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Geography - Applied Geomatics (GEOG*4480*w18)
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Objective 2

Create a GIS model: determine the type of model, devise a process to weigh factors, and design a model.

Through literature reviews, a Multi Criteria Evaluation (MCE) was determined to be the most fitting way to achieve the intended goal. A similar study conducted in Florida to determine placement of a railway station used Weighted Linear Combination (WLC)  (Rosenberg and Esnard, 2008). Since transit is being assessed in this study, it is advisable to use the same method. A WLC is often incorporated into MCEs as an initial step, and part of a larger process, so it is believed that an MCE will produce a more complex and informative result. 

To generate the criteria and constraint layers, the socioeconomic data is tabulated, extracted, and joined to the census tract shape file, linking their boundaries. They are then applied into a series of calculations that are crucial to an MCE, as expressed by the tables below. Table 1 explains the logistics of a pairwise comparison. A nine-point scale is typically used in such scenarios to conceptualize the importance of one criteria over another (Bonnycastle, Yang, and Mersey, 2014). Table 2 displays the actual rankings given to each of the criteria in this study over one another. For example, the criteria 'Density' is given a 3-1 ranking over 'Median Income', meaning that the population density of a census tract is moderately more important to this study than the census tract's median income. The sum of the relative ranking is calculated vertically on the bottom of the table for each respective criterion. The relative rankings in each cell are then divided by the sum of their column, and then the mean is calculated horizontally in order to dermine the final weight each criterion, as demonstrated by Table 3. These weights are what determine the overall strength of each criterion in the analysis.

Table 1. Pairwise Table for Relative Comparisons

1/9 1/7 1/5 1/3 1 3 5 7 9
Extremely Very Strongly Strongly Moderately Equally Moderately Strongly Very Strongly  Extremely

 

 

 

 

Table 2. Relative Pairwise Rankings 

  Median Income Immigration Minority Children Youth Adult Mature Senior Density PostSecondary 
Median Income 1 3 3 9 9 0.33 7 9 0.33 3
Immigration 0.33 1 1 9 7 0.2 5 7 0.14 0.2
Minority 0.33 1 1 9 7 0.5 3 7 0.11 0.14
Children 0.11 0.11 0.11 1 0.14 0.11 0.11 0.33 0.11 0.11
Youth 0.11 0.14 0.14 7 1 0.11 0.33 1 0.11 0.11
Adult 3 5 5 9 9 1 7 9 0.33 0.33
Mature 0.14 0.2 0.33 9 3 0.14 1 5 0.14 0.14
Senior 0.11 0.14 0.14 3 1 0.11 0.2 1 0.11 0.11
Density 3 7 9 9 9 3 7 9 1 3
Post Secondary  0.33 5 7 9 9 3 7 9 0.33 1
Sum 8.49 22.60 26.73 74 55.14 8.51 37.64 57.33 2.73 8.15

 

Table 3.  Individual Weights Calculation

  Median Income Immigration Minority Children Youth Adult Mature Senior Density Post Secondary  Weights
Median Income 0.118 0.1328 0.112 0.121 0.163 0.039 0.186 0.157 0.122 0.368 0.152
Immigration 0.039 0.044 0.037 0.121 0.127 0.024 0.133 0.122 0.052 0.023 0.072
Minority 0.039 0.044 0.037 0.121 0.127 0.059 0.079 0.122 0.041 0.018 0.069
Children 0.013 0.005 0.004 0.013 0.003 0.013 0.003 0.006 0.041 0.014 0.011
Youth 0.013 0.006 0.005 0.094 0.018 0.013 0.009 0.017 0.041 0.014 0.023
Adult 0.354 0.221 0.187 0.121 0.163 0.118 0.186 0.157 0.122 0.041 0.167
Mature 0.017 0.009 0.013 0.121 0.054 0.017 0.027 0.087 0.052 0.018 0.041
Senior 0.013 0.006 0.005 0.040 0.018 0.013 0.005 0.017 0.041 0.014 0.017
Density 0.354 0.309 0.337 0.121 0.163 0.353 0.186 0.157 0.366 0.368 0.271
Post Secondary 0.039 0.221 0.261 0.121 0.163 0.353 0.186 0.157 0.122 0.123 0.175
                       
Sum 1 1 1 1 1 1 1 1 1 1 1

 

Due to the amount of factors that were considered, it is helpful to use a consistency ratio to ensure the weights make sense logically (Bonnycastle, 2018). Table 4 shows the information used to calculate the consistency ratio. If the final number is less than 0.10, then the ranks given have a consistent ratio. The final calculated value is 0.06 so the ranks are weighted correctly relative to each other. 

Table 4. Consistency Ratio 

  Weights*Sum  Consistency Vector
Median Income 1.288 10.115
Immigration 1.638 7.957
Minority  1.839 7.083
Children 0.846 15.388
Youth 1.275 10.222
Adult 1.422 9.167
Mature 1.561 8.349
Senior 0.995 13.093
Density 0.741 17.580
Post Secondary  1.425 9.147
     
Sum 13.031 108.101

Average of Vectors 10.810

Consistency Index = (average - n) / (n - 1) = 0.090008

Random Inconsistency Index (Constant) = 1.49

Consistency Ratio = CI / RI = 0.060408

The consistency ratio shows that the ranks are consistent if the output value is lower than 0.10, therefore the calculated ranks are consistent.

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