The supplementary material has a separate DOI generated from ResearchGate: DOI: 10.13140/RG.2.2.30599.4496

Sharmin, Tania

Steemers, Koen

English

De Montfort University Open Research Archive

Supplementary material Effects of microclimatic and human parameters on outdoor thermal sensation in the high-density tropical context of Dhaka Tania Sharmina,1  and Koen Steemers1 Study area  Figure 1. Overview of the case study area (a) South Kafrul (b) Mid Kafrul (c) Baridhara DOHS (d) Mahakhali DOHS, (e) Banani Commercial Area and (f) TSC Shahbagh The case study areas were selected on the basis of providing distinct “local climate zones” (Stewart and Oke, 2012) as explained in (Sharmin, Steemers and Matzarakis, 2015). The residential areas South Kafrul and Mid-Kafrul are traditional residential areas of “spontaneous urban development”, whereas, Mahakhali DOHS and Baridhara DOHS are “formally planned residential areas”. Banani Commercial Area is a “high-rise development” for commercial activity and TSC Shahbagh is a comparatively “low-density area” with educational establishments. The areas correspond to the climate zones described by Stewart and Oke (2012) as: ‘Compact mid-rise-traditional’(sub-class), ‘Compact mid-rise-formal’(sub-class) ‘Compact high-rise’ and ‘Open mid-rise’ respectively.                                                      1 The Martin Centre for Architectural and Urban Studies, Department of Architecture, University of Cambridge, 1-5 Scroope Terrace, CB2 1PX, Cambridge, United Kingdom. aCorresponding author: ts531@cam.ac.uk Table 1. Description of the sample Gender Age Body Type Activity Female 311 (24%) 30 - 50 487 38% Normal 971 76% Light walking 479 37% Male 975 (76%) Over 50     65 5% Obese  69 5% Moderate walking 20 2%   Below 16    47 4% Skinny 229 18% Sitting 131 10%   16 - 30 678 53% NA's   17 1% Standing, light work 636 49%   NA's        9 1%    NA's 20 2%  Body exposure to the sun Clothing (clo) Time living in Dhaka Profession  Profession type No 92% Min. 0.10 Above 5 years 76% Student 31% Indoor type 73% Yes 5% Median 0.50 Below 1 year 5% Office job 37% Outdoor type 26% NA's 2% Mean 0.50 Below 5 years 19% Business 7% NA's 1%   Max. 1.20 NA's 0% Housewife 6%  100%   NA's 11.00   (Other) 18%         NA's 1%    Exposure to air-conditioned space in the last 30min  Travelling in last 30min  Reason for being on the site No 71% No 79% Close to home, office, school or station 80% Yes 29% Yes 21% To take rest and enjoy environment (sunshine, breeze, nice view) 6%     For No particular reason 4%     For prayer 2%     (Other) 9%     NA's 0%   Ordinal Logistic Regression (OLR) The ordinal logistic regression is a form of logistic regression which is used to model the relationship of an ordinal dependent variable and a set of independent variables that are either categorical or continuous. In an ordinal logistic regression model, the outcome variable is ordered and has more than two levels. The distance between the levels is generally unknown (Christensen, 2011). In this study, the ordinal outcome variable is the thermal sensation vote (TSV), which is coded on a 7-point scale as: Cold = -3; Cool = -2; Slightly cool = -1; Neutral = 0; Slightly warm = 1; Warm = 2; Hot = 3. In ordinal regression, instead of modelling the probability of an individual event, as done in logistic regression, the probability of that event and all others below it in the ordinal ranking are considered. That means it deals with cumulative probabilities rather than probabilities for discrete categories. This process in logistic regression to deal with the ordinal response is known as the proportional odds model (Fitrianto and Maziatul, 2014). The odds are modelled as:  𝜃𝜃𝑗𝑗 =  𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗)1 − 𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗) (1)  The ordinal regression model can be expressed in the logit form as the following:  𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 [𝜃𝜃𝑗𝑗] = 𝑙𝑙𝑙𝑙 � 𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗)1 − 𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗)� =  𝛼𝛼𝑗𝑗 + (−𝛽𝛽1𝑋𝑋1 − 𝛽𝛽2𝑋𝑋2 − ⋯− 𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖)  (2) Here, P is the probability, Y is the ordinal variable, Y ≤ j | (X1, X2, …, Xi) is the probability of being at or below category j, given a set of predictors (X1, X2, …, Xi), j is the number of ranking of the dependent variable = j =1, 2, …, J−1, αj are the cut-points and β1, β2, …, βi are logit coefficients.  By exponentiation of Equation (8) the following equation can be found:  �𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗)1 − 𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗)� =  𝑒𝑒𝛼𝛼𝑗𝑗 +(−𝛽𝛽1𝑋𝑋1−𝛽𝛽2𝑋𝑋2−⋯−𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖) =  𝑒𝑒𝛼𝛼𝑗𝑗 −∑𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖  => 𝑃𝑃(𝑌𝑌 ≤ 𝑗𝑗) =  𝑒𝑒𝛼𝛼𝑗𝑗 −∑𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖1 + 𝑒𝑒𝛼𝛼𝑗𝑗 −∑𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖 =   11 + 𝑒𝑒−(𝛼𝛼𝑗𝑗 −∑𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖)   (3) In the model, each logit has its own 𝛼𝛼𝑗𝑗 which is called the threshold value and its values do not depend on the values of the independent variable for a particular case. The model has the same effects 𝛽𝛽𝑖𝑖𝑋𝑋𝑖𝑖 for each logit. The equal logit slope or the proportional odds assumption (the assumption of the same coefficients across all cut-points/ thresholds) must be tested before applying an ordinal regression. In this study, the proportional odds assumption was tested by the method suggested in Agresti (2010) and is determined by chi-square test statistics before conducting each ordinal regression analysis. The probability of each category was determined: P(Y≤  −1), P (Y≤ 0), P(Y≤  1), P(Y≤  2) and P(Y≤  3), with P (Y≤ 3) =1, as per the condition of cumulative probability. While determining the category of each response, the category with the highest probability was chosen. For example, if the probability of a respondent feeling ‘Slightly cool’, ‘Neutral’, ‘Slightly warm’, ‘Warm’ or ‘Hot’ are 0.012 (1%), 0.141 (14%), 0.407 (41%), 0.289 (29%) and 0.151(15%) respectively, then the respondent is considered to belong in the ‘Slightly warm’ category with the highest probability of 41%. The probability of each category is predicted by the difference of the cumulative probability of each consecutive category. For example, P (Y≤ 3) is the cumulative probability of the earlier four categories plus its own (-1, 0, 1, 2 and 3). Therefore, P (3) =P (≤3)-P (≤2). To understand the process, OLR was carried out with a single predictor variable air temperature first. The coefficients and standard errors can be found in Table 2. Table 2. TSV_predicted ordinal single meteorological model Parameters Coefficients Standard error  Further model parameters Slightly cool=−1 10.799 0.927  Pseudo R2 0.229   Neutral=0 13.495 0.912  gamma 0.524   Slightly warm = 1 15.448 0.933  std. error 0.031   Warm=2 16.936 0.952  CI 0.463 - 0.584 Hot=3 0.000    cor.test 0.380   Air temperature 0.478 0.029      CI (2.5%, 97.5%) 0.422 - 0.535      Exponentiated Coefficient/ odds ratio 1.612        Figure 2. Probability diagram of air temperature against TSV2 The probability diagram for the ordinal single meteorological model can be seen in Figure 2. As the temperature increases, the probability of feeling ‘Slightly cool’ decreases and                                                      2 Since there was no response in ‘Cool’ (-2) and ‘Cold’ (-3) categories, these are not presented in the figure. Probability Air temperature, 0C reaches P (probability) = 0 at 35.00C. This means the probability of feeling ‘Slightly cool’ becomes zero at 35.50C. Likewise, the probability of feeling ‘Hot’ increases when air temperature exceeds 30.00C and reaches P (probability) = 1 at 45.00C. The probability of feeling ‘Neutral’, ‘Slightly warm’ and ‘Warm’ reaches highest levels at 26.00C, 31.00C and 35.00C respectively. The odds ratio, that is simply the inverse log (i.e. the exponential) of the estimated coefficient, can be read from Table 2. The interpretation of the odds ratio is that, groups greater than j versus those who are in groups less than or equal to j are compared, where j is the level of the response variable. This means that for a one-unit change in the predictor variable, the odds for cases in a group that is greater than j versus less than or equal to j are the proportional odds times larger. For example, when air temperature moves 1 unit, the odds of TSV being in the ‘Hot’ category are 1.612 times greater than TSV being in ‘Warm’ and lower category.  Bibliography Agresti, A. (2010) ‘Modeling Ordinal Categorical Data’, pp. 1–75. Available at: http://www.stat.ufl.edu/~aa/ordinal/agresti_ordinal_tutorial.pdf. Christensen, R. (2011) ‘Analysis of ordinal data with cumulative link models—estimation with the ordinal package’, R-package version, pp. 1–31. Available at: http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Analysis+of+ordinal+data+with+cumulative+link+models+?+estimation+with+the+R+-package+ordinal#0. Fitrianto, A. and Maziatul, M. I. (2014) ‘Modeling employments rate data using ordinal logistic regression’, Middle - East Journal of Scientific Research, 20(12), pp. 1715–1720. doi: 10.5829/idosi.mejsr.2014.20.12.21085. Sharmin, T., Steemers, K. and Matzarakis, A. (2015) ‘Analysis of microclimatic diversity and outdoor thermal comfort perceptions in the tropical megacity Dhaka , Bangladesh’, Building and Environment. Elsevier Ltd, 94(November), pp. 734–750. doi: 10.1016/j.buildenv.2015.10.007. Stewart, I. D. and Oke, T. R. (2012) ‘Local climate zones for urban temperature studies’, Bulletin of the American Meteorological Society, 93(12), pp. 1879–1900. doi: 10.1175/BAMS-D-11-00019.1.   

Supplementary material for: Effects of microclimatic and human parameters on outdoor thermal sensation in the high-density tropical context of Dhaka

https://www.dora.dmu.ac.uk/bitstream/handle/2086/17933/Supplementary%20material.pdf?sequence=1&isAllowed=y

Supplementary material for: Effects of microclimatic and human parameters on outdoor thermal sensation in the high-density tropical context of Dhaka

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