. Space Syntax
**2013**, 4, 18–37. [Google Scholar] - Lee, S.; Yoo, C.; Seo, K.W. Determinant Factors of Pedestrian Volume in Different Land-Use Zones: Combining Space Syntax Metrics with GIS-Based Built-Environment Measures. Sustainability
**2020**, 12, 8647. [Google Scholar] [CrossRef] - Hillier, B. Space is the Machine: A Configurational Theory of Architecture Cambridg; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar]
- Omer, I.; Goldblatt, R. Spatial patterns of retail activity and street network structure in new and traditional Israeli cities. Urban Geogr.
**2016**, 37, 629–649. [Google Scholar] [CrossRef] - Frank, L.D.; Schmid, T.L.; Sallis, J.F.; Chapman, J.; Saelens, B.E. Linking objectively measured physical activity with objectively measured urban form: Findings from Smartraq. Am. J. Prev. Med.
**2005**, 117–125. [Google Scholar] [CrossRef] [PubMed] - Porta, S.; Latora, V.; Wang, F.; Rueda, S.; Strano, E.; Scellato, S.; Cardillo, A.; Belli, E.; Càrdenas, F.; Cormenzana, B. Street Centrality and the Location of Economic Activities in Barcelona. Urban Stud.
**2012**, 49, 1471–1488. [Google Scholar] [CrossRef][Green Version] - Freeman, L.C. Centrality in social networks conceptual clarification. Soc. Netw.
**1978**, 1, 215–239. [Google Scholar] [CrossRef][Green Version] - Macioszek, E.; Świerk, P.; Kurek, A. The Bike-Sharing System as an Element of Enhancing Sustainable Mobility—A Case Study based on a City in Poland. Sustainability
**2020**, 12, 3285. [Google Scholar] [CrossRef][Green Version] - Pont, M.B.; Haupt, P. Space, Density and Urban Form; NAi Publishers: Rotterdam, The Netherlands, 2009. [Google Scholar]

**Figure 1.**Relationship among movement, function, and configuration [18].

**Figure 10.**The relationship among road width, closeness centrality, land use, and density: (

**a**) study area Colombo (

**b**) study area Kurunegala, and (

**c**) study area Mawanella (note: Land use axis A = Amenities, C = Commercial, R = Residential, W = working, ACRW = Amenities + Commercial + Residential + Working, Density axis: LRP = low rise point, MRP = mid-rise point, HRP = high rise point, LRS = low rise strip, MRS = mid-rise strip, HRS = high rise strip, LRB = low rise block, MRB = mid-rise block, HRB = high rise block).

**Figure 12.**Density regression model result in Colombo: (

**a**) spatial distribution of model and actual density categories and (

**b**) relationship between actual values and model values.

**Figure 13.**Density regression model result in Kurunegala: (

**a**) spatial distribution of model and actual density categories and (

**b**) relationship between actual values and model values.

**Figure 14.**Density regression model result in Mawanella: (

**a**) spatial distribution of model and actual density categories and (

**b**) relationship between actual values and model values.

Attributes | Case Study Areas | Data Source | ||
---|---|---|---|---|

Colombo | Kurunegala | Mawanella | ||

Type of urban form | Polycentric | Monocentric | Linear city | Compiled by authors |

Settlement hierarchy | First order | Second order | Third order | National Physical Plan, Sri Lanka, 2010 |

Building density index | 0.73 | 0.53 | 0.35 | Compiled by authors |

Population density | 115 (p/ha) | 53 (p/ha) | 30 (p/ha) | Department of Census and Statistics, Sri Lanka, 2012 |

Variable | Index | Data Source | ||
---|---|---|---|---|

Colombo | Kurunegala | Mawanella | ||

Land use | Land use Mix | UDA, Colombo, 2014 | UDA, Kurunegala, 2017 | Bus terminal development project—Mawanella, UDA, Kegalle, 2018 |

Density | Floor area ratio | |||

Plot coverage | ||||

Building height | ||||

Accessibility | Centrality of road network | JICA, 2015 | ||

Road width | UDA, Colombo, 2017 |

No | Density Category | Density Code |
---|---|---|

01 | Low-rise point | LRP |

02 | Mid-rise point | MRP |

03 | High-rise point | HRP |

04 | Low-rise strip | LRS |

05 | Mid-rise strip | MRS |

06 | High-rise strip | HRS |

07 | Low-rise block | LRB |

08 | Mid-rise block | MRB |

09 | High-rise block | HRB |

Parameters | Colombo | Kurunegala | Mawanella |
---|---|---|---|

Correctly classified instances | 79.2% | 83.41 | 79.104% |

Incorrectly classified instances | 20.8% | 16.56 | 20.89% |

Kappa statistic | 0.71 | 0.73 | 0.705 |

Mean absolute error | 0.101 | 0.099 | 0.114 |

Relative absolute error | 29.28% | 25.78% | 39.21% |

Study Area | Model | R Square | Adjusted R Square | Std. Error of the Estimate | Change Statistics | ||||
---|---|---|---|---|---|---|---|---|---|

R Square Change | F Change | df1 | df2 | F Change | |||||

Colombo | 1 | 0.667 ^{a} | 0.667 | 1.25885 | 0.667 | 1499.642 | 1 | 748 | 0.000 |

2 | 0.746 ^{b} | 0.746 | 1.09988 | 0.079 | 232.833 | 1 | 747 | 0.000 | |

3 | 0.766 ^{c} | 0.765 | 1.05732 | 0.020 | 62.348 | 1 | 746 | 0.000 | |

Kurunegala | 1 | 0.606 ^{a} | 0.603 | 1.14860 | 0.606 | 224.444 | 1 | 146 | 0.000 |

2 | 0.687 ^{b} | 0.682 | 1.02790 | 0.081 | 37.303 | 1 | 145 | 0.000 | |

3 | 0.726 ^{c} | 0.720 | 0.96460 | 0.039 | 20.654 | 1 | 144 | 0.000 | |

Mawanella | 1 | 0.703 ^{a} | 0.699 | 0.65784 | 0.703 | 153.941 | 1 | 65 | 0.000 |

2 | 0.762 ^{b} | 0.755 | 0.59365 | 0.059 | 15.817 | 1 | 64 | 0.000 |

^{a}Predictors: (constant), closeness.

^{b}Predictors: (constant), closeness, LU.

^{c}Predictors: (constant), closeness, LU, Road Width.

^{d}Dependent variable: density.

Study Area | Model | Variables^{a} | Unstandardized Coefficients | Standardized Coefficients | t | Partial | Part | Significance | Collinearity Statistics | |
---|---|---|---|---|---|---|---|---|---|---|

B | Beta | Beta | VIF | |||||||

Colombo | 1 | (Constant) | −0.532 | 0.120 | −4.447 | 0.000 | ||||

Closeness | 1.168 | 0.030 | 0.817 | 38.725 | 0.817 | 0.817 | 0.000 | 1.000 | ||

2 | (Constant) | 1.679 | 0.129 | −13.045 | 0.000 | |||||

Closeness | 0.927 | 0.031 | 0.648 | 30.138 | 0.741 | 0.555 | 0.000 | 1.361 | ||

LU | 5.391 | 0.353 | 0.328 | 15.259 | 0.487 | 0.281 | 0.000 | 1.361 | ||

3 | (Constant) | 1.581 | 0.124 | −12.719 | 0.000 | |||||

Closeness | 0.802 | 0.034 | 0.561 | 23.912 | 0.659 | 0.429 | 0.000 | 1.751 | ||

LU | 4.001 | 0.383 | 0.243 | 10.460 | 0.358 | 0.185 | 0.000 | 1.726 | ||

Roa Width | 0.166 | 0.021 | 0.205 | 7.896 | 0.278 | 0.140 | 0.000 | 2.144 | ||

Kurunegala | 1 | (Constant) | −2.435 | 0.390 | −6.241 | 0.000 | ||||

Closeness | 1.355 | 0.090 | 0.778 | 14.981 | 0.778 | 0.778 | 0.000 | 1.000 | ||

2 | (Constant) | −2.340 | 0.350 | −6.694 | 0.000 | |||||

Closeness | 0.943 | 0.105 | 0.542 | 8.963 | 0.597 | 0.417 | 0.000 | 1.692 | ||

LU | 4.698 | 0.769 | 0.369 | 6.108 | 0.452 | 0.284 | 0.000 | 1.692 | ||

3 | (Constant) | −3.099 | 0.368 | −8.419 | 0.000 | |||||

Closeness | 0.849 | 0.101 | 0.488 | 8.414 | 0.574 | 0.367 | 0.000 | 1.767 | ||

LU | 3.814 | 0.748 | 0.300 | 5.103 | 0.391 | 0.223 | 0.000 | 1.815 | ||

Roa Width | 0.308 | 0.068 | 0.228 | 4.545 | 0.354 | 0.198 | 0.000 | 1.319 | ||

Mawanella | 1 | (Constant) | −0.242 | 0.313 | −0.775 | 0.441 | ||||

Closeness | 7.069 | 0.570 | 0.839 | 12.407 | 0.839 | 0.839 | 0.000 | 1.000 | ||

2 | (Constant) | 0.153 | 0.299 | 0.512 | 0.610 | |||||

Closeness | 4.846 | 0.759 | 0.575 | 6.381 | 0.624 | 0.389 | 0.000 | 2.182 | ||

LU | 1.858 | 0.467 | 0.358 | 3.977 | 0.445 | 0.243 | 0.000 | 2.182 |

^{a}. Dependent variable: density.

Case Study Area | Colombo | Kurunegala | Mawanella | |
---|---|---|---|---|

R^{2} | 0.76 | 0.72 | 0.77 | |

Partial | Land-use mix | 0.35 | 0.35 | 0.27 |

Closeness centrality | 0.59 | 0.56 | 0.67 | |

Road width | 0.35 | 0.38 | 0.32 | |

Part | Land-use mix | 0.185 | 0.223 | 0.141 |

Closeness centrality | 0.424 | 0.367 | 0.312 | |

Road width | 0.140 | 0.198 | 0.089 | |

(Partial^2)% | Land-use mix | 12% | 12% | 7% |

Closeness centrality | 35% | 31% | 45% | |

Road width | 12% | 14% | 10% | |

(Part^2)% | Land-use mix | 3.4 | 4.9 | 1.9 |

Closeness centrality | 17.9 | 13.4 | 9.7 | |

Road width | 1.9 | 3.9 | 0.79 |

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**MDPI and ACS Style**

Jayasinghe, A.; Madusanka, N.B.S.; Abenayake, C.; Mahanama, P.K.S. A Modeling Framework: To Analyze the Relationship between Accessibility, Land Use and Densities in Urban Areas. *Sustainability* **2021**, *13*, 467.
https://doi.org/10.3390/su13020467

**AMA Style**

Jayasinghe A, Madusanka NBS, Abenayake C, Mahanama PKS. A Modeling Framework: To Analyze the Relationship between Accessibility, Land Use and Densities in Urban Areas. *Sustainability*. 2021; 13(2):467.
https://doi.org/10.3390/su13020467

**Chicago/Turabian Style**

Jayasinghe, Amila, N. B. S. Madusanka, Chethika Abenayake, and P. K. S. Mahanama. 2021. "A Modeling Framework: To Analyze the Relationship between Accessibility, Land Use and Densities in Urban Areas" *Sustainability* 13, no. 2: 467.
https://doi.org/10.3390/su13020467