Waste Management 126 (2021) 454–465 Contents lists available at ScienceDirect Waste Management journal homepage: www.elsevier.com/locate/wasman Identification of inference fallacies in solid waste generation estimations of developing countries. A case-study in Panama Jorge M. Torrente-Velásquez a,b,⇑, Maddalena Ripa a, Rosaria Chifari c, Mario Giampietro a,d a Institut de Ciència i Tecnologia Ambientals, Universitat Autònoma de Barcelona, Bellaterra, Spain b Universidad Tecnológica de Panamá, Panamá c Fundació ENT, Barcelona, Spain d Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain a r t i c l e i n f o a b s t r a c t Article history: The absence of sound sampling procedures and statistical analyses to estimate solid waste generation in Received 27 December 2019 many developing countries has resulted in incomplete historical records of waste quantity and composi- Revised 21 December 2020 tion. Data is often arbitrarily aggregated or disaggregated as a function of waste generators to obtain Accepted 22 March 2021 results at the desired spatial level of analysis. Inference fallacies arising from the generalization or indi- Available online 7 April 2021 vidualization of results are almost never considered. In this paper, Panama, one of the fastest-growing developing countries, was used as a case-study to review the main methodological approaches to esti- Keywords: mate solid waste generation per capita per day, and at different hierarchical levels (from households Solid waste generation intensity Estimation to the country). The solid waste generation intensity indicator is used by the Panamanian waste manage- Multilevel analysis ment authority to run the waste management system. It was also the main parameter employed by local Inference fallacies and foreign companies to estimate solid waste generation in Panama between 2001 and 2008. The Meta-analysis methodological approaches used by these companies were mathematically formalized and classified as Developing countries per the expressions suggested by Subramanian et al. (2009). Seven inference fallacies (ecological, individ- Panama ualistic, stage, floating population, linear forecasting, average population and mixed spatial levels) were identified and allocated to the studies. Foreign companies committed three of the seven inference falla- cies, while one was committed by the local entity. Endogenous knowledge played an important role in these studies to avoid spatial levels mismatch and multilevel measurements appear to produce more reli- able information than studies obtained via other means. Ó 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/). 1. Introduction ronmental impact due to the implementation of ineffective mea- sures (Buenrostro et al., 2001). Waste generation rates are rising. There are currently about 2 Common methodological shortcomings of SWG studies per- billion metric tons of municipal solid waste produced annually formed in developing countries include: uncertainty on the exact worldwide. The World Bank (2018a) estimates overall solid waste number of inhabitants generating waste in certain locations, generation (SWG) will increase to 3.4 billion metric tons by 2050. unrepresentative samples of inhabitants to represent large popula- Most of this solid waste will be generated from developing coun- tions, misallocation of population belonging to certain spatial tries due to their increasing population, economic growth and levels, SWG data collection from multiple unreliable sources, rapid urbanisation (Zohoori and Ghani, 2017). incomplete historical record of quantity and quality of SWG, and Accurate data is required to have a deeper understanding of use of old SWG data as updated data (Afon and Okewole, 2007; SWG behaviour in order to implement sustainable and feasible Wilson and Velis, 2014). waste management policies (Bandara et al., 2007). Failure of sound To mitigate these fallibilities, the SWG in developing countries SWG sampling and analysis may either over or under estimate the is commonly obtained from the solid waste generation intensity required capacity of waste treatment facilities and increase envi- (SWGI) indicator. The SWGI is the daily SWG of a determined spa- tial level or place, e.g. country, region, city, averaged over its ⇑ Corresponding author at: Institut de Ciència i Tecnologia Ambientals, Univer- population. sitat Autònoma de Barcelona, Bellaterra, Spain. This indicator normalizes SWG per capita thus allowing its E-mail address: jorgemiguel.torrente@uab.cat (J.M. Torrente-Velásquez). comparison among different places of equivalent spatial level https://doi.org/10.1016/j.wasman.2021.03.037 0956-053X/Ó 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 (Linster, 2003). However, benchmarking this value among non- studies performed in Panama, displays typologies of SWGI estima- equivalent spatial levels generates inconsistencies in SWG studies tions and identifies inference fallacies derived from their misuse. and potentially makes solid waste management (SWM) plans tech- Section 3 classifies the typology of SWGI estimated values from nically unfeasible and economically unviable (DEFRA, 2013). Con- the SWG studies presented. It compares these values among them sequences are that SWM plans in developing countries are and against literature and discloses inference fallacies perpetrated seldom implemented. Methodological approaches behind results by each analysed study. Finally, Section 4 concludes by discussing are never publicly disclosed due to constraints of data disclosure, the uncertainties and the lessons learned from this study. imposed by companies performing SWG studies. These studies become obsolete, new ones are then performed and the same pat- 2. Materials & methods tern is repeated (Voss et al., 2013). Inconsistencies derived from benchmarking SWGI values This section outlines the extent to which skewed multi-level among non-equivalent spatial levels are mostly due to the miscon- population distribution produces self-similar SWGI estimations ception of the unit of observation and the unit of analysis. The unit when approaching from broader spatial levels e.g. country- to of observation is at the level at which one observes, measures or more individual ones e.g. inhabitants. Panama serves as the case- collect the data. The unit of analysis is at the spatial level about study area. one wish to say something, i.e., the focal level of the study. These It also presents common SWG sampling approaches and intro- levels can be the same, but they need not be. For instance, when duces the measurement level as an intermediate spatial level to data exists only at the municipal level and the objective is to estimate SWGI values at the analysis level from values obtained understand the SWG behaviour of individuals, inferences may be at the observation level. It goes further to show how SWGI is drawn from the disaggregation of the data available. In this scenar- locally estimated, how precise estimations are carried out within io, known as cross-level inference, a mismatch of observation and SWG studies and their mathematical formalization. Finally, it high- analysis levels occurs, thus potentially creating inference errors or lights typologies of SWGI estimations and fallacies derived from fallacies (Alker Jr., 1974; Blakely and Woodward, 2000). their misuse. Inference fallacies are properly documented in epidemiology since Robinson’s study made a seminal contribution by demon- strating that correlations for the same two variables can be differ- 2.1. Study area and SWGI self-similarity as per population distribution ent depending on the level at which they are analysed (Robinson 1950). As indicated by Molina-Azorín et al. (2019), most data come In the past decade, Panama has been one of the fastest-growing from phenomena where subjects form nested hierarchies. In this economies worldwide (INEC, 2016) and the highest Economic regard, there are two ways to study nested data: aggregation (ob- Annual Growth Rate country of Latin-America (IMF, 2018). In July taining data at a lower level and combining the values of those 2018, Panama was re-classified from the upper-middle to the high- variables to the higher level) and disaggregation (data from income level group of countries by the World Bank (2018b). This in higher-level units are disaggregated into data on a larger number itself is an indicator of economic affluence. The fast-increasing eco- of lower-level units). Either of these two strategies may produce nomic transition sharply contrasts with Panama’s archaic waste errors when conclusions are drawn at the wrong level (Molina- management system struggling to react to the SWG derived from Azorín et al., 2019). unsteady resource consumption habits (JICA, 2005; Ragossnig The error due to aggregation is known as the ‘ecological fallacy’. and Vujić, 2015). This fallacy occurs where inferences about individuals are drawn Panama has around four million inhabitants. Like in most coun- from inferences on the group to which they belong, thus deriving tries, the population is unevenly distributed throughout spatial conclusions about individuals solely on the basis of group data levels, e.g. country, provinces, districts (Fig. 1a) (Fujimoto et al., analysis (Winzar, 2015). For instance, calculating the SWG at a 2015). Roughly, 37% of the country’s total population is concen- country level with the aggregation of SWGI per capita, obtained trated in 15% of its area, which is the Panama province (PP). 71% from a sample population of a specific town, generates an ecolog- of the population of PP is concentrated in 23% of its area which is ical fallacy. Here, the value fails to take into account the population Panama district (PD), while 5% of the population of PD is concen- distribution across other parts of the country (Afon and Okewole, trated in 0.3% of its area which is Bethania Town (BT) and so on 2007). (INEC, 2006). This multilevel population distribution entails that The error due to disaggregation is known as ‘atomistic or individ- the size of places is determined by additive population from sub- ualistic fallacy’. In this case, inferences about a group are based on sets of places within them (Addison, 2000). data belonging to individual members of that group, thus deriving For instance, in Fig. 1b, as places approach from left to right to conclusions about the entire group solely on the basis of individual the level of the smallest SWG unit (inhabitant or individual), pop- data analysis (Loney and Nagelkerke, 2014). ulation within same-level places (e.g. from province to province, This paper identifies and compares typologies of SWGI estima- from community to community, from household to household) tions to detect ecological and individualistic fallacies committed. It appears to have the same size, and the SWG of those places, that also goes further and discusses new inference fallacies derived now depends on fewer individuals’ values, derives on each time from flawed methodological approaches used for SWG surveying more self-similar SWGI estimations (Mandelbrot, 1967). For in three studies performed in Panama from 2001 to 2018. These instance, the variation in family memberships between households studies were conducted by foreign (INECO and JICA) and local is lower in comparison to the population variation between pro- (GDR) companies which estimated the SWGI from SWG values at vinces. Therefore, resource consumption habits (and consequently different hierarchical levels e.g. household, town, district SWG behaviour) will vary more from province to province than (Guerrero et al., 2013). from household to household. 1.1. Going forward, the study is structured as follows: 2.2. Introduction of the measurement level from SWG sampling methods to estimate SWGI Section 2 provides an overview of the study area. It explains self-similarity of SWGI estimations and examines common sam- There are several methods to derive SWGI values at the analysis pling methods of SWG data. It also presents details on the SWG level from SWG values available only at the observation level. Fig. 2 455 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 a) Panama country 10 Provinces 80 Districts 678 Towns 2,496 Communies 789,719 Households 4,034 M inh. b) Fig. 1. (a) Absolute figures of Panama at several spatial levels. (b) Multilevel population distribution from the country to household spatial level. PC: Panama country; PPC: Provinces of the Panama country; PP: Panama province; DPP: Districts of the Panama province; PD: Panama district; TPD: Towns of the Panama District; BT: Bethania Town; CBT: Communities of the Bethania Town; CDRC: Condado del Rey Community; HCDRC: Households of the Condado del Rey Community. illustrates four methods to infer SWGI at the analysis level of specific area of the town, instead of from all households. The Bethania, a town located in Panama district with a population of downside with this method is that the results may be inaccurate 50,000. because SWG behaviour may vary considerably between the sam- Estimation (a) (upper-left side) would be inferred by obtaining pled households and the rest of the population. SWG values of each household, then aggregating and averaging by Estimation (c) (upper-right side) considers the SWG behaviour the total population of the town. This method would be the most of households by clustering (Kohberger and Everitt, 1994) them reliable SWGI estimation of Bethania because each household is according to a defined variable like income which reflects the being surveyed; however, the entire process is very cumbersome resource consumption habits and the resulting SWG behaviour. and expensive. In this case, statistically representative samples of households Estimation (b) (lower-left side) may obtain SWG values from a within each cluster are randomly selected for surveying and aver- statistically representative sample of households located at a aging their SWG. The SWGI of Bethania is obtained by averaging 456 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 Fig. 2. Households’ SWG sampling methods to estimate SWGI of Bethania town. HH: Households. Blue arrows represent SWG. Dotted lines represent floating clusters of households. Green lines represent communities’ clusters of households. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) the SWGI of each sample by their population, and then averaging are several measurement levels to choose from, where choosing resulting SWGI by total clusters created. However, clustering one or another will affect the SWGI estimation. households without considering spatial distribution as per house- Fig. 3 shows the extent to which choosing from three different holds’ location produces floating clusters (Giampietro et al., measurement levels (secondary y-axes) i.e., town (Fig. 3a), com- 2009) that misses the causality of their SWG behaviour, necessary munity (Fig. 3b), and household (Fig. 3c) can change the average to assure reliability of the clustering process (Matuszewski, 2002). number of waste generating inhabitants at the analysis level (pri- Estimation (d) (lower-right side) introduces the measurement mary y-axes). This selection will determine SWGI estimations at level to make it possible to consider spatial distribution as per different observation levels (x-axes) i.e., country, capital province, households’ location. The measurement level is a spatial level in capital district, metropolitan towns, Bethania (as a stratified town) between the analysis and observation levels. In Panama, groups and communities of Bethania. Metropolitan towns are defined as a of households constitute communities while groups of communi- spatial sublevel between the levels of district and town, consisting ties constitute towns. As shown in Fig. 2d, communities (green line of a set of urban towns of the capital district. Furthermore, Betha- surrounding households) are a geopolitically predefined group nia has been named a stratified town since it contains a wide range introducing context for households to be clustered taking into of social classes, resource consumption habits, and SWG account SWG behaviour of the communities to which they belong. behaviours. The use of the measurement level in this example allows inferring When observed from the country and capital province observa- SWGI of the Bethania town by clustering households within com- tion levels, SWGI estimated from average waste generating inhab- munities and applying Estimation 3 within a known spatial level itants at the town measurement level, presents an eight-fold i.e., communities. This increases the reliability of the clustering difference (country and capital province bars of Fig. 3a). When process with the SWG behaviours defined by communities, as SWGI is estimated from average waste generating inhabitants at opposed to floating clusters of households, while keeping the pro- the community measurement level, results at the country and cap- cess feasible. ital province observation levels are much closer (country and cap- ital province bars of Fig. 3b). The SWGI estimation from average waste generating inhabitants at the household measurement level 2.2.1. Measurement level selection affecting SWGI estimations presents almost the same results when observed from the country The measurement level represents a geopolitically defined spa- and province observation levels (country and capital province bars tial level in between the analysis and observation levels. It gives of Fig. 3c). robust context to places at the observation level to obtain reliable The closer the measurement level is to the analysis level (from SWGI estimations at the analysis level. However, sometimes there Fig. 3a–c), the more even and reliable the SWGI value across 457 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 Fig. 3. Waste generating inhabitant of the analysis level at several observations levels by the measurement level of (a) towns, (b) communities and c) households. observations levels is. Consequently, it becomes more technically is applied to the rest of observation levels of Fig. 3a, and to unfeasible and economically unviable, due to lower spatial levels’ Fig. 3b and c. It should be noted that: as the measurement constraints, to collect SWG data e.g., the need for more entities level from Fig. 3a–c i.e. towns, communities, households, to collect data from in order to comply with statistical representa- respectively approaches the analysis level (inhabitants), self- tive samples. similarity is more and more present among their SWGI esti- Grey lines of Fig. 3 represent variations in the quantity of mated values because the number of inhabitants generating measurement levels at each observation level. For instance, waste present fewer variations across observation levels for the observation level ‘‘country” of Fig. 3a, the measurement (Nottale, 2010). level is towns, and the grey line indicates the number of SWGI estimations are affected if measurement levels are not towns at this observation level; a total of 678 that decreases correctly defined, leading to the fallacies which will be discussed to <100 at the ‘‘Capital province” observation level. The same in this study. 458 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 2.3. SWGI estimations by the local authority and SWG studies where SWGIJICA is the SWGI estimation that resulted from JICA study, n performed is the total number of apparent high-income towns, SWGi the SWG for the i apparent high-income towns, Pi the population in the i apparent 2.3.1. SWGI estimation by the national waste management authority high-income towns, CIHI the confidence interval of the SWGI estimation The national waste management authority (Autoridad de Aseo for apparent high-income towns. The same nomenclature is used for Urbano y Domiciliar or AAUD), assumes that population at every middle and low-income towns with their respective weighed SWG observation level i.e. from households to country have a normal contribution. distribution with a default SWGI estimation of 1.3 kg inh1d1, that is aggregated by the population of the analysis level at which 2.3.3. SWGI estimation by INECO SWG is to be obtained (JICA, 2003). To update the number of inhab- From 2015 to 2017, the Spanish public company INECO carried itants on the SWGI estimation, AAUD uses a compound annual out studies in Panama to set up the ‘‘National Integral Waste Man- population growth rate of 5% which is applied to population value agement Plan 2017–2027” (INECO, 2017) at a $4.5 M cost. Their of the 2010 census; Eq. (1) formalizes AAUD’s approach. methodology involved defining countrywide towns as the observa- tion levels of SWG and clustering them using geopolitically unde- SWGIAAUD ¼ 1:05  1:3  P2010 ðCY  2010Þ ð1Þ fined places which INECO defined by socio-economic criteria i.e. where SWGIAAUD is the SWGI estimation used by AAUD, 1.05 is the 5% economic level represented by the Human Poverty Index (HPI), compound annual population growth rate, 1.3 is the generic SWGI average income per capita and level of agricultural activities. These value in kg inh1d1, P2010 is the population as per 2010 national cen- places do not count as measurement levels according to the defini- sus and CY is the current year when SWGI is to be estimated. tion of measurement level given before; however, for the sake of From 2001 to 2018, three studies have been executed to: (i) simplification will be considered as such. estimate SWGI; (ii) evaluate the situation of the Panamanian The SWM system of developing countries is commonly com- SWM system; and (iii) develop a SWM plan with defined norma- posed of roughly origin, transport, and final disposal management tive and competence frameworks. stages. Unlike other studies which used the origin stage to observe SWG, INECO got SWG from values of waste arriving to the final dis- 2.3.2. SWGI estimation by JICA posal stage Over 75 days, INECO collated SWG data from the From 2001 to 2003, the Japanese company Kokusai Kogyo., Panama district landfill. However, this practice results in important ltd., representing the Japanese International Cooperation Agency misestimations because landfills serve several towns, and surveyed (JICA), carried out the ‘‘Study on the Solid Waste Management for waste collection trucks had plied undefined routes and unclear ori- the Municipality of Panama in the Republic of Panama 2003–2015” gins at their arrival to landfills i.e. from several communities across (JICA, 2003) at a $2M cost. SWG values were obtained at the various towns. This means that waste values collected at the final household observation level for 15 days to estimate SWGI at disposal stage actually account for Solid Waste Disposal (SWD) not the district analysis level. Households were clustered by mixing SWG. For this reason, going forward, SWG values surveyed by two different measurement levels: communities and towns. JICA INECO will be referred to as SWD. INECO attempted to correct this classified both levels as ‘‘town” without considering that com- flaw by using a ‘‘correction coefficient” of 1.24 i.e., SWG = 1.24 munities are sublevels of towns and there are different factors SWD, but this simplistic approach dismisses waste losses along influencing the SWG at each level. To keep things simple, the waste collection routes from origin to final disposal, commonly measurement level used by JICA will be referred to as ‘‘town” caused by waste collection and transport flaws e.g., containeriza- going forward. tion absence in the origin, incomplete waste collection routes Towns were clustered based on household ‘‘apparent” income and unspecialized collection human resource. level values. These clusters where determined by the physical loca- SWGI values at the measurement level was estimated by divid- tion of the households, and not based on official income level val- ing SWG values obtained at the observation level by the population ues. No statistical sampling technic was used to select the number of the clusters. Four clusters were obtained, and the per capita of households per cluster; twenty random households were chosen high-income level cluster was solely represented by Panama dis- per cluster (JICA, 2005). trict and its SWGI estimation mathematically formalized in Eq. (3). To estimate the SWGI, surveyed households’ SWG values were The SWGI value for the entire country (not shown in Eq. (3) for expressed per unit of an unspecified average value of waste gener- the sake of simplification) was obtained by aggregating SWGI esti- ating inhabitants per household. mated values from clusters and multiplying by the whole country The SWGI was estimated from households’ clusters formed population. Results were forecasted to 2027, not linearly but con- using apparent income level data rather than official income level sidering population growth and the changing SWG behavior. values. Despite this fact, the average SWG contribution of each 0Pn 1 SWDi cluster was weighed based on official income level values i.e. 11% P i¼1 B n i¼1 Pi C 1 n for high-income level population, 46% for middle-income level SWGIINECO ¼ 1:24B @ n A C ð3Þ population and 43% for low-income level population. JICA per- formed a linear forecast of SWGI values from 2003 2015 suing population growth as the main parameter, without considering a where SWGIINECO is the SWGI that resulted from INECO study, 1.24 the possible change in SWG behaviors which could potentially distort correction coefficient, n is the total number of Panama district towns, such a linear forecast. SWDi the SWD for the i Panama district towns, and Pi the population Eq. (2) mathematically formalizes the SWGI estimated by JICA in the i Panama district town. and shows the aggregation of the weighted averages of SWGI results per cluster. 2.3.4. SWGI estimation by GDR In 2018, the local company Gestión de Residuos (GDR) carried 1 Xn SWGi 1 Xm SWGj out ‘‘Dynamic characterization study of the Urban Solid Waste of SWGIJICA ¼ 0:11ð þ CIHI Þ þ 0:46ð Bethania town by community clusters according to its sociodemo- n i¼1 Pi m j¼1 Pj graphic characteristics” (MUPA, 2018) at a $27 K cost. The method- 1 Xp SWGk ology involved using the community measurement level to cluster þ CIMI Þ þ 0:43ð þ CILI Þ ð2Þ p k¼1 Pk and survey SWG values of random observation level households by 459 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 their income level to estimate SWGI at the Bethania town analysis Expressions type (c) and (d) (lower-left side) cannot be speci- level - refer to Eq. (4). Four out of 26 communities were randomly fied on their own, they will either take the form of expressions selected to represent low, middle, upper-middle and high house- types (a) or (e), respectively. holds’ income levels, depending on the sample statistical represen- The expression type (b) (upper-right side) is a multilevel tativity and the feasibility of surveying tasks. SWGI was estimated expression obtained by: (i) surveying SWG values at the observa- by dividing SWG by communities’ population. GDR did not pro- tion level, aggregating them at several measurement levels and duce SWGI forecast. dividing by the total measurement levels used; (ii) for each mea- Pn surement level used, an average SWG value is obtained by dividing 1 Xn i¼1 SWGii SWGIGDR ¼ ð4Þ the number of waste generating entities which constitute each n i¼1 nPi measurement level used; and (iii) dividing the aggregation of each where SWGIGDR is the SWGI estimation that resulted from GDR study, n average by the total amount of measurement levels used to esti- is the total number of representative communities in Bethania town, mate SWGI at the analysis level. The expression type (b) aims to SWGii the SWG of each representative community made up of the represent observation level values in analysis level terms (Alker aggregation of the SWG of the households making up each community, Jr., 1974). This is possible by considering the input that every anal- averaged by the total amount of households in each community n and ysis level entity exerts in the SWGI estimation at the observation the inhabitants Pi of each household i. level from values surveyed directly at the measurement level. The expressions type (b) enhances the possibility for cross-level 2.4. Typologies of SWGI estimations and main fallacies derived from approaches that supports discerning about the relative contribu- their misuse tion, of both analysis and measurement level, to results at the observation level when aggregating the SWGI estimation by total By applying the approach suggested by Subramanian et al. waste generating entities. The simultaneous assessment of many (2009), ”Typology of health and disease studies”, Fig. 4a shows five waste generating entities in the context of the measurement levels mathematical expressions configuring observation and measure- shaping their SWG behavior, allows for a better representation of ment levels to estimate analysis level SWGI. the effect that selected measurement levels exerts in waste gener- Expression type (a) (upper-left side) takes an individualistic ating entities, given that their relation is mutually causal. This focus. It is performed by aggregating, at the measurement level, approach also supports a more comprehensive framework to average SWG values obtained at the observation level. Then divid- understand the ways in which the measurement level could con- ing by the total amount of analysis level waste generating entities textually affect the SWG of waste generating entities of the analy- i.e., inhabitants, or places in cases where SWGI is not to be sis level or, alternatively, waste generating entities of the analysis expressed in ‘‘per capita” terms. It aims to represent the SWGI of level could causally affect measurement levels (Subramanian et al., entities belonging to the same observation level from the stand- 2009). point of the individual contribution of entities’ samples at the anal- ysis level (James, 1890). The generalization of SWGI estimations obtained from the type (a) expression to analysis levels of other 2.5. Practical example to illustrate SWGI estimation typologies observation levels, different from the ones to which waste generat- ing entities belong, lead to the individualistic or atomistic fallacy. A numerical example is shown in Fig. 4b to demonstrate differ- Here, it is assumed that a causal relationship exists between waste ent SWGI per capita estimations using expressions of Fig. 4a. It pre- generating entities of different observation levels. Also, that the sents a community (analysis level) consisting of 4 households replication of SWGI estimations, obtained from the analysis level (measurement level) with 5, 2, 3 and 4 inhabitants (observation of a first observation level, to the analysis level of a second obser- level) each. SWGij and SWGi represent random SWG values for vation level is equally or more reliable than a SWGI estimation inhabitants and households respectively; their aggregation is the obtained from direct SWG data of the second observation level actual total SWG value at the community level. SWGI estimations (Blakely and Woodward, 1999). are shown in the lower square in the same order as presented in Expression type (e) (lower-right side) takes a generalizing focus Fig. 4a. This simple example makes the best-case scenario feasible and matches the observation and measurement levels so that col- i.e., surveying actual number of inhabitants at each household and lection and aggregation of SWG values can be performed at the their SWG. It demonstrates the extent at which there are differ- same level. SWGI estimations are directly obtained by dividing ences in the SWGI estimations. Results obtained from expressions by the total amount of waste generating entities of the analysis types (c) and (d) match those obtained from expressions types (a) level. It intends to attribute to all waste generating entities the and (e), respectively. The extent to which expressions types (c) and SWGI estimated value obtained from their large-scale contribution (d) could be replaced by expressions types (a) and (e), respectively, to the observation level (also the measurement level in this case), depends on the more households to survey SWG from, which limit thus reflecting their SWGI estimation at the analysis level from is imposed by technical feasibility and economic viability issues of their perspective as a whole group (Robinson, 1950). The individu- the surveying process. alization of SWGI estimations, obtained from the type (e) expres- The result obtained from expression type (b) represents the sion at certain observation level, to the individual basis of the highest SWGI estimation, which is preferable over other results analysis levels of another observation level, lend to the ecological to offset uncertainty arising in the SWG surveying process fallacy. The term ‘‘ecological” refers to a large-scale context as (Wittwer et al., 2008). per hierarchy of different spatial levels (Moon et al., 2005; Selvin, 1958). Idrovo (2011) propose three criteria for the identification of the ecological fallacy which must be integrally met for it to be 3. Results and discussion determined. They have been applied to the context of SWG in this paper as follows: (a) SWGI estimation must be obtained from The first part of the results classifies the typologies of SWGI val- large-scale SWG data; (b) SWGI estimation must be inferred to dif- ues, estimated from the SWG studies presented according to ferent analysis levels than the one aggregated at the measurement Fig. 4a, and compares these values among them and also against level to obtain SWG; (c) and SWGI estimated from expression type literature. The second part discloses inference fallacies committed (e) must be different from that estimated with expression type (a). by each analysed study. 460 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 Fig. 4. (a) Mathematical expressions configuring the observation and measurement levels to estimate SWGI of waste generating inhabitants or places at the analysis level. Where, n is the variable for the total waste generating inhabitants or places of a determined level, m; the total levels constituting each determined level n, i the sum index for waste generating inhabitants or places of the same determined level, j the sum index for waste generating inhabitants or places of the same level at each i determined level, and Pi the population of the waste generating inhabitants or places of a determined level i. (b) Numerical example showing different SWGI estimations per capita at different measurement and observation levels using expressions of (a). Where, arrows leaving inhabitants are scaled up as per SWGI estimation of each inhabitant, n is the number of households of the community and m the number of inhabitants within each household. 3.1. Identification and comparison of typologies of SWGI estimations ment levels as per income levels. For instance, the analysis level of GDR and the main clustering unit of the measurement level of Table 1 compares the main characteristics of the studies per- JICA were both Bethania town, and the analysis level of JICA and formed by GDR, JICA and INECO, all of which used different obser- the main clustering unit of the measurement level of INECO were vation and measurement levels according to the way SWGI values both Panama district. were estimated in relation to their analysis levels. It shows the The approach used by JICA to estimate SWGI corresponds to a typology of SWGI estimation each study used according to type (a) configuration, by INECO to a type (d) configuration which Fig. 4a. Also compares SWGI results at the analysis and measure- ended up being type (e), and by GDR, although it was meant to be 461 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 Table 1 in resource consumption and SWG patterns compared to other Comparison among the reviewed studies performed by GDR, JICA and INECO. similar income level countries (IMF, 2018). Company JICA INECO GDR SWGI estimation type from a d, e b, d Fig. 4a 3.2. Inference fallacies committed in the reviewed studies Observation level Household Town Household Measurement level Town Defined by Community Methodological inference fallacies have been identified for socio- economic SWGI estimations in the studies analysed (Table 3). criteria JICA committed the ‘‘individualistic fallacy” by generalizing the Main clustering unit at the Bethania Panama Communities SWGI estimation to the whole Panama district directly from house- measurement level/income town/ district/high/ of Bethania/ holds. JICA did not considered that income level varies broadly level/SWGI (kg/inh*d) middle/ 1.55 high/0.96 among households of a district so it cannot be generalized at this 0.66 Analysis level/income level/ Panama Country/ Bethania analysis level directly from the households’ observation level SWGI (kg/inh*d) District/ upper- town/middle/ (Zohoori and Ghani, 2017). high/0.59 middle/1.26 0.76 Following the three criteria for the identification of the ‘‘ecolog- ical fallacy” proposed by Idrovo (2011), INECO committed condition (a) for ecological fallacy when using large-scale solid waste data configured type (b), it ended up being type (d). The SWGI estima- surveyed in the landfill. JICA, INECO and GDR committed condition tion of INECO and AAUD at the analysis level shows little variance, (b) for ecological fallacy when inferring the SWGI, estimated at the 1.26 and 1.30 kg inh1 d1, respectively. JICA presented the lowest analysis level, to observation level entities, others than the ones SWGI estimation at the Panama district analysis level (0.59 kg aggregated at the measurement level. To avoid condition (b) for inh1 d1), in contrast with INECO’s value which was almost triple ecological fallacy, SWGI estimations should be directly surveyed JICA’s (1.55 kg inh1 d1). JICA also presented the lowest SWGI esti- from observation level entities, but this is a complex task to per- mation at the Bethania town measurement level (0.66 kg inh1 form. To mitigate condition (b), the observation level should be as d1), very close to GDR’s at its analysis level (0.76 kg inh1 d1). close to the measurement level as possible, and the measurement GDR’’s SWGI estimation at the measurement level (0.96 kg inh1 level should consider very diverse observation level entities. The d1) was between its value at the analysis level (0.76 kg inh1 SWGI estimation of GDR will be used as proper reference for the d1) and INECO’s SWGI estimation at the country analysis level evaluation of condition (c) to ecological fallacy incurred by INECO (1.26 kg inh1 d1). and JICA, because GDR kept the closest relation between the mea- Comparisons of the SWGI estimation at the country analysis surement level i.e., households and the observation level i.e., level of INECO (1.26) with literature values at the countrywide inhabitants, it is therefore likely to be closer to the SWGI estima- observation level by income levels (Table 2), show that INECO’s tion type (a). JICA and INECO committed condition (c) for ecological SWGI estimation is over the average of upper-middle income level fallacy. JICA mixed communities and towns together, handling countries (1.06 kg inh1 d1) and under the average of high-income them all as towns to cluster households based on their apparent level countries (1.66 Kg inh1 d1). This may be due to fallacies in income levels as clustering variable, whereas GDR used the actual the configuration of the observation and measurement levels. income. INECO complies with all conditions for ecological fallacy, Unsteady economic growth rates and high social inequalities of therefore as Idrovo (2011) proposed, this implies ecological fallacy Panama (Indexmundi, 2015) are also influencing factors, reflected perpetration. Table 2 Reference SWGI estimations (kg inh1 d1) from literature by income level at a country analysis level, where upper-middle income (bold) match the income category for Panama. Income level1 Source High Upper-middle Lower-middle Low Adamović et al., 2017 1.67 1.03 0.71 – Shimura et al., 2001 – 0.95 0.67 – OECD, 2008 1.53 – – – Kofoworola and Gheewala, 2009 – – 0.72 – Afon and Okewole, 2007 1.80 1.24 0.70 0.50 Watson and Reichel, 2013 1.51 – – – Wang and Wang, 2013 – 0.88 – – Wilson et al., 2012 1.67 – – – Mejía, 2009 1.22 – – – Hoornweg and Bhada, 2012 – 1.20 0.79 0.60 Kumar et al., 2009 – – 0.39 – Kaseva and Gupta, 1996 – – – 0.17 Thanh et al., 2010 – – 0.78 0.58 Forouhar and Hristovski, 2012 – – –– 0.31 Troschinetz and Mihelcic, 2009 1.67 – 0.80 – Achankeng, 2003 – – – 0.33 Kollikkathara et al., 2009 1.84 1.10 – – Din and Cohen, 2016 – – – 0.30 US EPA, 2014 1.99 – – – Isugi and Niu, 2016 – – – 0.33 Average 1.66 1.06 0.69 0.39 1 The income categories are following the World Bank’s gross national income (GNI) per capita. Low income: US$995 or less; lower-middle income: US$996 – US$3945; upper- middle income: US$3946 –US$12 195; and high income: US$12 196 or more (World Bank, 2014). Although Panama has recently been reclassified as an upper income level country (The World Bank, 2018b), this paper considers Panama’s income level as it was classified before 2018, as an upper-middle income level country, to match the years SWG studies were carried out. 462 J.M. Torrente-Velásquez, M. Ripa, R. Chifari et al. Waste Management 126 (2021) 454–465 Table 3 The ‘‘Mixed Spatial Levels fallacy” is the introduction of a mea- Fallacies found in the last SWG measurement studies performed. surement level composed of geopolitically undefined spatial levels Fallacy JICA INECO GDR to cluster observation level entities (inhabitants or places). This fal- 1. Ecological (a + b + c) X lacy was committed by JICA when clusters were formed by mixing a. Results obtained with ecological (population) data x towns and communities, under the assumption that they were at b. Data inferred to individuals from ecological levels x x x the same spatial level. Also, a combination of the Individualistic c. Results obtained with individual data are contradictory x x and Mixed Spatial Levels fallacies may have caused JICA’s low 2. Individualistic X 3. Stage X SWGI estimation, where observation levels (households) and mea- 4. Floating Population X surement levels (undefined between communities and towns) are 5. Linear Forecasting X very close to each other. 6. Average Population X The ‘‘Average Population fallacy” occurs when using multilevel 7. Mixed Spatial Levels X estimations of type (b) without accounting for the actual popula- tion of the surveyed observation level. GDR committed this fallacy by using average inhabitants per household instead of actual’s to estimate the SWGI, probably because of insufficient budget to exe- 3.3. Apart from the ecological and individualistic fallacies, other cute this task. inference fallacies have been identified. The reason for the difference between GDR’s and JICA’s SWGI estimations of the analysis level and main clustering unit at the The ‘‘Stage fallacy” is the assumption that, after applying a cor- measurement level, respectively, may be an offset between the rection coefficient, the results obtained at any stage of the SWM effects of the Average Population fallacy incurred by GDR and the system e.g., final disposal, can also be considered valid for other Mixed Spatial levels fallacy incurred by JICA. stages e.g., waste generation. Correction coefficients are supposed The effect of the Average Population fallacy incurred by GDR is a to summarize in a single value the complexity of SWM system pro- lower SWGI estimation, because instead of carrying on a multilevel cess subtleties at each of its stages. From the generation to the final estimation of type (b), it uses an estimation of type (d) by consid- disposal stage e.g. waste weight losses/gains during containeriza- ering the same population at each measurement level. tion due to excessive rain, underground waste market transactions by the waste transport civil servants or waste pickers of the streets, and informal recycling performed by waste pickers of the landfills 4. Conclusions and recommendations (Scheinberg et al., 2011). However, in developing countries waste lost data along the SWM process is almost unaccountable since SWM systems in developing countries are incipient and far from SWM information systems are seldom established. INECO incurred efficient when compared with developed countries. One of the the Stage fallacy by equating their SWD study with a SWG study main barriers to embedding robust SWM systems is the lack of using a correction coefficient. Incurrence on this fallacy or poor data to understand the SWM situation. To create, develop and estimation of the correction coefficient may be causal of a 3-fold implement SWM system plans, diagnoses of the current waste SWGI estimation between INECO and JICA. management systems are carried out by companies contracted The ‘‘Floating Population fallacy” is a direct effect of studies using by the government in power. SWG surveys play a key role in those SWD values as SWG values. This fallacy represents unreliability of diagnoses; useful indicators such as SWGI can be obtained for solid waste disposal intensity (SWDI) estimations derived from planning sustainable SWM systems. However, methodologies to weighing collection trucks that dispose waste in landfills with estimate SWGI often contain inference fallacies that undermine unclear origins and undefined collection routes. The report on the reliability of results. SWM plans based on these results propose waste collection routes, commonly used by the local waste man- solutions that are difficult to implement because they are derived agement authority (AAUD, 2014) for their waste collection activi- from incongruent SWGI estimations which do not represent the ties, presents waste collection routes that either partially or actual SWM system situation. totally mix communities. This makes it almost impossible to esti- This paper reviewed the methodological approaches used for mate the population from which waste is collected and disposed SWG surveying by the local SWM authority (AAUD) and three offi- of. INECO committed the Floating Population fallacy by estimating cial studies performed in Panama. The generalized approach used SWDI using data from this report to select waste collection trucks by AAUD to estimate SWGI produces ineffective allocation of tech- to be sampled at the landfill, but also using fixed population values nical, logistic, economic and human resources to the SWM system at the town level, not precisely belonging to mixed communities (AAUD, 2018; ANAM, 2002; La Prensa, 2018, 2011; Linowes and included in each route. Brown, 2006). Seven inference fallacies (ecological, individualistic, The ‘‘Linear Forecasting fallacy” presumes that future change will stage, floating population, linear forecasting, average population be a simple and steady extension of past trends, i.e. estimating and mixed spatial levels) were identified and allocated to each SWGI over years without considering SWG and population of the reviewed study. It was determined that foreign companies com- analysis level, both unpredictable extensive variables with many mitted three of the seven inference fallacies presented, while one factors shaping their context (Pereira et al., 2006). JICA committed was committed by the local entity. Endogenous knowledge and this fallacy when linearly forecasting a SWGI estimation for expertise played an important role in the latter. INECO committed Panama district and its constituting towns in 2015 based on results the ecological, stage and floating population fallacies; JICA commit- obtained in 2002. When subjected to similar changes, the SWM ted the individualistic, linear forecasting and mixed spatial levels system may behave in similar patterns over time and past events fallacies while GDR committed the average population fallacy. can lead to predictions about its behaviour, however the timing When there is a clear distinction between the spatial level at or frequency of such behaviour cannot be predicted. Forecasting which the SWG is surveyed (observation level), the spatial level SWGI values considering no changes in the state of a SWM system at which the SWG is aggregated (measurement level) and the spa- over years will give results quite different from the reality, because tial level at which the SWGI estimation is expressed (analysis over time the environment pushes the SWM system far away from level), then population distribution is taken into account (Loney its equilibrium state into chaos which can result in sudden, unpre- and Nagelkerke, 2014). 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