Steps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices

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1 Steps for Computng the Dssmlarty, Entropy, Herfndahl-Hrschman and Accessblty (Gravty wth Competton) Indces I. Dssmlarty Index Measurement: The followng formula can be used to measure the evenness between resdental use and non-resdental land uses. D = 0.5 n = 1 X Y Ths mplementaton of the ndex, D N, examnes the dstrbuton of land uses at subneghbourhood level (.e., a grdcell) and provdes an estmated of ts smlarty to the dstrbuton pattern at the neghbourhood level. We denote n as the number of grds n the neghbourhood, X as the rato of the resdental area n grd to the resdental area n the neghbourhood, and Y as the rato of the non-resdental area n grd to the nonresdental area n the neghbourhood. The frst step to operatonalze ths ndex s to dvde the neghbourhoods nto grdcells wth user-defned unform sze whch are consdered sub-neghbourhoods. Then the comparson of the dstrbuton of land uses wthn each of the grds to the neghbourhood as a whole can be made. The ndex of dssmlarty equals to 0 f dstrbuton of land uses wthn each grd s smlar to the dstrbuton at the neghbourhood level,.e., the proportons of the resdental and nonresdental land uses wthn each of the grds are dentcal to the proportons at the

2 neghbourhood level respectvely. The ndex equals to 1 f there are ether only resdental land uses, or there are only non-resdental land uses wthn each of the grds. NOTE: Ths measure s dfferent from Cervero s dssmlarty ndex measure. See Song and Rodríguez for detals. Steps of Computaton: 1. Decde to whch neghbourhood each taxlot belongs: a. Convert the taxlot polygons nto centrods by usng XTool; b. Spatal jon the neghbourhood polygons and the taxlot centrods so that each taxlot would be assgned wth a neghbourhood ID and all taxlot centrods that are nsde a neghbourhood wll have the same neghbourhood ID; 2. Construct grds whch would ntersect wth the study area: a. create grds wth user-defned sze by usng Coordnate Grd Maker ArcVew scrpt whch can be downloaded from ESRI s webste; 3. Assgn each taxlot by grd: a. Spatal jon the grd (polygon) shape fle and the taxlot centrods (pont) shape fle so that all taxlot centrods that are nsde a grd cell wll have the same grd cell ID; 4. Calculate total area of resdental uses for each grd cell by summarzng the table of taxlot centrods shape fle based on the grd cell ID. You would obtan a table

3 wth the grd cell ID as the key. Each grd cell also has a neghbourhood ID ndcatng the neghbourhood to whch the grd cell belongs. 5. Calculate total area of non-resdental uses for each grd cell by summarzng the table of taxlot centrods shape fle based on the grd cell ID. You would obtan a table wth the grd cell ID as the key. Each grd cell also has a neghbourhood ID ndcatng the neghbourhood to whch the grd cell belongs. 6. Based on the common grd cell ID, combne the table created from step 4 and the table created from step 5 nto a sngle table. The resulted new table ncludes the followng felds: grd cell ID (key), resdental area by each grd cell, nonresdental area by each grd cell, and neghbourhood ID. 7. Usng the attrbute table of taxlot centrods, calculate total resdental area by each neghbourhood by summarzng resdental area based on neghbourhood ID. Ths would result a table wth neghbourhood ID as the key. 8. Usng the attrbute table of taxlot centrods, calculate total non-resdental area by each neghbourhood by summarzng non-resdental area based on neghbourhood ID. Ths would result a table wth neghbourhood ID as the key. 9. Based on the common grd cell ID, combne the table created from step 7 and the table created from step 8 nto a sngle table. The resulted new table contans the followng felds: neghbourhood ID (key), resdental area by each neghbourhood, and non-resdental area by each neghbourhood. 10. Based on the common neghbourhood ID, jon the table created from step 9 to the table created from step 6. In addton to the exstng felds n the table created

4 from step 6, the new table wll also have nformaton on total area of neghbourhood resdental and non-resdental uses by each grd cell. 11. In the table created from step 10, dvde total resdental area n grd cell by total resdental area n neghbourhood. A new feld contanng the nformaton on the rato s added to the table. 12. In the table created from step 11, dvde total non-resdental area n grd cell by total non-resdental area n neghbourhood. A new feld contanng the nformaton on the rato s added to the table. 13. Calculate the dfference between the two ratos obtaned from step 11 and 12 and add the new feld - rato dfference - to the table. 14. Calculate Dssmlarty Index: a. Use the table created from step 13 to summarze the grd cell rato dfferences by neghbourhood ID; b. Dvde the summarzed total dfferences by 2 for each neghbourhood. Ths s the value of dssmlarty ndex for each neghbourhood. II. Entropy measures The entropy ndex (Shannon Index) s commonly calculated through the followng formula: k Entropy = { [( p )(ln p )]}/(ln k)

5 Researchers n varous felds have mplemented ths measure n multple ways to examne the dsperson of objects at nterests. Examples nclude: Measurement: To examne the dstrbuton pattern of dfferent land uses wthn a neghbourhood, the ndex spells out that p =proportons of each of the sx land use types such as sngle famly resdental, mult-famly resdental, commercal, ndustral, publc nsttutonal and park uses, and s=the number of land uses. In ths case, s=6 (Song and Knaap, 2004). Steps of Computaton: 1. Decde to whch neghbourhood each taxlot belongs: a. Convert the taxlot polygons nto centrods by usng XTool; b. Spatal jon the neghbourhood polygons and the taxlot centrods so that each taxlot would be assgned wth a neghbourhood ID and all taxlot centrods that are nsde a neghbourhood wll have the same neghbourhood ID; 2. Calculate the total area of each of the sx land use types n each neghbourhood: a. Usng the taxlot centrods attrbute table, summarze the area of taxlots by each land use type and by neghbourhood ID. The resulted table ncludes the followng felds: neghbourhood ID, land use type, and the total area by land use type.

6 3. Calculate total area of all land uses n each neghbourhood: a. Usng the taxlot centrods attrbute table, summarze the area of taxlot by neghbourhood ID. 4. Based on the common neghbourhood ID, jon the table created from step 3 to the table created from step 2. The new table ncludes the followng felds: Neghbourhood ID, land use type, area by land use type, and total neghbourhood area. 5. Usng the table created from step 4, dvde the area of each sngle land use type by total neghbourhood area. New felds proportons of each land use type ( ) are added to the table. p 6. Calculate p )(ln p ) and create the new felds wth the values. ( 7. Calculate { k [( p )(ln p )]}: Summarze the feld ( p )(ln p ) for all 6 land use types by neghbourhood ID and create new felds. 8. Fnally calculate entropy ndex for each neghbourhood usng the formula: k Entropy = { [( p )(ln p )]}/(ln k). III. Herfndahl-Hrschman Index (HHI) Followng the same notaton as the entropy ndex, the formula of calculatng HHI among k uses of land s: K HHI ( k) = ( = 1 P *100) 2

7 where p s the percentage of each type of land use n the neghbourhood, and K s the number of land use types. Steps of Computaton: 1. Usng the table created from step 4 n the entropy ndex, dvde the area of each sngle land use type by total neghbourhood area. New felds proportons of each land use type ( p ) are added to the table. 2. For each newly created feld n step 1, calculate ( ) 2 wth these new values. p 100 and create new felds K 2 3. Calculate ( P *100) : Summarze the feld created n step 2, ( p ) 2 *100, for all = 1 k land use types by neghbourhood ID and create new felds. IV. Gravty-based Measure wth Competton Measurement: AG = n A d j m j= 1 k = 1 d β j β kj where

8 AG = accessblty of resdental land use (e.g., house unts or neghbourhoods) to nonresdental land use (e.g., non-resdental land parcels or actvty centres) j A j = attractveness of non-resdental land use j, n ths case, t s measured by floorspace of retalng stores dj or = dstance from resdental use, or housng unt k, to non-resdental use j d kj β j β d kj d or = mpedance functon based on the nverse power functon β = dstance decay parameter n = number of one type of non-resdental land uses m = number of resdental land uses For example to calculate sngle-famly household s accessblty to retalng, there are n commercal retal stores and m houses n the study area. AG s the accessblty level of household to retal servces. Servce supply s measured by the floor space of retal stores. In other words, f a certan store provdes more floor space, t s assumed that store has a larger capacty for goods and customers, and therefore provdes a hgher level of accessblty to area resdents. Ths supply capacty s weghted by the dstance that an ndvdual customer has to travel. If the store s farther from home, household members are less wllng to take a trp to that store, and therefore that establshment provdes a lower level of accessblty.

9 Steps of Computaton: 1. Import the attrbute table of sngle famly taxlots to Mcrosoft Access database named as db1.mdb and name the table as SFR. 2. Import the attrbute table of commercal stores to db1.mdb database and name the table as STORE. 3. Create a new table named as RES to store the nformaton on dstances and store floorspaces. Modfy the table by applyng the developed C++ program. 4. Create a new table named as NEWSTORE to store the nformaton on the summaton of dstances among sngle famly housng unts to commercal stores. Apply the developed C++ program to obtan the values. 5. Create a new table named as ACCESS to store the fnal values of the ndex. Apply the developed C++ program to obtan the fnal values. Note: You need Mcrosoft Vsual C++ along wth ADO to run the developed C++ program. The code snppet s avalable upon request.

Air Transport Demand. Ta-Hui Yang Associate Professor Department of Logistics Management National Kaohsiung First Univ. of Sci. & Tech.

Air Transport Demand. Ta-Hui Yang Associate Professor Department of Logistics Management National Kaohsiung First Univ. of Sci. & Tech. Ar Transport Demand Ta-Hu Yang Assocate Professor Department of Logstcs Management Natonal Kaohsung Frst Unv. of Sc. & Tech. 1 Ar Transport Demand Demand for ar transport between two ctes or two regons