Model selection and averaging in the assessment of the drivers of household food waste to reduce the probability of false positives

PLOS ONE, Feb 2018

Food waste from households contributes the greatest proportion to total food waste in developed countries. Therefore, food waste reduction requires an understanding of the socio-economic (contextual and behavioural) factors that lead to its generation within the household. Addressing such a complex subject calls for sound methodological approaches that until now have been conditioned by the large number of factors involved in waste generation, by the lack of a recognised definition, and by limited available data. This work contributes to food waste generation literature by using one of the largest available datasets that includes data on the objective amount of avoidable household food waste, along with information on a series of socio-economic factors. In order to address one aspect of the complexity of the problem, machine learning algorithms (random forests and boruta) for variable selection integrated with linear modelling, model selection and averaging are implemented. Model selection addresses model structural uncertainty, which is not routinely considered in assessments of food waste in literature. The main drivers of food waste in the home selected in the most parsimonious models include household size, the presence of fussy eaters, employment status, home ownership status, and the local authority. Results, regardless of which variable set the models are run on, point toward large households as being a key target element for food waste reduction interventions.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0192075&type=printable

Model selection and averaging in the assessment of the drivers of household food waste to reduce the probability of false positives

February Model selection and averaging in the assessment of the drivers of household food waste to reduce the probability of false positives Matthew James Grainger 0 1 Lusine Aramyan 1 Simone Piras 1 Thomas Edward Quested 1 Simone Righi 1 Marco Setti 1 Matteo Vittuari 1 Gavin Bruce Stewart 0 1 0 School of Natural and Environmental Sciences, Newcastle University , Newcastle upon Tyne , United Kingdom , 2 Wageningen Economic Research, Wageningen , The Netherlands , 3 Department of Agricultural and Food Sciences, Alma Mater Studiorum - University of Bologna , Bologna , Italy , 4 Waste & Resources Action Programme (WRAP) , Second Floor, Blenheim Court, Banbury, Oxfordshire , United Kingdom 1 Editor: Andre M. N. Renzaho, Western Sydney University , AUSTRALIA Food waste from households contributes the greatest proportion to total food waste in developed countries. Therefore, food waste reduction requires an understanding of the socioeconomic (contextual and behavioural) factors that lead to its generation within the household. Addressing such a complex subject calls for sound methodological approaches that until now have been conditioned by the large number of factors involved in waste generation, by the lack of a recognised definition, and by limited available data. This work contributes to food waste generation literature by using one of the largest available datasets that includes data on the objective amount of avoidable household food waste, along with information on a series of socio-economic factors. In order to address one aspect of the complexity of the problem, machine learning algorithms (random forests and boruta) for variable selection integrated with linear modelling, model selection and averaging are implemented. Model selection addresses model structural uncertainty, which is not routinely considered in assessments of food waste in literature. The main drivers of food waste in the home selected in the most parsimonious models include household size, the presence of fussy eaters, employment status, home ownership status, and the local authority. Results, regardless of which variable set the models are run on, point toward large households as being a key target element for food waste reduction interventions. - Data Availability Statement: All relevant data are available from Open Science Framework at the following URL: https://osf.io/rnkyc/. Funding: This work was carried out under the H2020 project REFRESH - Resource Efficient Food and dRink for the Entire Supply cHain. REFRESH is funded by the Horizon 2020 Framework Programme of the European Union under grant agreement no. 641933. Introduction Food waste has been drawing increasing scholarly attention due to the sizeable proportions it has assumed, and its socio-economic and moral implications ([ 1 ];after having been well below 100, the yearly number of scientific papers including the keyword ªfood wasteº reached 100 in 2007, then grew to 219 in 2011, and peaked 722 in 2016 see https://www.scopus.com/). Its definition has been characterized by a lively debate that lead different national and international organizations to identify different boundaries emphasizing diverse elements characterizing the food waste issue [2±4]. In what follows, we define food waste as ªavoidable food wasteº, i.e. any ªfood and drink thrown away that was, at some point prior to disposal, edibleº [ 5 ]. In developed countries, households are responsible for the relatively largest proportion of all food wasted [1±3, 6]. Indeed, economic development and urbanisation result in the adoption of lifestyles, working conditions and social dynamics typical of urban areas which, in turn, increase food waste in the downstream segments of the value chain (retail, food services, and households) [ 7 ]. Furthermore, developed countries differ from one another as for the food waste generated and the policies adopted to address this challenge. Cross-country differences in waste generating behaviours may also depend on habits embedded in the national culture [ 6, 8 ]. This holds although urbanisation and globalisation create increasingly homogeneous dietary and food waste patterns worldwide [8]. Some authors have detected geographical differences in the individual behaviours towards food waste among EU countries, due to factors such as per-capita income, and citizens' perception of sustainability issues [7, 9±11]. Although developed countries present high per-capita incomes, hunger in these countries is a reality: e.g., approximately 4% of US households, and more than 5% of Australian households are experiencing hunger [ 12 ]. On the other hand, the abundance of food results in high food waste levels [ 13 ]. For example, household food waste account for 6.7 million tonnes of edible food or 33% of all food purchased in the UK, 6.3 million tonnes or 20% of food purchased in Australia, and more than 160 million tonnes in the US [ 12 ]. If redistributed to people in need, this food could help reduce hunger, while food waste levels could also decrease. Food waste generates negative environmental impacts and economic costs. It has been estimated that nearly one third of the food mass, and one quarter of the food calories globally produced are either lost or wasted, corresponding to 3.3 Gtonnes of CO2 equivalent [ 2, 7 ]. In the EU-28, annual food waste amounts to 180 kilograms per person, i.e. 25% of the food purchased by households [ 2,7 ]. Hence, the valorisation of physiological and unavoidable waste and residues as inputs for diverse productive processes, such as bioenergy or the production of biobased products, might create socio-economic benefits and reduce environmental repercussions. Indeed, most wasted foods are of primary interest to biofuel production [ 13 ]. Nevertheless, the social, economic and environmental viability of food waste as a source of biofuel remains underdeveloped, thus requiring effective strategies to reduce food waste generation. Overall, food waste is a broad topic that has been discussed from different angles in recent literature [1±3, 6, 12, 13]. In order to contribute to the understanding of and the reduction of food waste, various attempts have been made to identify and analyse the socio-demographic factors influencing food waste behaviours (e.g. [7, 14±22]). This study focuses on the drivers of food waste generation at household level. Indeed, a proper identification of them could help design effective policies for food waste prevention and reduction. The rest of the paper is organised as follows. The next section provides a background on food waste drivers at household level, and addresses the issues of complexity related to the empirical modelling of these drivers. A detailed description of the data and methodology can be found in the subsequent section, followed by the results and their discussion. Food waste drivers at household level Individual and situational factors leading to the generation of household food waste include household characteristics, shopping habits and location in relation to shops, eating/cooking 2 / 16 behaviours, and awareness (e.g. the understanding of date labels on products, attitudes to waste and recycling, consumer preference for perceived high-quality food, etc.). Literature suggests that food waste is influenced by household characteristics with a major factor represented by the composition of the family: · in absolute terms, larger households waste more food than smaller households, but they are also more efficient, wasting less food per person than smaller households; instead, singleperson households tend to throw away more food on a per capita basis [6, 20±25]; · adults waste more in absolute terms than children, but households with children tend to waste more than households without children, with food waste rates varying with children's age [6, 20±25]; · the gender of the person mainly responsible for grocery shopping, and for food storing and cooking might also have implications [ 6, 7, 20, 24 ]; · differences between older and younger people are not consistent, yet retired households seem to waste less because they have more available time (compared to younger households and households with children) and tend to be smaller [6, 20±23, 26, 27]; · income levels matter, but the relationship between individual income, food behaviours, and household food waste [ 10, 28, 29 ]. As for shopping habits, the frequency of shopping [20, 30±32], the location of the stores related to the frequency of the purchase, and the planning of the shopping [ 24, 33 ] represent other aspects of consumer behaviour related to food waste. On the one hand, consumers may over-purchase if they need to shop infrequently [ 24, 33 ]; on the other hand, frequent shopping may induce unplanned and impulsive purchases, which tend to increase food waste [ 34 ]. Not planning shopping trips, absence of shopping lists, not planning meals, and not checking stocks lead to the generation of food waste at household level [3, 7, 35±39]. Lack of awareness and/or knowledge is one of the most commonly identified drivers of food waste at household level [2, 10, 21±23, 30, 32, 37, 40]. This includes consumers' confusion with product labelling, as well as a lack of knowledge on how to use food efficientlyÐe.g. making the most of leftovers, or cooking with available ingredients [ 37, 38 ]. Consumers are rarely aware of the difference between the labels ªuse byº and ªbest beforeº; hence, they are not using them effectively when planning food usage and/or discard to avoid the risks associated to food safety [ 3, 37, 38, 41, 42 ]. Not understanding and/or not abiding by food storage and use instructions provided on food packages also leads to food waste [42]. Finally, consumers may not use packaging functionality, e.g. taking some products out of their packaging after getting home, thus losing the protection of modified atmosphere packaging, or not using cool bags to bring chilled food home [ 33, 35, 43, 44 ]. While food waste drivers have been discussed extensively in recent literature, their relative importance and their interactions have received little attention. Literature suggests that food waste drivers are multiple and interrelated, characterizing the problem as ªwide and multifacetedº [ 7 ]. This framework is further complicated by the time and location gap ªbetween choices made upstream (food purchasing and using decisions) and actions downstream (frequency of household food waste)º, which prevents intentionality and commitment from working effectively [ 10 ]. Besides, since different authors propose different definitions of food waste, the boundaries of the systems considered are also different (e.g., what is avoidable and non-avoidable food waste) [ 4 ]. This lack of consistency in the notion of food waste may lead consumers to resort to their subjective perception of what food waste is, when asked to assess related 3 / 16 behaviours and quantities. Indeed, the adoption of different methodologies for data collection (questionnaires, diaries, waste sorting analysis), or of poor or no measurements hampers the lack of consistency in terms of quantification [ 4, 45 ]. Due to the high costs of measuring household food waste, most studies in the existing literature base their inference on self-reported measures detected by means of questionnaires. Here, the use of real food waste as a dependent variable helps overcome the problem of underestimation for social desirability bias, and of misreporting due to other behavioural biases, thus reducing the risk of incorrect inference. Addressing complexity in food waste models The high number of interconnected food waste drivers described above implies that traditional modelling approaches may not be appropriate, or need specific adjustments. The approaches to address multivariate problems have traditionally followed a procedure whereby data are collected on several variables that may plausibly explain the response variable, and analysed to find a single ªbestº model [ 46 ]. The model's structure is often defined a priori, and the estimate from this model then forms the basis of inference. This approach ignores the potential for other models to explain the data, and this model uncertainty increases the potential for incorrect or misleading inference [ 47 ]. This is shown empirically for sociological models (OLE regression) by Young [ 48 ], where statistical significance is overturned by minor and sensible changes in model structure. Hence, there is a higher probability of false inferences (i.e. Type I errors or false positives, and Type II errors or false negatives). False positives (Type I) are often more costly than false negatives (Type II) because they lead to wasted resources on further research and ineffective policy interventions [ 49 ]. The probability of Type I errors can be increased by increasing the number of parameters modelled but also by ªresearcher degrees of freedomº (sensu [ 49 ]). Unreported aspects of the research can lead to increased risk of false positives through changes in the selection of dependent variables or covariates, altering sample sizes and only reporting subsets of experimental conditions [ 49 ]. Food waste drivers are multiple, interconnected and influenced by a number of diverse factors related to the influence of the technological, institutional and social ªcontextsº where they are situated [ 7 ]. Addressing such a complexity requires the inclusion of multiple explanatory variables, increasing the risk of Type I and Type II errors. However, most assessments of food waste use a regression framework with multiple explanatory variables without addressing issues of model structural uncertainty, and rely on a single model specification, based either on the extant literature or on the author's hypotheses, to make inferences from (e.g. [ 9, 10, 32, 50, 51 ]). Basically, while the set of variables gathered are bounded to be selected according to the theory of the collectors, it is possible to avoid any further bias on the model construction due to the artificial selection of variables and interaction terms to be included in the model itself. This theory-based approach (using one single model) is blinkered to other possible explanatory models (within the realms of the data collected). In presence of multiple potential explanatory variables, model selection has long been championed as being more robust to Type I errors [ 52 ]. Here, we adopt a novel empirical approach to identifying the drivers of food waste to inform waste reduction policies. Our approaches for variable and model selection, differ from the more common (and highly biased; [ 53 ]) stepwise selection based on the coefficients' level of significance. With this approach, the aim is to identify the key drivers of household food waste, whilst more accurately reflecting the uncertainty inherent in the analysis of observational multidimensional data. 4 / 16 Materials and methods Data Data on UK consumers' demographics and behaviours collected by The Waste and Resources Action Programme [ 5 ] are used in order to appraise the weight of ªavoidable food waste per householdº using model selection and model averaging [ 54 ] to account for model uncertainty. The dataset consists of face-to-face in-home interview responses (categorical data) on socio-demographic aspects of households and behavioural responses to food waste, along with data on the amount of waste collected from the kerbside. We undertook a complete case analysis utilising only the households for whom all information was reported, which resulted in a sample size of 1,770 (from 1,799) UK households. Household waste was collected from outside each home (flats and houses with shared waste collections were not assessed) by ad hoc teams. After collection, the waste of each household was weighed and sorted. All non-food items were removed and weighed. Food items without packaging were sorted by food type and then weighed. Food items with packaging were removed from the packaging, weighed separately, and any details on the packaging (e.g. best before dates) were recorded (for more details, see [ 5 ] and references within). Finally, food waste was standardised per household (i.e. food waste per person was calculated) to account for the difference that a larger number of family members could make to the amount of waste produced. Variable reduction With 50 variables, the set of potential models was well over a quadrillion and, therefore, variable reduction was first undertaken using the random forest algorithm [ 55 ]. The ªBorutaº algorithm (in the package ªBorutaº, [ 56 ], in the R statistical environment [ 57 ]; all R code for analyses is provided in S1 File) adds randomness to the variable set by creating shuffled copies of all variables (ªshadow featuresº). It then runs a random forest classifier on the extended dataset, and assesses the mean decrease in accuracy to evaluate the importance of each variable (higher means are more important). At each iteration, ªBorutaº assesses if each variable has a higher Z-score than the maximum Z-score of its shadow features. Variables with scores lower than shadow features are deemed highly unimportant, and removed from the set. The algorithm runs until all variables are confirmed or rejected (or it reaches a specified limit of runsÐ here, we used 500 trees maximum). Modelling Generalised Linear Models (GLMs) were applied to assess correlations between ªavoidable household food wasteº and the socio-demographic and behavioural variables retained after applying the ªBorutaº algorithm (Table 1). All categorical variables were treated as factors in the analysis. The Akaike Information Criterion corrected for small sample size (AICc) was used to determine a set of plausible models; modelling averaging [ 54 ] was used to obtain estimates of the effect of predictors on ªavoidable household food wasteº. Variables that were retained in the model selection procedure were assessed for interaction. GLMs, model selection and model averaging were carried out using the ªglmultiº package [ 58 ] in the R programme. Exploratory sensitivity analysis The variables summarizing the self-reported discard of different types of food have the potential to introduce circularity, as they may predict overall food waste. Therefore, after running the variable reduction and model-selection procedures, we removed them from the full model, 5 / 16 Food and drink thrown away that was, at some point prior to disposal, edible, e.g. milk, lettuce, fruit juice, meat (excluding bones, skin, etc.) The ownership status of the house, e.g. privately rented or owned with mortgage The employment status of the person responsible for the majority of the household shopping and cooking PLOS ONE | https://doi.org/10.1371/journal.pone.0192075 Measurement Weight (g) Minimum: 0 1st Quartile: 379 Median: 1080 Mean: 1668 3rd Quartile: 2300 Maximum:19836 Male/Female Mixed aged household Under 65 years old only 65 years and above only 1,2,3,4,5,or 6 people Couple Owned outright Owned with a mortgage Privately rented Other Bungalow Detached house Semi-detached house Terraced house Flat Other Yes/No Family with at least one child under 18 years olds Family with child(ren) all 18 years or over Single occupancy Other Council/housing association rented ABC1: Higher & intermediate managerial, administrative, professional occupations or Supervisory, clerical & junior managerial, administrative, professional occupations C2: Skilled manual occupations DE: Semi-skilled & unskilled manual occupations, Unemployed and lowest grade occupations Not working Paid work Retired Not stated All main meals are planned Most main meals are planned Few main meals are planned Decide on the day Measurement Yes No Don't Know Don't buy the item Yes/No Don't eat this food Wrapped / box / bag Original packaging No wrapping Other / don't know Don't buy / store Use fridge (and possible other place to store) Use fruit bowl/Use cupboard Other storage Don't know / can't remember Yes No (Continued ) 7 / 16 Proportion of occupants of the household classed by the survey respondent to be fussy eaters Measurement Yes No Yes No Don't Know Not Applicable Quite a lot A reasonable amount A small amount Hardly any None Don't eat it I buy almost all my food in a main shop I buy some food in a main shopping trip and some in `top-up' shops I mostly buy food in smaller, `top-up' shops Not stated I do a main shop more than once a week I do a main shop about once a week I do a main shop about once a fortnight I do a main shop about once a month I almost never do a main shop Proportion (between 0 and 1) and re-ran these two steps. Similarly, the local authority was considered as a non-designed confounder (it was recorded but without any underlying justification). Again, we removed this variable in the full model and re-ran the analysis. Finally, we re-ran the analysis with both discard behaviours and local authority removed. Results Model set reduction The ªBorutaº algorithm consistently identified household size, home ownership status, household composition, employment status and the presence of fussy eaters as significant drivers of food waste in all sets of variables (Fig 1a±1d), including those reduced for exploratory sensitivity analysis. Household size was always the most important variable in the variable set (Fig 1a±1d). 8 / 16 Fig 1. a) Variable importance (the loss of accuracy of classification) as determined by the ªBorutaº algorithm for the full variable set. Variables retained for model selection (those with high or medium importance) are highlighted in green and yellow. Shadow feature minimum, mean and maximum are highlighted in blue; b) with ªDiscard behavioursº removed from the variable set; c) with ªLocal authorityº removed from the variable set; d) with both ªlocal authorityº and ªdiscard behavioursº removed from the variable set. Model selection The key drivers of consumers food waste included in the full model (as determined by the ªBorutaº algorithm, Fig 1a) were household size, local authority, household composition, house type, home ownership status, employment status, the presence of fussy eaters, the presence of children aged between 3 and 11, age of the respondent, social grouping, checking cupboards for tinned food prior to shopping, and discard behaviours related to vegetables, cheese, and food past its sell by date. This equated to a potential 16,384 models. Of the 14 variables, seven were retained in the final model sets (the most parsimonious models, ΔAICc <2; see Table 2). The variables with the largest positive effect included the presence of fussy eaters, household size, and one particular local authority (individual local authority identity was anonymized). Variables with the largest negative effect included discard behaviours interacting with the presence of fussy eaters, employment status interacting with the presence of fussy eaters, four specific local authorities and home ownership status (owning a house outright). Exploratory sensitivity analysis The variables included in the model with discard behaviours removed (Fig 1b) were household size, local authority, household composition, house type, home ownership status, the presence of fussy eaters, and employment status. This equated to a potential 128 models. The final model set included six of these variables: household size, local authority, home ownership 9 / 16 Component models: Avoidable waste per Household ~ Discard Sellby+ Discard vegetables+ Fussy eaters + Household size + employment+ Local Authority + Home ownership+ Discard Vegetables:Fussy eaters+ Fussy eaters:Employment Avoidable waste per Household ~ Age+ Discard Sellby+ Discard vegetables+ Fussy eaters + Household size + employment+ Local Authority + Home ownership+ Discard Vegetables:Fussy eaters+ Fussy eaters:Employment Avoidable waste per Household ~ Age+ Discard Sellby+ Discard vegetables+ Fussy eaters + Household size + employment+ Local Authority +Discard Vegetables:Fussy eaters+ Fussy eaters:Employment Avoidable waste per Household ~ Age+ Discard vegetables+ Fussy eaters + Household size + employment+ Local Authority + Home ownership+ Discard Vegetables:Fussy eaters+ Fussy eaters:Employment Avoidable waste per Household ~ Sellby+ Discard vegetables+ Fussy eaters + Household size + employment+ Local Authority + Home ownership+ Discard Vegetables:Fussy eaters+ Fussy eaters:Employment df logLik AICc 47 -15481.2 31059.1 delta weight 0 0.28 status, the presence of fussy eaters, respondent age, and employment status (S2 Table). Variables with the largest positive effect included the presence of fussy eaters, employment (working), household size (increasing with a larger number of occupants) and age (35±64). Variables with the largest negative effect included interactions between fussy eaters and employment, age (35±64), employment (not working), two specific local authorities, and home ownership status (with a mortgage or owned outright). Variables with the largest positive effect in the model with local authority removed (see Fig 1c for the variables retained) included household size (two, three, four or five people), while variables with the largest negative effect included home ownership (owned outright and owned with a mortgage) and employment (retired) (See S3 Table). The results of the models with both local authority and discard behaviours excluded were very similar (See S4 Table). Discussion The drivers of UK household food waste The variables selected in the most parsimonious models always included household size, the presence of fussy eaters, employment, home ownership status, and local authority. Household size (i.e. the number of people in the household) appears to be a generally well-supported explanatory variable [14, 16±18, 20±22, 59]. Levels of avoidable food waste per household increased with increasing household size. Aschermann-Witzel et al. [ 60 ] suggest that household size and composition (i.e. the age of household members) are the key demographic drivers of food waste, because they relate to multiple behavioural factors, which typically differ across household types. These include, for example, the purported advanced food skills of the older generation (making use of leftovers, etc.), higher food security and safety concerns of households with children, greater levels of fussiness in households with children, and lower degrees of planning in young or single-person households. Our results support the idea that fussiness in a household has a small but noteworthy effect on food waste generation. Regardless of variable set, our results point toward families (i.e. large households) as being a key target group for food waste reduction initiatives. Targeted initiatives (such as educational campaigns and increased frequency and modalities of waste collection) in areas with a high density of larger households need to be prioritised for study and intervention. Other evidence [61] indicates that the reasons these households waste food are more likely to be due to cooking or serving too much or fussy eating (rather than not using food before it goes off). Survey respondents stating that they discard ªa reasonable amountº of vegetables was related to higher levels of waste compared to other food categories. Discarding ªquite a lotº had a similar mean value of the remaining food categories, but greater variation. Low levels of 10 / 16 vegetables discarded by consumers logically lead to reduced avoidable food waste as vegetables are the single largest food group contributing to household food waste in the UK [ 5 ]. However, there may be some discrepancy between stated and actual levels of discard due to a range of factors [ 62 ]. Interventions aimed at preventing vegetable waste through, for example, supporting the purchase of an appropriate amount, storing it optimally or providing recipes to help use up leftovers may help further reduce food waste. Local authority was not intended as a predictive variable in the original data collection, as there were no socio-demographic assumptions underlying the sampling regime. The fact that this descriptive variable (treated as a random variable in the model) is an important explanatory variable highlights the large geographical variability in the food waste behaviours observed. A combination of imprecision and high heterogeneity in the variables used to assess consumer food waste may explain the difficulty in determining significant relationships. An alternative explanation is that regional factors are important (but we could not determine any evidence for this in our dataset). The location could be a proxy for socio-economic factors, as well as factors related to the availability and the identity of retailers. Further investigation into the drivers of these regional differences is warranted. Developing an evidence-based approach to food waste By using model selection to identify the most suitable structure of a model, researchers can reduce the probability of spurious results. The danger of Type I errors is that they lead to increased uncertainty in the effectiveness of interventions, because of both incorrectly targeting consumers' behaviours and wrongly assigning significance to specific interventions. Selective reporting, where only some of the variables measured are reported in the outcome, further reduces the ability to synthesise across studies (e.g. through systematic review and meta-analysis) an issue already highlighted as a constraint in consumer food waste research [ 63 ]. Type II errors are reduced effectively by increasing the sample size; however, Type I errors may still be highly probable where a large number of variables are used (i.e. ªp-hackingº), and/or where many models are run but only those which confirm pre-conceived ideas or theories are reported. To effectively reduce Type I error (one can never totally eliminate Type I or Type II errors), researchers can take a number of potential approaches: 1. Careful selection of variables with a rationale for inclusion: a pre-published protocol can be used to identify the variables that will be tested and processed to reduce the biases undertaken by the researcher. This is a popular approach in meta-analysis and systematic review, but can be applied more widely. 2. Provision of all analysis and data in the rawest possible form in an open online data repository (e.g. Open Science Foundation, https://osf.io) to allow independent analysis (data sharing is not always appropriate or possible, due to commercial sensitivities, etc.). 3. Transparent variable selection and model averaging, as well as reporting multiple model results with a clear indication of the range of potential outcomes and the errors associated with these (e.g. confidence limits, credible intervals, etc.) should be standard practice. Our approach accounts for model structural uncertainty in a frequentist paradigm. Of course, the issue of Type I errors becomes irrelevant when using Bayesian models, however with frequentist statistics still dominating research in consumer science there is a need to reduce the probability of spurious results in a robust manner. Stepwise approaches (which are superficially similar to our approach) have largely been discredited in many fields (e.g. in 11 / 16 medicine and ecology; [ 53, 64 ]) because they increase (among other problems) the Type I error rate. In addition to the problems of variable choice and Type I errors in models of consumer research, there are problems with the typical approaches to complexity adopted in this field. There is a well-developed body of complexity theory (e.g. [ 65 ]) which appears to be largely ignored in favour of a generic mixed methods approach to data acquisition and regression based modelling (e.g. factor analysis, structural equation modelling, mixed regression model, etc.). The lack of a coherent framework is often justified with adoption of a single theoretical perspective exacerbated by failure to consider model (structural) uncertainty. The tools to undertake more structured and nuanced analysis exist (e.g. agent based models, network analysis, systems dynamics; [ 66 ]) and should be routinely deployed in consumer research as they are in other scientific disciplines. Conclusions The drivers of food waste are complex and interrelated, and may not lend themselves well to traditional modelling approaches. This high complexity may be better analysed through other statistical models or paradigmsÐsuch as Bayesian analysisÐin order to reduce the probability of false positives. What is clear is that food waste policies must be developed using an evidence-based approach, since traditional modelling paradigms are not sufficient to address this complexity. This field of study can learn much from medicine and ecology, where data are often similarly complex and uncertain [ 67 ]. Standard protocols for data collection and definition would need to be agreed to allow meta-analysis. For data collection, protocols are emerging, such as the FUSIONS Definitional Framework for Food Waste [ 4 ] and Food Waste Quantification Manual [ 68 ] and the World Resources Institute Food Loss and Waste Standard (http://flwprotocol.org/). With more rigorous evidence-based approaches, the drivers of food waste can better be determined, and the effectiveness of any trialled intervention can be more certain. This will lead to decreased cost and a more meaningful contribution to the understanding of food waste. Among the most important drivers identified is household size; however, the procedure of model reduction and selection allows us to uncover a positive relationship between household size and food waste, at odds with most of the previous literature on the issue [ 14, 23, 26, 69 ]. Other important drivers are the various dimensions of the household composition, for which the results corroborate those of the literature. Interestingly, some of the drivers identified as important by the literature, such as awareness of the food waste problem and shopping habits, here are found as not important. This testifies the relevance of unbiased model selection of an evidence-based approach to data analysis. Finally, no evidence emerges on the behavioural characteristics of individuals at the point of purchase (i.e. in the supermarket), and on how they may influence the food waste generation. Any further research and, in particular, those focusing on large households, would need to include this aspect. Supporting information S1 File. The complete R Code. (DOCX) S1 Table. Model average coefficients for the full model including interaction terms. The variables are sorted by z value. (DOCX) 12 / 16 S2 Table. Selected models and averaged coefficients (sorted by z value) for the model with discard behaviour variables excluded. (DOCX) S3 Table. Selected models and averaged coefficients (sorted by z value) for the model with local authority excluded. (DOCX) S4 Table. Selected models and averaged coefficients (sorted by z value) for the model with local authority and discard behaviours excluded. (DOCX) Acknowledgments This work was carried out under the H2020 project REFRESHÐResource Efficient Food and dRink for the Entire Supply cHain. REFRESH is funded by the Horizon 2020 Framework Programme of the European Union under Grant Agreement no. 641933. The views reflected in this article represent the professional views of the authors and do not necessarily reflect the views of the European Commission or other REFRESH project partners. We thank Toine Timmermans, Hilke Bos-Brouwers, Hans van Trijp, Erica van Herpen, Graham Moates and Keith Waldron for comments on an earlier draft of this paper. Author Contributions Conceptualization: Matthew James Grainger, Gavin Bruce Stewart. Data curation: Thomas Edward Quested. Formal analysis: Matthew James Grainger. Funding acquisition: Marco Setti, Matteo Vittuari, Gavin Bruce Stewart. Investigation: Matthew James Grainger. Methodology: Matthew James Grainger, Gavin Bruce Stewart. Project administration: Matteo Vittuari. Supervision: Gavin Bruce Stewart. Visualization: Matthew James Grainger. Writing ± original draft: Matthew James Grainger, Gavin Bruce Stewart. Writing ± review & editing: Matthew James Grainger, Lusine Aramyan, Simone Piras, Thomas Edward Quested, Simone Righi, Marco Setti, Matteo Vittuari, Gavin Bruce Stewart. 13 / 16 14 / 16 15 / 16 1. Stenmarck Å , Jensen C , Quested T , Moates G . Estimates of European food waste levels . Wageningen: FUSIONS Project . 80 pp., 2016 . 2. Gustavsson J , Cederberg C , Sonesson U , van Otterdijk R , Meybeck A . Global Food Losses and Food WasteÐextent, causes and prevention . Rome: FAO, 2011 . 3. Gunders D. Wasted: How America is losing up to 40 percent of its food from farm to fork to landfill getting food . Natural Resources Defence Council. Issue Paper IP 12-06-B , 2012 . 4. OÈ stergren K , Gustavsson J , Bos-Brouwers H , Timmermans T , Hansen O-J , Møller H , et al. FUSIONS definitional framework for food waste , Wageningen: FUSIONS Project . 134 pp., 2014 . 5. WRAP. Household Food and Drink Waste in the United Kingdom 2012 . WRAP: Banbury, 2013 . 6. Parfitt J , Barthel M , Macnaughton S . Food waste within food supply chains: Quantification and potential for change to 2050 . Philos Trans R Soc Lond B Biol Sci . 2010 ; 365 ( 1554 ), 3065 ± 81 . https://doi.org/10. 1098/rstb. 2010 .0126 PMID: 20713403 7. Canali M , Amani P , Aramyan L , Gheoldus M , Moates G , OÈ stergren K , et al. Food Waste Drivers in Europe, from Identification to Possible Interventions . Sustainability. 2017 ; 9 ( 37 ), 1 ± 33 . http://www. mdpi.com/2071-1050/9/1/37. 8. Thyberg KL , Tonjes DJ . Drivers of food waste and their implications for sustainable policy development . Resour. Conserv. Recycl . 2016 , 106 , 110± 123 . 9. Secondi L , Principato L , Laurato T. Household food waste behaviour in EU-27 countries: A multilevel analysis . Food Policy . 2015 ; 56 : 25 ± 40 . 10. Setti M , Falasconi L , Segrè A , Cusano I , Vittuari M. Italian consumers' income and food waste behavior . Br Food J . 2016 ; 118 ( 7 ): 1731 ± 46 . 11. Grainger MJ , Aramyan L , Logatcheva K , Piras S , Righi S , Setti M , et al. The use of systems models to identify food waste drivers . Glob Food Sec. Forthcoming 2018 12. Wilson A , Szwed N , Renzaho A . Developing Nutrition Guidelines for Recycled Food to Improve Food Security Among Homeless, Asylum Seekers, and Refugees in Victoria, Australia . Journal of Hunger & Environmental Nutrition 2012 , 7 : 2 ± 3 , 239 ± 252 . 13. Renzaho AMN , Kamara JK , Toole M. Biofuel production and its impact on food security in low and middle income countries: Implications for the post-2015 sustainable development goals . Renewable and Sustainable Energy Reviews 2017 , 78 , 503± 516 . 14. Wenlock R , Buss D , Derry B , Dixon E. Household food wastage in Britain . Br J Nutr . 1980 ; 43 ( 1 ): 53 ± 70 . PMID: 7370218 15. Sonesson U , Anteson F , Davis J . Home transport and wastage: environmentally relevant household activities in the life cycle of food . Ambio . 2005 ; 34 : 371 ±375 PMID: 16092271 16. Wassermann G , Schneider F. Edibles in Household Waste . In: Cossu, R. , Stegmann , R . (Eds.). Sardinia 2005 Tenth International Waste Management and Landfill Symposium, S. Margherita di Pula , Cagliari, Italy, 3 ±7 October, 2005 , Proceedings, 913 ± 4 . 17. Barr S. Factors Influencing Environmental Attitudes and Behaviors A U.K. Case Study of Household Waste Management . Environ Behav . 2007 ; 39 : 435 ± 473 . 18. IGD. Beyond Packaging: Food Waste in the Home . Institute of Grocery Distribution, Watford, UK, 2007 . 19. Godfray HCJ , Beddington JR , Crute IR , Lawrence H , Lawrence D , Muir JF , et al. Food security: The challenge of feeding 9 billion people . Science . 2010 ; 327 , 812 ± 818 . https://doi.org/10.1126/science. 1185383 PMID: 20110467 20. Koivupuro HK , Hartikainen H , Silvennoinen K , Katajajuuri JM , Heikintalo N , Reinikainen A , et al. Influence of socio-demographical, behavioural and attitudinal factors on the amount of avoidable food waste generated in Finnish households . Int J Consum Stud . 2012 ; 36 , 183 ± 91 . 21. WRAP. Household food and drink waste: A people focus . WRAP, Banbury, 2014a 22. Parizeau K , von Massow M , Martin R . Household-level dynamics of food waste production and related beliefs, attitudes, and behaviours in Guelph, Ontario . Waste Manage . 2015 ; 35 , 207 ± 17 . 23. WRAP. Helping consumers reduce fruit and vegetable waste . WRAP: Banbury , 2009 . 24. Silvennoinen K , Katajajuuri J-M , Hartikainen HA , HeikkilaÈ LB , Reinikainen A . Food waste volume and composition in Finnish households . Br Food J . 2014 ; 116 ( 6 ): 1058 ± 68 . 25. JoÈrissen J , Priefer C , BraÈutigam K-R . Food waste generation at household level: Results of a survey among employees of two European research centers in Italy and Germany . Sustainability. 2015 ; 7 ( 3 ), 2695 ± 715 . 26. Osner R. Food Wastage . Food Sci Nutr . 1982 ; 82 ( 4 ), 13 ± 16 . 27. Hamilton C , Denniss R , Baker D. Wasteful consumption in Australia . Discussion Paper Number 77 , March 2005 . Manuka, Australia: The Australia Institute . ISSN 1322-5421. 28. WRAP. Econometric modelling and household food waste . WRAP, Banbury, 2014b . 29. Qi D , Roe BE . Household Food Waste: Multivariate Regression and Principal Components Analyses of Awareness and Attitudes among U.S. Consumers . PLoS ONE . 2016 ; 11 ( 7 ). https://doi.org/10.1371/ journal.pone. 0159250 PMID: 27441687 30. Quested TE , Marsh E , Stunell D , Parry AD . Spaghetti soup: The complex world of food waste behaviours . Resour Conserv Recycl . 2013 ; 79 , 43 ± 51 . https://doi.org/10.1016/j.resconrec. 2013 . 04 .011 31. Stefan V , Van Herpen E , Tudoran AA , LaÈhteenmaÈki L. Avoiding food waste by Romanian consumers: The importance of planning and shopping routines . Food Qual Prefer . 2016 ; 28 : 375 ± 81 . https://doi. org/10.1016/j.foodqual. 2012 . 11 .001 32. Stancu V , Haugaard P , LaÈhteenmaÈki L. Determinants of consumer food waste behaviour: Two routes to food waste . Appetite . 2016 ; 96 , 7 ± 17 . https://doi.org/10.1016/j.appet. 2015 . 08 .025 PMID: 26299713 33. WRAP. Reducing supply chain and consumer potato waste . WRAP: Banbury , 2012 . 34. Graham-Rowe E , Jessop DC , Sparks P . Identifying motivations and barriers to minimising household food waste . Resour Conserv Recycl . 2014 ; 84 , 15 ± 23 . 35. WRAP. Food behaviour consumer research: quantitative phase . WRAP: Banbury , 2007 . 36. Baker D , Fear J , Denniss R. What a waste. An analysis of household expenditure on food . The Australia Institute. Policy Brief No. 6 , November 2009 . 37. Monier V , Escalon V , O'Connor C. Preparatory study on food waste across EU 27 . Brussels: European Commission-DG Environment , Technical Report, No. 54 , 2010 . 38. Barilla Centre for Food and Nutrition. Food waste: causes, impacts and proposals . Parma: Barilla CFN; 2012 . 39. Evans D. Beyond the throwaway society: ordinary domestic practice and a sociological approach to household food waste . Sociology . 2012 ; 46 ( 1 ), 43 ± 58 . 40. Abeliotis K , Lasaridi K , Chroni K. Attitudes and behaviour of Greek households regarding food waste prevention . Waste Manag Res . 2014 ; 32 ( 3 ), 237 ± 40 . https://doi.org/10.1177/0734242X14521681 PMID: 24525671 41. Buzby JC , Wells HF , Axtman B , Mickey J . Supermarket loss estimates for fresh fruit, vegetables, meat, poultry, and seafood and their use in the ERS loss-adjusted food availability data . USDA Economic Information Bulletin. No. 44 , March 2009 . 42. WRAP. Consumer insight: date labels and storage guidance . WRAP: Banbury , 2011 . 43. WRAP. Reducing food waste through the chill chain. Part 1: Insights around the domestic refrigerator . WRAP: Banbury , 2010a . 44. WRAP. Waste arisings in the supply of food and drink to households in the UK . WRAP: Banbury, 2010b . 45. Vittuari M , Politano A , Gaiani S , Canali M , Azzurro P , Elander M , et al. Review of EU legislation and policies with implications on food waste . Wageningen: FUSIONS Project . 54 pp., 2015 46. Chatfield C . Model uncertainty, data mining and statistical inference . J R Stat Soc Ser A Stat Soc . 1995 ; 158 : 419 ± 466 . 47. Zhang P. Inference after variable selection in linear regression models . Biometrika . 1992 ; 79 : 741 ± 746 . 48. Young C . Model uncertainty in sociological research: an application to religion and economic growth . Am Sociol Rev . 2009 ; 74 : 380 ± 397 49. Simmons JP , Nelson LD , Simonsohn U . False-positive psychology: undisclosed flexibility in data collection and analysis allows presenting anything as significant . Psychol Sci . 2011 ; 22 : 1359 ±1366 https:// doi.org/10.1177/0956797611417632 PMID: 22006061 50. Visschers VHM , Wickly N , Siegrist M. Sorting out food waste behaviour: A survey on the motivators and barriers of self-reported amounts of food waste in households . J Environ Psychol . 2016 ; 45 : 66 ± 78 . 51. Lorenz B , Hartmann M , Hirsch S , Kanz O , Langen N. Determinants of plate leftovers in one German catering company . Sustainability . 2017 ; 9 : 807 52. Leamer EE . Let's take the con out of econometrics . Am Econ Rev . 1983 ; 73 : 31 ± 43 . 53. Whittingham MJ , Stephens PA , Bradbury RB , Freckleton RP . Why do we still use stepwise modelling in ecology and behaviour? J. Anim. Ecol . 2006 ; 75 : 1182 ± 1189 . https://doi.org/10.1111/j.1365- 2656 . 2006 . 01141 . x PMID : 16922854 54. Burnham KP , Anderson DR. Model Selection and Multimodel Inference : A Practical Information-Theoretic Approach , Springer; 2002 . 55. Breiman L. Random Forests . Mach Learn . 2001 ; 45 : 5± 32 . 56. Kursa BK , Rudnicki WR . Feature Selection with the Boruta Package . J Stat Softw . 2010 ; 36 ( 11 ), 1 ± 13 . http://www.jstatsoft.org/v36/i11/. 57. R Core Team. R: A language and environment for statistical computing . R Foundation for Statistical Computing , Vienna, Austria. https://www.R-project. org/ , 2016 . 58. Calcagno V , de Mazancourt C. glmulti: An R Package for Easy Automated Model Selection with (Generalized) Linear Models . J Stat Softw . 2015 ; 34 : 1± 29 . 59. Glanz R. ( 2008 ). Causes of Food Waste Generation in HouseholdsÐAn Empirical Analysis . Master's Thesis . University of Natural Resources and Applied Life Sciences, Vienna and Cranfield University, 2008 , https://zidapps.boku.ac.at/abstracts/download.php?dataset_id=7178&property_id= 107 . 60. Aschemann-Witzel J , de Hooge I , Amani P , Bech-Larsen T , Oostindjer M . Consumer-related food waste: Causes and potential for Action . Sustainability 2015 ; 7 ( 6 ), 6457 ± 6477 . https://doi.org/10.3390/ su7066457 WRAP. Household food and drink waste: A product focus . WRAP, Banbury, 2014c . 62. Van Herpen E , van der Lans I , Nijenhuis-de Vries M , Holthuysen N , Kremer S , Stijnen D. Consumption life cycle contributions. Assessment of practical methodologies for in-home waste measurement . EU Horizon 2020 REFRESH. Wageningen, The Netherlands: Wageningen University and Research, 131 pp, 2016 . 63. SibriaÂn R , Komorowska J , Mernies J . Estimating Household and Institutional Food Wastage and Losses (No . ESS/ESSA/001e). Statistics Division Working Paper Series. FAO , 2006 . 64. Altman DG , Anderson P K. Bootstrap investigation of the stability of a cox regression . Stat. Med . 1989 ; 8 ( 7 ), 771 ±783 PMID: 2672226 65. Midgley G. Systemic Intervention : Philosophy, Methodology, and Practice. 1st edition: Springer Science & Business Media; 2001 66. Luke DA , Stamatakis KA . Systems science methods in public health; Dynamics, Networks, Agents . Annu Rev Public Health . 2012 ; 33 : 357 ±376 https://doi.org/10.1146/annurev-publhealth- 031210 - 101222 PMID: 22224885 67. Stewart GB , Schmid CH . Lessons from meta-analysis in ecology and evolution: the need for trans-disciplinary evidence synthesis methodologies . Res Synth Methods . 2015 ; 6 ( 2 ): 109 ± 10 . https://doi.org/10. 1002/jrsm.1152 PMID: 26099477 68. Tostivint C , OÈ stergren K , Quested T , Soethoudt H , Stenmarck Å , Svanes E , et al. Food waste quantification manual to monitor food waste amounts and progression . Wageningen: FUSIONS Project . 165 pp., 2016 . 69. Van Garde SJ , Woodburn MJ . Food discard practices of householders . J Am Diet Assoc . 1987 ; 87 : 322 ± 9 . PMID: 3819252


This is a preview of a remote PDF: http://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0192075&type=printable

Matthew James Grainger, Lusine Aramyan, Simone Piras, Thomas Edward Quested, Simone Righi, Marco Setti, Matteo Vittuari, Gavin Bruce Stewart. Model selection and averaging in the assessment of the drivers of household food waste to reduce the probability of false positives, PLOS ONE, 2018, DOI: 10.1371/journal.pone.0192075