# Evaluation of the Space Syntax Measures Affecting Pedestrian Density through Ordinal Logistic Regression Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Materials and Methods

#### 3.1. AA and VGA Measures

#### 3.2. Determining the Most Proper Measure

^{2}, and (4) parallel lines. Model fitting examines −2 log-likelihood. A significant (p < 0.05) change in the −2 log-likelihood statistics between the baseline model and the final model indicates that the predictors were significant based on these tests [48]. Two types of the goodness of fit tests called Pearson chi-square, and deviance statistics evaluate the discrepancy between the current model and the full model. However, these tests are sensitive to empty cells. If there are many empty cells in the model, −2 log-likelihood is considered a more robust indicator than Pearson chi-square and deviance statistics [49,50]. Pseudo R

^{2}values are used to estimate the variance explained by the independent variable. When these values are closer zero, model fitting diminishes. Lower R

^{2}values do not prevent interpreting parameters. One of the assumptions underlying ordinal logistic regression is based on that the relationship between each pair of outcomes is the same. In other words, ordinal logistic regression assumes that the coefficients defining a relationship between the lowest and all higher categories of the response variable are the same as those that describe the relationship between the next lowest category and all higher categories. This is called the parallel lines assumption, and the chi-square test is used to test the validity of the assumption of parallelism. At the end of the regression analysis process, the test sensitivities of each ordinal logistic regression model created in this study were checked. The most suitable model reflecting the pedestrian density was determined according to the results of parameter estimation tables.

#### 3.3. Analysing the Effect of Master Plan

_{0}and H

_{a}. The t-value is used in the statistical evaluation of the test. The calculated t-value is compared with the corresponding value from the t distribution table for a selected confidence level. If the calculated t-value is higher than the critical value, H

_{0}is rejected. Rejection shows that means statistically differ from one another [42].

## 4. Results

#### 4.1. Calculated Values for Measures

#### 4.2. Ordinal Logistic Regression Analysis

^{2}tests were not evaluated because the data contained a large number of empty cells and sorting the models was unnecessary. All of the 16 models provided the assumption of parallel lines because of p > 0.05. When the fit values explaining the significance of the model were evaluated, the four models highlighted in gray in Table 5 were found statistically significant because of p < 0.05.

^{β}and w-values are used to interpret the effects of variables like ß-values. e

^{β}-value takes values less than one when ß-value is negative and greater than one when it is positive. A high ß coefficient for a variable indicates that its effect on the dependent variable is considerable. Briefly, AA integration in this model was more effective than the periods in explaining the pedestrian density.

^{β}-value is lower than one. The ß-value, e

^{β}-value, and w-value for $m{d}^{AA}$ were lower than the values of $in{t}_{HH}^{AA}$ has. These statistical results show that $m{d}^{AA}$ does not reflect pedestrian density as successful as $in{t}_{HH}^{AA}$ does.

^{β}-value, and w-value for choice. The results for periods variable are similar to the models established with $in{t}_{HH}^{AA}$ and $m{d}^{AA}$.

^{β}-value, and w-value for control. The results for periods variable are similar to the models established with $in{t}_{HH}^{AA}$, $m{d}^{AA}$ and $c{h}^{AA}$.

#### 4.3. Evaluation of Current and Master Plan Datasets

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Obs. Gates | $\mathit{i}\mathit{n}{\mathit{t}}_{\mathit{H}\mathit{H}}^{\mathit{A}\mathit{A}}$ | $\mathit{i}\mathit{n}{\mathit{t}}_{\mathit{r}\left(3\right)}^{\mathit{A}\mathit{A}}$ | $\mathit{i}\mathit{n}{\mathit{t}}_{\mathit{r}\left(6\right)}^{\mathit{A}\mathit{A}}$ | $\mathit{m}{\mathit{d}}^{\mathit{A}\mathit{A}}$ | $\mathit{c}{\mathit{h}}^{\mathit{A}\mathit{A}}$ | $\mathit{c}\mathit{o}{\mathit{n}}^{\mathit{A}\mathit{A}}$ |
---|---|---|---|---|---|---|

1 | 0.639 | 0.211 | 0.627 | 7.39 | 0 | 1 |

2 | 1.310 | 2.396 | 1.730 | 4.12 | 1219 | 4 |

3 | 1.063 | 2.081 | 1.526 | 4.84 | 306 | 3 |

4 | 1.527 | 3.339 | 2.117 | 3.67 | 4474 | 7 |

5 | 1.063 | 2.021 | 1.417 | 4.84 | 786 | 3 |

6 | 1.131 | 2.396 | 1.620 | 4.61 | 852 | 4 |

7 | 0.941 | 1.571 | 1.400 | 5.34 | 1051 | 2 |

8 | 0.759 | 2.081 | 1.451 | 6.38 | 407 | 3 |

9 | 0.906 | 1.833 | 1.289 | 5.51 | 538 | 3 |

10 | 0.992 | 1.379 | 1.175 | 5.12 | 785 | 2 |

11 | 1.201 | 2.212 | 1.456 | 4.40 | 2708 | 4 |

12 | 1.361 | 2.081 | 1.672 | 4.00 | 2309 | 3 |

13 | 1.015 | 1.896 | 1.364 | 5.02 | 1153 | 3 |

14 | 1.255 | 2.933 | 1.750 | 4.25 | 1411 | 6 |

15 | 1.319 | 3.476 | 1.820 | 4.09 | 2856 | 8 |

16 | 1.037 | 1.819 | 1.381 | 4.94 | 133 | 2 |

17 | 0.910 | 2.218 | 1.347 | 5.48 | 596 | 4 |

18 | 0.979 | 1.774 | 1.330 | 5.17 | 622 | 3 |

19 | 0.823 | 1.698 | 1.089 | 5.96 | 72 | 3 |

20 | 0.923 | 1.274 | 1.197 | 5.42 | 168 | 2 |

21 | 0.796 | 1.819 | 1.405 | 6.13 | 471 | 2 |

22 | 0.720 | 3.923 | 1.729 | 6.67 | 739 | 8 |

Obs. Gates | $\mathit{i}\mathit{n}{\mathit{t}}_{\mathit{H}\mathit{H}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{i}\mathit{n}{\mathit{t}}_{\mathit{T}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{i}\mathit{n}{\mathit{t}}_{\mathit{p}\mathit{v}\mathit{a}\mathit{l}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{m}{\mathit{d}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{c}\mathit{o}{\mathit{n}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{c}\mathit{n}{\mathit{t}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{c}\mathit{b}{\mathit{l}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{e}\mathit{n}{\mathit{t}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{r}\mathit{e}\mathit{n}{\mathit{t}}^{\mathit{V}\mathit{G}\mathit{A}}$ | $\mathit{c}{\mathit{c}}^{\mathit{V}\mathit{G}\mathit{A}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 16.0 | 1.0 | 1.36 | 1.7 | 7457 | 1.1 | 0.4 | 1.4 | 1.9 | 0.8 | |

2 | 17.1 | 1.0 | 1.49 | 1.7 | 8211 | 1.1 | 0.5 | 1.3 | 1.9 | 0.7 | |

3 | 14.0 | 1.0 | 1.24 | 1.8 | 8146 | 1.1 | 0.5 | 1.6 | 1.8 | 0.8 | |

4 | 16.0 | 1.0 | 1.35 | 1.7 | 7308 | 1.0 | 0.4 | 1.4 | 2.0 | 0.7 | |

5 | 10.9 | 0.9 | 0.95 | 2.0 | 3107 | 1.0 | 0.2 | 1.3 | 2.3 | 0.7 | |

6 | 10.8 | 0.9 | 0.93 | 2.1 | 2890 | 0.5 | 0.2 | 1.3 | 2.3 | 0.7 | |

7 | 12.5 | 0.9 | 1.06 | 1.9 | 2363 | 1.0 | 0.1 | 0.9 | 2.6 | 0.4 | |

8 | 10.1 | 0.9 | 0.86 | 2.2 | 1460 | 1.2 | 0.1 | 1.1 | 2.5 | 0.6 | |

9 | 14.5 | 1.0 | 1.25 | 1.8 | 6939 | 1.0 | 0.4 | 1.5 | 1.9 | 0.7 | |

10 | 17.0 | 1.0 | 1.46 | 1.7 | 7914 | 1.1 | 0.4 | 1.3 | 1.9 | 0.7 | |

11 | 16.8 | 1.0 | 1.43 | 1.7 | 7630 | 1.1 | 0.4 | 1.3 | 2.0 | 0.7 | |

12 | 18.0 | 1.0 | 1.53 | 1.7 | 8464 | 1.2 | 0.5 | 1.3 | 1.9 | 0.7 | |

13 | 13.0 | 0.9 | 1.10 | 1.9 | 4599 | 0.8 | 0.3 | 1.3 | 2.2 | 0.6 | |

14 | 13.5 | 0.9 | 1.17 | 1.9 | 6071 | 1.0 | 0.4 | 1.5 | 2.0 | 0.8 | |

15 | 10.7 | 0.9 | 0.90 | 2.1 | 1759 | 0.9 | 0.1 | 1.1 | 2.5 | 0.5 | |

16 | 10.1 | 0.9 | 0.87 | 2.2 | 2189 | 0.7 | 0.2 | 1.3 | 2.4 | 0.6 | |

17 | 11.8 | 0.9 | 1.02 | 2.0 | 3389 | 0.9 | 0.2 | 1.3 | 2.3 | 0.8 | |

18 | 9.5 | 0.9 | 0.81 | 2.3 | 675 | 0.3 | 0.0 | 1.0 | 2.7 | 0.5 | |

19 | 9.4 | 0.9 | 0.80 | 2.3 | 943 | 0.6 | 0.1 | 1.1 | 2.6 | 0.6 | |

20 | 14.2 | 0.9 | 1.22 | 1.8 | 7224 | 1.2 | 0.4 | 1.6 | 1.9 | 0.7 | |

21 | 10.0 | 0.9 | 0.86 | 2.2 | 1677 | 0.8 | 0.1 | 1.2 | 2.5 | 0.5 | |

22 | 10.8 | 0.9 | 0.93 | 2.1 | 1351 | 0.9 | 0.1 | 0.9 | 2.7 | 0.4 |

JNB | Class | Min. Limit | Max. Limit | Num. of Data | GVF |
---|---|---|---|---|---|

1st | low | 9 | 262 | 106 | 0.823 |

medium | 284 | 856 | 25 | ||

high | 2040 | 2040 | 1 | ||

2nd | low | 9 | 154 | 75 | 0.870 |

medium | 159 | 370 | 44 | ||

high | 414 | 676 | 10 |

Variables | Types | Classes | Num. of Data | Percentage | |
---|---|---|---|---|---|

Dependent | Pedestrian density | Ordinal | low | 75 | 56.8% |

medium | 44 | 33.3% | |||

high | 13 | 9.8% | |||

Independents | Periods | Nominal | T1(08:30–10:30) | 31 | 23.5% |

T2(10:30–12:30) | 40 | 30.3% | |||

T3(12:30–14:30) | 29 | 22.0% | |||

T4(14:30–16:30) | 32 | 24.2% | |||

Measures | Continuous | Covariates data (Table 1 and Table 2) | 100.0% |

Measures | Significance (p-Value) | |
---|---|---|

Model Fit | Test of Parallel Lines | |

$in{t}_{HH}^{AA}$ | 0.005 | 0.170 |

$in{t}_{r\left(3\right)}^{AA}$ | 0.095 | 0.841 |

$in{t}_{r\left(6\right)}^{AA}$ | 0.090 | 0.294 |

$m{d}^{AA}$ | 0.021 | 0.126 |

$c{h}^{AA}$ | 0.024 | 0.277 |

$co{n}^{AA}$ | 0.111 | 0.941 |

$in{t}_{HH}^{VGA}$ | 0.110 | 0.937 |

$in{t}_{T}^{VGA}$ | 0.106 | 0.941 |

$in{t}_{pval}^{VGA}$ | 0.107 | 0.939 |

$m{d}^{VGA}$ | 0.112 | 0.942 |

$co{n}^{VGA}$ | 0.102 | 0.940 |

$cn{t}^{VGA}$ | 0.037 | 0.776 |

$cb{l}^{VGA}$ | 0.776 | 0.940 |

$en{t}^{VGA}$ | 0.107 | 0.632 |

$ren{t}^{VGA}$ | 0.108 | 0.857 |

$c{c}^{VGA}$ | 0.107 | 0.183 |

Variables | Estimate (ß) | Wald (w) | Odds Ratio (e^{β}) | Significance (p) | |
---|---|---|---|---|---|

Dependent Variable | low | 1.967 | 4.680 | 0.031 | |

medium | 4.064 | 17.475 | 0.000 | ||

Independent Variables | $in{t}_{HH}^{AA}$ | 2.132 | 6.930 | 8.432 | 0.008 |

T1 | −0.966 | 3.546 | 0.060 | ||

T2 | −1.058 | 4.696 | 0.347 | 0.030 | |

T3 | −0.069 | 0.020 | 0.888 |

Variables | Estimate (ß) | Wald (w) | Odds Ratio (eβ) | Significance (p) | |
---|---|---|---|---|---|

Dependent Variable | low | −2.383 | 4.797 | 0.029 | |

medium | −0.321 | 0.088 | 0.766 | ||

InDependent Variables | $m{d}^{AA}$ | −0.416 | 4.256 | 0.660 | 0.039 |

T1 | −0.942 | 3.428 | 0.064 | ||

T2 | −1.069 | 4.861 | 0.343 | 0.027 | |

T3 | −0.092 | 0.035 | 0.852 |

Variables | Estimate (ß) | Wald (w) | Odds Ratio (e^{β}) | Significance (p) | |
---|---|---|---|---|---|

Dependent Variable | Low | 0.059 | 0.023 | 0.879 | |

medium | 2.117 | 22.033 | 0.000 | ||

InDependent Variables | $c{h}^{AA}$ | 0.000 | 3.398 | 0.065 | |

T1 | −0.949 | 3.493 | 0.062 | ||

T2 | −1.080 | 4.988 | 0.340 | 0.026 | |

T3 | −0.101 | 0.042 | 0.837 |

Variables | Estimate (ß) | Wald (w) | Odds Ratio (e^{β}) | Significance (p) | |
---|---|---|---|---|---|

Dependent Variable | low | −1.501 | 3.453 | 0.063 | |

medium | 0.545 | 0.456 | 0.499 | ||

InDependent Variables | $cn{t}^{VGA}$ | −1.273 | 2.639 | 0.104 | |

T1 | −0.915 | 3.311 | 0.069 | ||

T2 | −1.150 | 5.688 | 0.317 | 0.017 | |

T3 | −0.181 | 0.138 | 0.711 |

Years | Number of Axial Lines | Mean of the Integration | Paired Samples | Means | p-Value |
---|---|---|---|---|---|

2019 | 96 | 0.388 | 96 | 0.388 | 0.002 |

Master | 137 | 0.356 | 0.370 |

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**MDPI and ACS Style**

Hacar, Ö.Ö.; Gülgen, F.; Bilgi, S.
Evaluation of the Space Syntax Measures Affecting Pedestrian Density through Ordinal Logistic Regression Analysis. *ISPRS Int. J. Geo-Inf.* **2020**, *9*, 589.
https://doi.org/10.3390/ijgi9100589

**AMA Style**

Hacar ÖÖ, Gülgen F, Bilgi S.
Evaluation of the Space Syntax Measures Affecting Pedestrian Density through Ordinal Logistic Regression Analysis. *ISPRS International Journal of Geo-Information*. 2020; 9(10):589.
https://doi.org/10.3390/ijgi9100589

**Chicago/Turabian Style**

Hacar, Özge Öztürk, Fatih Gülgen, and Serdar Bilgi.
2020. "Evaluation of the Space Syntax Measures Affecting Pedestrian Density through Ordinal Logistic Regression Analysis" *ISPRS International Journal of Geo-Information* 9, no. 10: 589.
https://doi.org/10.3390/ijgi9100589