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Energy 36 (2011) 5610e5620

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Energy

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Do homes that are more energy efficient consume less energy?: A structuralequation model of the English residential sector

Scott Kelly*

Centre for Climate Change Mitigation, Department of Land Economy, University of Cambridge, 19 Silver St, Cambridge CB39EP, United Kingdom

a r t i c l e i n f o

Article history:Received 13 November 2010Received in revised form30 June 2011Accepted 7 July 2011

Keywords:ResidentialEnergyEfficiencyStructuralEquationModelling

* Tel.: þ44 7942 617 428; fax: þ44 1223 764 867.E-mail address: sjk64@cam.ac.uk.

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.07.009

a b s t r a c t

Energy consumption from the residential sector is a complex socio-technical problem that can beexplained using a combination of physical, demographic and behavioural characteristics of a dwellingand its occupants. A structural equation model (SEM) is introduced to calculate the magnitude andsignificance of explanatory variables on residential energy consumption. The benefit of this approach isthat it explains the complex relationships that exist between manifest variables and their overall effectthough direct, indirect and total effects. Using the English House Condition Survey (EHCS) consisting of2531 unique cases, the main drivers behind residential energy consumption are found to be the numberof household occupants, floor area, household income, dwelling efficiency (SAP), household heatingpatterns and living room temperature. In the multivariate case, SAP explains very little of the variance ofresidential energy consumption. However, this procedure fails to account for simultaneity bias betweenenergy consumption and SAP. Using SEM its shown that dwelling energy efficiency (SAP), has reciprocalcausality with dwelling energy consumption and the magnitude of these two effects are calculable.When non-recursivity between SAP and energy consumption is allowed for, SAP is shown to havea negative effect on energy consumption but conversely, homes with a propensity to consume moreenergy also have higher SAP rates.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Buildings are a significant contributor to greenhouse gas emis-sionswith space heating alone responsible for over half of all end useemissions from UK dwellings [1]. In 2007, the UK government put inplace a National Energy Efficiency Action Plan (NEEAP) to reduceemissions from the UK housing stock by 31% on 1990 levels by 2020.More recently, the government’s own Climate Change Act [2] setsa legally binding target to reduce greenhouse gas emissions by atleast 80% on 1990 levels by 2050. It is recognised that meeting sucha target will only be possible through radical reductions in energyconsumption and necessary but strategic changes to energy supplyand delivery. In addition, the residential sector has been repeatedlyidentified by government departments [1,3e6]; commercial orga-nisations [7,8], non governmental organisations [1,9] and byacademia [10e12] as having one of the lowest costs and largestimpacts for reducing CO2 emissions. Still, there remains significantdebate about the best approach for reaching the CO2 reductionsimminently required. Moreover, there is insufficient empirical

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research quantifying the complex relationship between majordriving forces purporting to explain residential energy consumptionand in particular, the contribution that improved building efficiencycan have on reducing final end use energy demand.

1.1. Contribution

This paper presents the first known application of structuralequation modelling (SEM) for the explanation of residential energyconsumption in England. This powerful statistical technique allowsfor the calculation of both direct and indirect effects that explainenergy consumption in the residential sector. For example, house-hold (HHLD) income is directly correlated with energy consump-tion but is also indirectly correlated andmediated by dwelling floorarea. This is because homes having high annual incomes tend toalso have larger floor areas and therefore require more heating.Using SEM it is possible to decompose the relative magnitude ofthese effects and therefore gain deeper understanding for whatvariables have the most impact when attempting to understandresidential energy consumption. With this technique, it is possibleto show the relative sensitivities of different explanatory variableson residential energy consumption. Sensitivity analysis is impor-tant for identifying where leverage points may be exploited within

S. Kelly / Energy 36 (2011) 5610e5620 5611

the system for maximum impact. In addition, this research presentsnew evidence to quantify the extent that SAP has on reducingresidential energy consumption. More importantly, empirical proofis provided showing a reciprocal relationship between SAP andenergy consumption, and that, ceteris paribus: dwellings witha propensity to consume more energy will, on average, have higherSAP ratings. However, the reverse is also true and dwellings witha high SAP value will, ceteris paribus, have reduced energyconsumption owing to increased efficiency. Finally, these twoeffects are separately and empirically calculated.

1.2. Structure of paper

The first section of this paper presents important recentdevelopments in the state-of-the-art in residential energy model-ling. A thorough review of the literature has shown a serious lack inrecent years in the development of bottom-up statistical models forexplaining the driving forces behind residential energy consump-tion. In order to tackle this problem, a structural equation model isintroduced with an emphasis on how this relatively modernstatistical technique can be applied and used to provide deeperinsight into understanding the cause and effect relationshipsbehind residential energy consumption. What follows is a descrip-tion of the dataset and preparation of the variables prior to analysis.The importance of SEM for conducting this type of analysis ishighlighted by the results obtained from a typical multivariateregression model, a technique unable to directly measure non-recursivity or easily distinguish direct and indirect effects. Statis-tical results are then presented before leading into a discussion andthe implication of this research for policy makers.

2. The epistemology of residential sector energy modelling

2.1. Energy demand modelling in the residential sector

Over the last two decades, there has been a plethora of nationallevel domestic energy models that vary in data requirement,disaggregation level, socio-technical assumptions and the type ofscenarios or predictions that can be modelled [13]. This briefliterature review is intended to provide an overview of the majorepistemic approaches that have previously been used for modellingresidential energy consumption and emissions in the UK. Due to thefact that several relatively recent publications provide excellentreviews on different residential sector modelling techniques, thissection has purposefully been kept brief [13e21].

Since the advent of computers many national level models havebeen developed to assist in the prediction and analysis of domesticenergy consumption. Most authors agree that the majority ofmodels generally take two broad epistemic approaches describedas being either top-down or bottom-up. Top-down methods useeconometrics and multiple linear regression methods for theexplanation of variance between dependent and independentcovariates. Such models lack the resolution required to calculatethe potential of different technologies or policy options availablefor estimating energy demand. Several models have been devel-oped in the UK using these methods [22e24].

Advances in recent years have seen the development of sophis-ticated hybrid models that integrate both of these approaches intoa singlemodel. Inparallelwith these integrated techniques, a numberof advances have been made in machine learning, new statisticalapproaches and GIS methods [25] capable of modelling the interac-tion between energy, economy, environmental systems and tech-nology in the built environment. For example, a neural-networkbased national energy consumption model has been developed forthe Canadian residential sector [26] and other innovative statistical

techniques such as decision tree analyses are being used to modelresidential energy consumption at the national level in Hong Kong[14]. However, Hitchcock [27] argues that energy consumptionpatterns are a complex technical and social phenomenon and inorder to be understood appropriately must be tackled from bothengineering and social science perspectives concurrently.

Although aggregate regression methods help to show trends intotal dwelling stock energy consumption patterns, they cannotexplain the various components that contribute to energyconsumption at the household level. For this type of analysis it isnecessary to conduct investigations at the micro-level. Bottom-upmethods take a disaggregated approach and estimate energydemand and emissions using high resolution data using a combina-tion of physical, social, behavioural and demographic properties fora household [28e30]. The empirical data requirement for bottom-upmodels is significantly more demanding requiring large, high reso-lution datasets that contain specific characteristics for each dwellingthat include physically measured variables, demographic informa-tion and details about energy consuming behaviour [31]. Withbottom-up methods, it is also possible to combine, or aggregatemicro-level data in order to generate new variables that provideinformation about the total dwelling stock. There are two types ofbottom-up methods that are contingent on the data and structure ofthe analysis required. These are the engineering method and thestatistical method. The engineering method uses a sample of housesand technologies to represent the national housing stock and applyheat balance equations to estimate energy demand. In the UK severalengineering models exist for the UK residential sector [10,32e34].

More in line with the research presented in this paper arebottom-up econometric methods. Such models are largely neglec-ted in reviews on residential energy modelling and almost entirelyneglected for estimating energy consumption in the UK. While oneor twomodels were developed in the 80’s and early 90’s using largestatistically powerful datasets [35] the full potential of thesemodels has never been realised. More recent models rely on dataobtained from very small-localised datasets representing justa small subset of the population with, perhaps, a few hundredrepresentative cases [36]. Themain reason for this significant gap inthe literature can be explained by a serious lack of statisticallysignificant, high quality, high resolution data combining householdlevel energy consumption data along with the physical character-istics of the dwelling and user behaviour. Indeed, there are manybenefits of Multiple Linear Regression (MLR) techniques over othermethods including their simplicity and adaptability to almost anyproblem. A downside of this approach is the assumption thata single dependent variable is a linear function of multiple inde-pendent variables. It is also difficult to ascertain the underlyingcausal mechanism behind the model as standard multiple regres-sion techniques only provide evidence of correlation and thereforecan sometimes suffer frommulticollinearity and misinterpretation.As shown in this paper, structural equation modelling is a robust,well known statistical method and when applied to the residentialsector is able to provide new insight and overcome many of theweaknesses and pitfalls of many other methods.

3. Methodology

3.1. The dataset

The model is based solely on publicly available data andcomprises information available from two principle datasets: The1996 English House Condition Survey (EHCS) and the 1996 Fuel andEnergy Survey (FES). The EHCS is conducted every five years and isthe only survey to provide thorough data on the condition of thenational housing stock [37]. The 1996 EHCS consists of 12,131 real

S. Kelly / Energy 36 (2011) 5610e56205612

cases selected to represent the dwelling stock in England. Usuallythe EHCS focuses primarily on the physical condition of dwellingsand other building characteristics with limited scope for otherdemographic and economic information. In 1996 however,a supplemental FES was carried using a sub-sample of 2531 casesfrom the EHCS. Importantly, the FES sub-sample includes metredelectricity and gas consumption data, information on energy usageas well as data on energy expenditure. The interviews were con-ducted from January to May 1996, with the fuel survey collectingactual energy and fuel usage over eight consecutive quarters. Thusinformation on a dwelling’s physical condition, the economic statusof its inhabitants as well as demographic and behavioural infor-mation can all be used in an analysis to determinewhat factors mayexplain residential energy consumption. A similar survey of thisscale and type has not been completed in England since 1996 butone is planned for release at the end of 2011 [38].

The relevance of this data for solving the problems of today canbe emphasised in several respects. Firstly, one strength of theapproach adopted here is that it develops a structural relationshipbetween model variables. In the residential sector, such relation-ships are grounded in physical laws and defined by economicrelationships. For example, homes with a large floor area will takemore energy to heat and homes occupied by people with higherincomes will be more likely to have higher energy expenditure. Forthis reason, the structural relationships estimated from historicaldata are still relevant for understanding the consumption patternsof today and in the future. This is because, the structural relation-ship between variables remains relatively constant over time.Moreover, the underlying inertia of the residential sector is slowchanging and takes many years for any noticeable changes to thebuilding stock to manifest.

3.2. Explanatory variables

The EHCS and FES are two large national housing surveys inEngland. They cover all tenure types and involve a physical inspec-tion of the property by certified professionals. Included in thedataset are hundreds of variables thatmeasure almost every physicalproperty of the dwelling and demographic characteristics of theoccupants. Several previous studies have used this information togain valuable insight into energy and emissions [39e41]. Armedwith such information it is possible to develop a model consisting ofan enormous number of variables pertaining to explain residentialenergy consumption. However, in SEM, as it is in science moregenerally, parsimony is highly valued. If two explanations fora phenomenon are equally good, then the more parsimoniousexplanation is the preferred option. With this in mind, variableswere chosen based on previous research and theory on the premisethat they were likely to explain a large proportion of the variance inenergy consumption. If the addition of a variable to the model per-formed just as well as the simpler, more parsimonious model, thenew variable was discarded in favour of the more parsimoniousmodel. The following variables were chosen due to their knownrelevance in explaining residential energy consumption.

Number of occupants is the number of people living at thedwelling at the time the survey was conducted.

Household Income is the annual net income for the householdafter tax and national insurance contributions have been deducted.

Floor Area is the internal useful floor area for the dwelling andexcludes integral garages, balconies, stores accessed from theoutside and the area under partition walls.

SAP is the UK Governments standard assessment procedure formeasuring the energy efficiency of dwellings. The values in thisdataset were calculated using the 1996 SAP calculation procedureand were derived by the Building Research Establishment (BRE),

the organisation responsible for managing SAP for the UKGovernment. In this analysis, values range from 0 to 110 with lowvalues indicating poor dwelling efficiency.

Temperature Difference is the difference between the internalliving room temperature and the outside temperature at the timethe survey was conducted.

Energy Pattern is a scale from 0 to 5 describing how frequentlythe occupants heat their home. Each question requires a binaryresponse from which a scale can be constructed. A zero valuemeans the respondent answered negative to all questions whilea value of five means the respondent answered positively to everyquestion.

� Is the bedroom heated on the weekend?� Is the bedroom heated during the week?� Is the living room heated on the weekend?� Is the living room heated during week?� Is the home heated during the week and throughout the day?

Dwelling Energy Expenditure was collected over eight consecu-tive quarters and takenwith permission from the energy supplier ofthe dwelling. Average annual energy expenditure is then calculatedand used in the model.

The age of the head of the household is a categorical indicatorrepresenting six age groups from 16 to 65 and over.

Degree days is a measure of the temperature difference betweenthe outside temperature and a base temperature of 18.5� Celsiusand the length of time this temperature persists over a period ofa year.

The following dummy variables were also tested:Urban dummy is a binary indicator for the location of the

dwelling [42].Owner dummy is a binary number indicating whether the

occupier owns the dwelling.Economic status dummy is a binary indicator for the employment

status of the head of the household.Energy prices were also considered as an important driver for

explaining residential energy consumption. As this study useda cross-sectional analysis, it was not possible to control for theeffect of energy prices on energy demand. As shown by Summer-field [43], energy prices in the UK are relatively inelastic with anestimated elasticity of �0.20. This means a 50% increase in energyprice will lead to an approximate 10% decline in energy demand.Similar results were found by others [44,45] with most studiesfinding elasticities in the range�0.05 to�0.50 [46e48]. Descriptivestatistics for the variables included in the model can be accessedonline under supplemental materials.

3.3. Preparing the data for analysis

The final dataset was created by combining the 1996 EHCS withthe 1996 FES sub-sample using a field code common to bothdatasets. After the datasets were combined the final sample con-tained 2531 cases. The sum of grossing weights from the finalsample represents the number of residential buildings in Englandin 1996 and is equal to 19.265 million homes.

3.4. Dealing with outliers

Datasets that contain univariate or multivariate outliers havethe potential to significantly distort statistics leading to both Type Iand Type II errors. Histograms and box andwhisker plots facilitatedthe detection and deletion of a very small number of univariateoutliers. Histogram plots of HHLD Income, Floor Area and EnergyExpenditure revealed long right-hand tails with potential to

S. Kelly / Energy 36 (2011) 5610e5620 5613

adversely affect model results. The distributions of these variableswere therefore truncated to five standard deviations from themean. Multivariate outliers were found using Cook’s distance andthe Centred Leverage statistic but were found unproblematic afterthe univariate outliers had been removed.

3.5. Missing data

Missing data in substantive research is common [49] and can beproblematic for structural equation modelling if not handledcorrectly [50]. A well recognised statistical benchmark suggestsdatasets with missingness less than 5% is not a problem [51,52].Within this dataset no single variable had less than 5%missing dataand was therefore not considered a problem to conduct furtherstatistical tests. The Expectation Maximisation (EM) method waschosen to replace missing values in the dataset [53].

3.6. Applying sample grossing weights

Sample weights are defined as the application of a constantmultiplying factor to data to vary the contribution that any entrycan make to the overall estimates. As shown by Dorofeev [54] littlehas been published on the subject of weighting and is generallyignored in texts on statistics and survey research. Dorofeev [54]shows that statistical procedures conducted on a sample withoutapplying the grossing weights prior to the analysis may lead toincorrect inferences about the population including underestima-tion of standard errors of estimators leading to inflated Type I andType II errors as well as erroneous model diagnostics. Grossingweights as they are used in the EHCS incorporate expansion factors,which mean the sum of the weights represents the size of thepopulation (the total number of dwellings).

The EHCS and FES are large complex stratified surveys designedwith a priori weighting designed to efficiently represent thedwelling stock of England. Each case in the sample is associatedwith a grossing weight derived from a stratified multi-stage clustersampling process and calibrated to auxiliary variables subject tosurvey non-response adjustments. This is to allow for accurateanalyses of particular groups of dwellings. For example, the samplesize for particular groups of dwellings such as local authoritydwellings, unfit dwellings and RSL dwellings need to be sufficientlylarge to provide a statistically significant sample. In order tomaximise the efficiency of data-gathering while still achievingstatistical significance, survey stratification is needed. This tech-nique requires over representation of small groups of dwellings andunder representation of common groups of dwellings in thesample. Grossing weights are then applied to the final dataset toundo the effects of stratification and for the dataset to accuratelyrepresent the population. The post-weighted dataset, after adjust-ments are made for non-response and response bias shouldtherefore be an accurate reflection of the population. If grossingfactors are not taken into account, the final results will not beaccurate or meaningful at the national level and therefore biastowards groups that have been unequally sampled.

The overall effect of applying weights is increased accuracy ofmodel estimates and therefore reduced bias. However, this comesat the expense of precision [54]. This is because weighting involvesa substantive increase in the standard error of estimates, thusintroducing wider confidence intervals and a loss of discriminationin significance testing. The loss in precision is directly proportionalto the range in weights being applied to the sample, the greater therange in weights the greater the loss in precision. For any weightedsample the overall loss in precision can be obtained by calculatingthe “effective sample size” given by nc in Eq. (1.1). The ratio of actualsample size to effective sample size is known as the Weight Effect

(WE) and is typically greater than 1.0 for weighted samples.Therefore the actual standard error (or confidence interval) of anestimate like the mean, x, can be calculated by multiplying theactual estimate by the weight effect and therefore the standarderror of an estimate can be expressed by Eq. (1.3). Equation

nc ¼�Pn

i¼1wi�2

Pni¼1w

2i

¼ 1;025 (1.1)

Hence,

WE ¼ nnc

¼ 2;5311;025

¼ 2:47 (1.2)

s:eðxÞ ¼ffiffiffiffiffiffiffiffiWE

p Sffiffiffin

p ¼ Sffiffiffiffiffiffiffiffiffiffiffiffiffin=WE

p ¼ Sffiffiffiffiffinc

p (1.3)

Where, nc, is the calibrated sample size, S, is the standard deviationof the original variable x from the post-weighted calibrated sample,and n is the original un-weighted sample size. The result of usingthe calibrated sample size, nc, has the same effect of reducing thesample size by 1/WE and therefore has the overall effect ofincreasing standard errors. Not applying the weighted samplecorrection factor will lead to incorrect computation of variance andmargin of error calculations of the model estimates.

3.7. Testing for normality

Critical deviation from normality was tested for all model vari-ables, including the use of frequency histograms. Model resultsfrom the untransformed dataset were compared against results foreach dataset containing a transformed variable. Differences in theoutput for all transformed datasets were insignificant and thereforeit can be concluded that the model is robust to minor deviationsfrom normality.

4. Model development

Based on substantive prior research a structural equation modelwas developed to represent the expected underlying causal rela-tionships likely to explain domestic energy consumption inEngland. This is represented in pictorial form as a path diagram. Themodel developed is based on the premise that domestic energyconsumption can be explained by several manifest variables. Usingsuch a model it is possible to test a number of hypotheses about theexplanatory power and statistical significance between modelvariables and what their relative effect on residential energyconsumption might be. Importantly, the underlying data used bythe model is not used in any way to make inferences about thedirection of causality. A researcher armed with such prior knowl-edge about the variables under question is thus only able to inferweak causal ordering to the underlying structural relationshipbetween variables [55]. For example, in Fig. 1 when an arrow isdrawn from Floor Area to Energy Expenditure it does not show thatFloor Area causes higher energy consumption it says that if FloorArea and Energy Consumption are causally related it is likely to bein the direction of the arrow and not the reverse.

4.1. Importing the dataset into AMOS 18.0

A major benefit of using AMOS 18.0 is the ability to import thecorrelation matrix of the dataset as opposed to the entire samplefor solving the model. As AMOS 18.0 does not allow for unequalweights to be used during model estimation it was necessary toimport a post-weighted correlation matrix into AMOS 18.0. The

Fig. 1. Path diagram of Structural Equation Model (SEM) showing direct and indirect effects that explain annual energy expenditure.

S. Kelly / Energy 36 (2011) 5610e56205614

benefit of using this approach is that grossing weights can becorrectly applied to represent the calibrated sample size, nc, beforebeing used to produce the correlation matrix thus ensuring thatvariance and standard error estimates are correctly calculated forthe sample being used.

4.2. Model identification and non-recursivity

Ensuring the degrees of freedom (dof) within the model areequal to or larger than the number of parameters to be estimated isa necessary but insufficient condition for identification. In SEMover-identification is preferred as over-identification allows for theevaluation and overall quality or fit of the model. The secondcondition that must be met is empirical identification and requiresthe data being used on the model to produce semi-positive definitematrices. The addition of feedback loops in SEM automaticallyintroduces non-recursivity thus making the model more difficult tosolve due to the added restrictions placed on the model. Oneassumption for non-recursive models is the assumption of statio-narity, requiring the causal structure of the model not to changeover time. For cross-sectional data, like in this analysis, there is alsothe assumption of equilibrium. This means that any changes in thesystem underlying the feedback relationship have already man-ifested and the system has reached a steady state [51]. The struc-tural equation model developed here satisfies both of theseconditions. Firstly, the stationarity assumption is satisfied becausethe causal effects of residential energy consumption do notsubstantially change over time. Secondly, the variables identifiedare long lasting and slow to change (number of occupants, floorarea, income etc) and therefore the effects of these indicators areassumed tomanifest on energy consumption over many years priorto the survey being taken. For example, people living in homes witha high household income have a degree of familiarity withreceiving a high income and therefore Income effects on energyconsumption would have already manifested in the home prior tothe survey being taken and therefore can be assumed to havereached a state of equilibrium.

4.3. Model precision and confidence intervals

Estimating model parameters is only part of the solution.Checking the precision and accuracy of the model is necessary ifone is to have any confidence in the results. This requires the

calculation of standard errors and confidence intervals for eachmodel parameter. In this section a bootstrapping method is intro-duced for assessing the precision that can be obtained from themodel and underlying data.

4.4. Weighted random sampling with replacement

Previously, the estimation of the model was achieved by directlyimporting the correlation matrix from the post-weighted sampleinto AMOS 18.0. However, there are several alternatives for esti-mation using a weighted dataset in AMOS 18.0. One such method isto use sampling procedures to create a new sub-sample from theoriginal dataset. This method is known as weighted randomsampling with replacement (WRSWR). It is a probabilistic samplingmethod where the grossing weights for each case represent theprobability a case is selected and added to the sub-sample. Supposethat wi are the grossing weights produced by the complex sampledesign, the probability that case i is selected from the sample isthen given by PðXi ¼ xÞ ¼ wi=

Pwi. Each time a case is selected it

is replaced back into the sample at which point a new case isselected and saved in the new sample. Repeating this process Ntimes creates a new sub-sample representative of a post-weightedsample. Similar to bootstrapping, the new sample will containsome cases that are repeated multiple times while other cases willnot be represented at all. Because case selection is based onweighted probability it simulates the effect of selecting a case atrandom from the population and therefore the sub-sample repre-sents a post-weighted sample of the population. Importinga representative dataset into AMOS 18.0 rather than the correlationmatrix allows for deeper statistical analysis such as bootstrapping.

4.5. Bootstrapping

A key advantage of AMOS 18.0 is the functionality to performbootstrapping on the model from the imported dataset. Withbootstrapping it is possible to determine empirical estimates ofstandard errors of any parameter, even standard errors of standarderrors [55]. In addition, with nonparametric bootstrapping it is notnecessary to have data that fits to a normal distribution, thus priortransformation of the data is not necessary. In fact the onlyrequirement is for the distribution of the sample to be the samebasic shape as the distribution of the population. Confidenceintervals for each of the model parameters are therefore calculable.

Table 1Multiple Linear Regression diagnostics.

Unstandardised Coefficients Standardised Coefficients t-statisic 95.0% Confidence Interval for B

B Std. Error b Lower Bound Upper Bound

Intercept (A) 163.6** 0.262 624.9 163.0 164.1SAP (b1) 0.971** 0.003 �0.053** �280.6 �1.0 �1.0Number in household (b2) 62.67** 0.043 0.297** 1447.4 62.6 62.8Floor Area (m2) (b3) 2.380** 0.002 0.262** 1214.5 2.4 2.4HHLD Income (000’s £) (b4) 3.944** 0.006 0.140** 644.6 3.9 4.0Temperature Difference (C) (b5) 2.390** 0.011 0.042** 221.5 2.4 2.4Energy Pattern (categorical) (b6) 25.76** 0.044 0.112** 585.4 25.7 25.8

R2 ¼ 0.314, Adj R2 ¼ 0.314, Std. Error of Estimate ¼ 235.1.*significant at 5% level, **significant at 1% level.

S. Kelly / Energy 36 (2011) 5610e5620 5615

5. Results

5.1. Multiple linear regression

Before any structural equation model was developed a standardmultiple linear regression model was created to understand howmuch of the variance in energy consumption could be explainedusing standard methods. Many national level domestic energymodels rely on household efficiency indicators such as SAP topredict future domestic energy consumption. It therefore followsthat SAP should be a good indicator and have statistically significantpredictive power for estimating domestic energy consumption. Inorder to test this hypothesis anMLRmodel was employed as shownin Eq. (1.4).

y ¼ Aþ B1xþ B2xþ B3xþ B4xþ B5xþ ε (1.4)

Eq. (1.4) measures the predictive power and statistical signifi-cance of SAP on energy consumption while controlling for severalother important factors known to influence energy consumption.The results of this analysis are shown in Table 1.

The null hypothesis for this experiment was that SAP is bothstatistically significant (p < 0.01) and correlated with energyconsumption (R2 > 0.1) after controlling for other covariates. Asshown in Table 1, the model is reasonably well specified(Adj.R2 ¼ 0.314) and SAP is shown to be a statistically significantvariable (p < 0.01). However, although SAP has the correct sign(increasing SAP reduces the expected level of energy consumption)the power for SAP to predict energy consumption is lower thanexpected as shown by the small standardised regression weight,bð�0:053Þ, indicating that only a small proportion of the variance in

Table 2Coefficient estimates of model parameters.b

HHLD Income <— OccupantsFloor Area <— OccupantsTemperature <— Energy PatternFloor Area <— HHLD IncomeTemperature <— HHLD IncomeAnnual Energy Expenditure <— OccupantsAnnual Energy Expenditure <— HHLD IncomeAnnual Energy Expenditure <— Energy PatternAnnual Energy Expenditure <— Floor AreaAnnual Energy Expenditure <— TemperatureAnnual Energy Expenditure <— SAP ValueSAP Value <— Annual Energy ExpenditureOccupants <—> Energy Pattern

a C.R is the critical ratio (B/Std. Err) and is also known as the t-statistic.b Estimates are based on the calibrated effective sample size (1025).

energy consumption can be explained by SAP. The result of thissimple analysis brings into question the basic premise of manydomestic energy models, which rely on SAP measurements toaccurately predict household energy consumption.

As the results from the MLR show, SAP performs less thanexpected as a predictor for HHLD energy consumption. This processhowever does not allow for reciprocal causality between energyconsumption and SAP. A basic assumption of MLR regression is thatthe independent variables have a direct effect on energyconsumption but also, the dependent variable does not have anyeffect on the independent variables. When both variables arethought to affect each other, the relationship is described as non-recursive or cyclical. Separating and quantifying two bi-directional effects is difficult but made possible utilising theproperties of an over identified non-recursive structural equationmodel. The correlation matrix was created using the post-weightedsample and the calibrated sample size, nc, and can be accessedonline where this paper is published under the supplementalmaterials section.

The results of the structural equation model are presented inFig. 1. Standardised regression weights are shown on each of thearrows connecting two indicator variables and represent the directeffects that one variable has on another variable. The standardisedand unstandardised regression coefficients are also shown inTable 2 alongside the respective statistical tests for significance. Akey advantage of using standardised regression coefficients is theability to compare the relative magnitude of effects across differentvariables.

Table 3 presents the standardised indirect effects each variablehas on each related variable, andmeasures the effect of one variableon another variable through an intermediary variable i.e. HHLD

StandardisedCoefficients

UnstandardisedCoefficients

Significance

b B Std. Err C.R.a P (sig.)

0.329 2463 (221.8) 11.1 ***

0.188 4.362 (0.677) 6.44 ***

0.087 0.354 (0.126) 2.80 0.0050.381 0.001 (0.000) 13.0 ***

0.092 0.000 (0.000) 2.95 0.0030.306 64.52 (6.094) 10.5 ***

0.145 0.004 (0.001) 4.76 ***

0.123 28.27 (6.205) 4.56 ***

0.271 2.464 (0.276) 8.93 ***

0.046 2.584 (1.514) 1.71 0.088�0.216 �3.924 (0.869) �4.52 ***

0.235 0.013 (0.003) 4.08 ***

0.128 0.213 (0.053) 4.05 ***

Table 3Standardised indirect effects.

Energy Pattern Occupants HHLD Income Temperature Floor Area SAP Value Annual Energy Expenditure

HHLD Income 0 0 0 0 0 0 0Temperature 0 0.030 0 0 0 0 0Floor Area 0 0.126 0 0 0 0 0SAP Value 0.029 0.099 0.057 0.010 0.061 �0.048 �0.011Annual Energy Expenditure �0.002 0.113 0.095 �0.002 �0.013 0.010 �0.048

S. Kelly / Energy 36 (2011) 5610e56205616

Income has an effect on Annual Energy Expenditure through themediating variable of Floor Area. Total effects are simply the sum ofthe direct effects and the indirect effects of all variables that areshown to explain the statistical variation in that variable. Theresults for total effects are shown in Table 4. Tables 3 and 4 shouldbe read as the column variable affecting the row variable.

5.2. Other paths tested

A large number of other causal relationships between differentvariables were tested before arriving at the final solution as shownin Fig. 1. These are referred to as nested models and defined as anymodel that can be derived from the initial model by deleting oradding paths between variables. Each path was systematicallytested for significance and power but only paths that made theo-retical and logical sense were tested. Paths not shown in Fig. 1 werefound to have no statistically significant causal effect within themodel and therefore fixed to zero (represented by no path).

5.3. Testing for non-recursivity

In order to test for non-recursivity between SAP and EnergyExpenditure it is necessary to test two competing, but nestedmodels. When two models are nested it is possible to analyse thechange in c2 to test for improved model fit. The model with one ormore paths deleted is more constrained, has higher dof, and istherefore more parsimonious. To test whether the non-recursive,less parsimonious model is a statistically better fit it is necessaryto calculate Dc2 and the D dof between the two models, this isshown in Table 5. Looking up Dc2 and D dof in probability tablesshows the related probability (p < 0.01); indicating the additionalpath between Energy Expenditure and SAP resulted in a statisticallysignificant increase inDc2. Not only does the typical recursive (onecausal pathway going from SAP to Energy Consumption) fit worsethan the non-recursive model, but it fits statistically significantlyworse. Even though the recursive model is more parsimonious, itcomes at too great a cost in terms of model fit. In conclusion, thenon-recursivity between SAP and Energy Expenditure is shown tobe an important parameter in explaining residential energyconsumption.

5.4. Variables analysed but not used in the final model

The statistical results for variables that do not explain EnergyExpenditure or contribute to the overall statistical fit of the modelcan be downloaded from the supplemental materials section.

Table 4Standardised total effects.

Energy Pattern Occupants HHLD Income

HHLD Income 0 0.329 0Temperature 0.087 0.030 0.092Floor Area 0 0.314 0.381SAP Value 0.029 0.099 0.057Annual Energy Expenditure 0.121 0.419 0.241

Testing the significance of variables involved adding the variable tothe model and testing overall model fit. The only variable shown tobe statistically significant during this analysis was the UrbanDummy indicating if the house was located in an urban or ruralenvironment. Unfortunately, with the addition of this variable theoverall model fit statistics declined from (c2 ¼ 7.3, RMSEA ¼ 0.000,TLI ¼ 1.00, AIC ¼ 47.3) to (c2 ¼ 52.9, RMSEA ¼ 0.052, TLI ¼ 0.909,AIC ¼ 96.9) and therefore this variable was dropped from the finalmodel as it did not improve the overall explanatory power of themodel.

6. Model verification and validation

6.1. Results from bootstrapping exercise

Bootstrapping allows the calculation of standard errors andtherefore confidence limits of the statistics of interest. Table 6shows the upper and lower bounds for both the standardised andunstandardised direct effects in the model. Note the similarity inregression weights from the bootstrap method to those weightsobtained from the correlation matrix method. This shows thecorrelation matrix method and the Weighted Random SamplingWith Replacement (WRSWR) method compare well and verify theWRSWR method described in Section 5.4 is appropriate for thisanalysis.

6.2. Model fit statistics

Identifying and using model fit indices in SEM’s remains greatlydebated. There is still no general agreement on the form or type offit indices that should be used to measure model integrity. Thedevelopment of different indices has beenmotivated, in part, by theknown sensitivity of the c2 statistic to large sample sizes. Conse-quently, most literature suggests a selection of fit indices need to bepresented with SEM results [56] as shown in Table 7, all indicesshow an extremely good fit of the model to the data and thereforewe have confidence that the model itself could have produced theunderlying data.

The degrees of freedom parameter (dof) is calculated as thenumber of distinct sample moments (28) minus the number ofdistinct sample parameters to be calculated (20) and thereforemeasures the degree to which the model is over identified. In SEMthe null hypothesis (H0) is that the model to be tested is unlikely tobe due to chance and the alternative (Ha) is that it is not. Thec2statistic and its p-value therefore measure the probability thatthe model fits perfectly to the population. Therefore, if c2 is not

Temperature Floor Area SAP Value Annual Energy Expenditure

0 0 0 00 0 0 00 0 0 00.010 0.061 �0.048 0.2240.044 0.258 �0.206 �0.048

Table 5Test for non-recursivity in model.

c2 dof

Recursive model 25 9Non-recursive model 7.3 8Difference Dc2 ¼ 17.7 Ddof ¼ 1

S. Kelly / Energy 36 (2011) 5610e5620 5617

statistically significant (p-value > 0.05) then we cannot reject thenull hypothesis that the model is accurate and we therefore haveevidence that themodel may explain reality. As shown in Table 8, c2

is largewith a p-value>0.05, thereforewe have evidence themodelmay be a good representation for the structural relationships in thepopulation.

The Goodness of Fit Index (GFI) is analogous to R2 in MLR andprovides an estimate for the amount of covariance accounted for bythe model. PGFI is simply a parsimony adjusted value for GFI. Twosimilar indices are also listed, the comparative fit index (CFI) andthe Tucker-Lewis Index (TLI) and they compare the fit of theexisting model with the null-model. TLI makes a slight adjustmentfor parsimony but all four indexes, and particularly PGFI, areadversely affected by sample size, though much less than c2. For allthree, values over 0.95 suggest very good fit of the model to thedata while values over 0.9 suggest an adequate fit. The Root MeanSquare Error of Approximation (RMSEA) is a measure of the error ofapproximation, with values below 0.05 suggesting close fit andvalues under 0.08 suggesting a reasonable fit [55]. The standardisedroot mean square residual (SRMR) is among the best fit indexes andis a measure of the mean absolute value of the covariance residuals[51]. Perfect model fit is indicated by SRMR ¼ 0 and values under0.1 are generally considered to be favourable. In addition, non-recursive models have a further statistic that measures thestability of the model. This is known as the stability index andshould be used only after equilibrium has been shown to exist onrational grounds (Section 5.2). Values below 1.0 are thought toindicate a stable model. In summary, all model fit indices indicatethat the model under analysis may be used to approximate realityand that the model and data are consistent.

6.3. Model validation

Due to the paucity of disaggregated residential data within theUK and a serious lack of bottom-up statistical residential buildingstock models, strong validation of this model against previous

Table 6Upper and lower bounds calculated from bootstrap estimates.a,b,c,d

Stand

b

HHLD Income <— Occupants 0.33Floor Area <— Occupants 0.19Temperature <— Energy Pattern 0.10Floor Area <— HHLD Income (000's) 0.38Temperature <— HHLD Income (000's) 0.09Annual Energy Expenditure <— Occupants 0.30Annual Energy Expenditure <— HHLD Income (000's) 0.13Annual Energy Expenditure <— Energy Pattern 0.12Annual Energy Expenditure <— Floor Area 0.29Annual Energy Expenditure <— Temperature 0.03Annual Energy Expenditure <— SAP Value �0.21SAP Value <— Annual Energy Expenditure 0.22Occupants <—> Energy Pattern 0.23

a Bootstrap confidence intervals are based on the bias-corrected percentile method.b Estimates are based on the bootstrap sample size (10,000 cases).c Confidence intervals are calculated at the 95% level.d Covariances are listed under standardised estimates while correlations are listed un

studies is difficult. Nevertheless, validation of model parameters(over and above statistical significance tests and bootstrappingexercises presented earlier) can be accomplished by comparingthese results with other bottom-up energy demand models. Usingpath analysis on the US residential sector, Steemers and Yun [57]have showed the importance of floor area ðb ¼ 0:255Þ, house-hold income ðb ¼ 0:166Þ, occupancy levels ðb ¼ 0:109Þ andbehaviour ðb ¼ 0:124Þ for explaining residential heating demand.In a similar fashion with a limited number of variables Baker andRylatt [58] performed clustering and regression techniques ona small sample of homes in Leicester in the UK and confirmed theimportance of floor area for explaining energy consumptionðr2 ¼ 0:272Þ. Given the results presented in this analysis are ofsimilar magnitude, scale and type to other bottom-up statisticalmodels we have confidence in the results obtained in this analysis.

7. Discussion

Many of the conclusions drawn from this research can beidentified through careful observation of the path diagram in Fig. 1and from Tables 2e4. Starting with the exogenous variable, repre-senting the number of people living in the home, HouseholdOccupancy is shown to have a direct and positive effect on bothdwelling Floor Area (b ¼ 0.19**) and HHLD Income (b ¼ 0.33**).Household Occupancy also has direct and positive effect on AnnualEnergy Expenditure (b ¼ 0.31**). A similar analysis can becompleted for total effects, which is calculated as the sum of directand indirect effects (Table 4). For example, for each extra personliving in a dwelling, the expected mean floor area will increase by7.27 m2 (b ¼ 0.31**), the mean annual household income willincrease by £2463 (b ¼ 0.33**), and the mean energy bill willincrease by £88/year (b ¼ 0.42**). Moreover, by considering thestandardised regression weights for total affects it is possible tocompare the relativemagnitude of effects across different variables.Here, it is shown that Household Occupancy has the largest overalleffect on energy expenditure (b ¼ 0.419**) followed by Floor Area(b ¼ 0.258**) and HHLD Income (b ¼ 0.241**). It is important tonote however, that Household Occupancy is strongly mediated byboth HHLD income (b ¼ 0.33**) and Floor Area (b ¼ 0.19**). Thisimplies that although the direct effect of Household Occupancy onenergy expenditure is just (b ¼ 0.31**) when the indirect effect ofoccupancy through larger floor area and higher household incomeis allowed for, the total effect of household occupancy increases to(b ¼ 0.419**). Where, b-values can be interpreted as a change of

ardised Coefficients Unstandardised Coefficients

Lower Upper B Lower Upper

5 0.320 0.356 2538 2402 26923 0.174 0.213 4.52 4.09 5.027 0.090 0.129 0.425 0.357 0.5127 0.369 0.402 1.199 1.141 1.2535 0.078 0.116 0.046 0.037 0.0562 0.284 0.320 64.071 60.0 68.20 0.114 0.151 3.655 3.222 4.2720 0.107 0.140 27.680 24.5 32.37 0.275 0.314 2.692 2.51 2.869 0.0211 0.0553 2.264 1.23 3.212 �0.249 �0.184 �3.899 �4.55 �3.387 0.197 0.262 0.012 0.011 0.0141 0.199 0.261 0.139 0.120 0.156

der unstandardised estimates.

Table 7Model fit indices.

N dof c2 P-value GFI PGFI TLI CFI RMSEA SRMR Stability Index

Correlation method 1025 8 7.30 0.504 0.998 0.285 1.00 1.00 0.001 0.016 0.048

S. Kelly / Energy 36 (2011) 5610e56205618

one standard deviation in the independent variable correspondsb-std. deviations change in the dependent variable.

Because the units of b are standardised to z-scores, it is possibleto derive the relative impact of each independent variable on thedependent variable. For example, it is shown that HHLD Income hasa larger relative effect on Floor Area (b ¼ 0.38) then it does onEnergy Expenditure (b ¼ 0.15). In fact, for each additional £1000 inannual HHLD Income the mean Floor Area increases by 1.18 m2.However because Floor Area and Temperature Difference are bothmediating variables between HHLD Income and Energy Expendi-ture it is necessary to compare total effects (Table 4) to calculate theoverall effect that HHLD Income will have on Energy Expenditure.For instance, using total effects, a £10,000 increase in annual HHLDIncome will lead to an expected average increase in EnergyExpenditure of £68/year. On the other hand, if we consider only thedirect effects of HHLD Income on Energy Expenditure the averageincrease in Energy Expenditure is only £41/year. The remaining£27/year difference comes from the mediating effect that HHLDIncome has on Energy Expenditure through an increase in FloorArea and a small but modest increase to Internal Temperature.

An increase in Energy Pattern, as expected, increases bothTemperature Difference and Energy Expenditure. The EnergyPattern is an ordered categorical variable ranging between 1 and 5where 1 represents someone who is never home and rarely usestheir heating compared to 5, representing a dwelling where heatingis on almost all the time. The difference in annual Energy Expen-diture between these two extremes (i.e. 1 and 5) is, on average£139/year. A correlation between Energy Pattern and Occupancywas identified by the modification indices and found to be signif-icant. Such a correlation indicates the possibility of a sharedcommon variable that explains both Energy Pattern and Occupancy.A logical choice for such a shared common variable is the type ofrelationship between occupants living in the dwelling. Forexample, a family consisting of several children where one partnerstays at home during the week has a positive effect on bothOccupancy and Energy Pattern. On the other hand, someone wholives alone with a full time job will have a much smaller effect onboth Occupancy and Energy Pattern. It was decided the addition ofa variable representing the relationships between occupants didnot materially add any further insight into residential energyconsumption and therefore, for the sake of parsimony, was notadded to the model. A summary of real effects on annual energyexpenditure are shown in Table 8.

The EHCS does not contain longitudinal internal temperaturemeasurements. Therefore, internal and external temperaturereadings taken on the day of the survey were used as proxies for

Table 8Real effects on annual energy expenditure (£1996).

Variable Effect Annual HHLDEnergy Expenditure

HHLD income Increase £10,000 £67.80Number of occupants Each extra person £88.32Floor area Each extra 10m2 £23.44Temperature Each 1�C increase £2.50Energy pattern Living room heated week £27.70Energy pattern Bedroom heated week £27.70SAP 30 -> 90 SAP -£222.00

average internal temperature measurements. As only one day oftemperature measurements were recorded, it is sensible to treatany relationships related to Temperature Difference with caution.Large measurement error and therefore weak statistical signifi-cance between Temperature Difference and annual EnergyExpenditure (P ¼ 0.088) is therefore not an unusual finding and ifmore robust data on temperatures were available the significanceof this variable would no doubt improve. For completeness, thetemperature variable was included in the final model as it does leadto an improvement in the overall model fit statistics and does leadto additional insight into the contribution of how different factorsmay contribute to final energy consumption. Removing this vari-able from the analysis had very little effect on all the other variableswithin the model but does, itself, provide additional insight.

One of the most important findings of this research was thediscovery and estimation of a non-recursive relationship betweenEnergy Expenditure and SAP. Standard multiple linear regressionmethods do not allow the calculation of reciprocal relationshipsbetween variables, and therefore it is necessary to use SEM to solvesuch problems. Only after the non-recursive relationship betweenSAP and Energy Consumption has been allowed for, can the trueeffect of SAP on energy consumption be demonstrated. Here, it isshown the effect of SAP on Energy Expenditure has a moderate butstatistically significant effect (b ¼ �0.22**), while Energy Expen-diture is also shown to effect SAP (b ¼ 0.23**). That is, for eachstandardised unit increase in the SAP rating a subsequent decreasein Energy Expenditure of b ¼ �0.22** is expected, Ceteris Paribus.Similarly and to put this in context, it is necessary to examine theunstandardised regression weights. Remembering that SAP is ona scale from (0e100), for each unit increase in SAP the averagesaving in annual Energy Expenditure will be £3.73. For example, ifa dwelling with a poor energy efficiency rating with SAP of 30, isrenovated to, say, SAP of 90 the expected annual average saving inenergy expenditure will roughly be £222 per annum (£UK1996)Ceteris Paribus.

Perhaps what is more interesting is the finding that dwellingswith a propensity to consume more energy due to higher occu-pancy rates, higher household incomes, larger floor areas, increasedenergy patterns and warmer internal temperatures are more likelyto have higher SAP ratings. This therefore suggests that homes witha propensity to consumemore energy would, in fact, consume evenlarger amounts of energy if it were not for the fact that these homeswere already relatively more efficient when compared to the rest ofthe building stock.

7.1. The rebound effect

The rebound effect is a phenomenon known to limit the efficacyof energy efficiency improvements in dwellings [59e61]. In mostcircumstances, an increase in dwelling efficiency will not result ina commensurate decrease in energy consumption. This is oftenreferred to as ‘rebound’ or ‘take-back’ and occurs when a propor-tion of the energy savings are consumed by additional energy use.This is often explained by an increase in thermal comfort due to theoccupant choosing higher internal temperatures. Said differently,the occupant will ‘take-back’ a fraction of their energy savings anduse it to increase their thermal comfort. This analysis supports thepremise that a rebound effect may exist. This analysis shows there

S. Kelly / Energy 36 (2011) 5610e5620 5619

is indeed a relationship between dwelling efficiency (SAP) andenergy demand, and each variable has a direct effect on the other.That is to say, increasing efficiency has a negative effect on energyconsumption and therefore drives down total energy use, ceterisparibus. On the other hand, homes that consume more energy alsohave greater motivation to make there homes more energy effi-cient. This is a chicken and egg type problem. First, homes that are,on average, more energy efficient have greater energy savings andtherefore can afford to spend these savings on increased energyconsumption i.e. the rebound effect. On the other hand, homeswitha propensity to consume more energy have a greater motivation tomake their homes more efficient, which therefore leads to thesehomes having higher SAP values than average. Research attemptingto calculate household rebound effects must therefore considerboth of these simultaneous effects in order to estimate the reboundeffect accurately.

8. Policy implications and conclusions

In this paper, a structural equation model is used to determinethe explanatory power and significance of covariates on residentialenergy consumption. Using SEM, it is possible to test the structure ofrelationships and therefore show how direct, indirect and totaleffects interact and drive residential energy consumption. It isshown the largest determinants for explaining residential energyconsumption are the number of occupants living at the dwelling,household income, floor area, household energy patterns, temper-ature effects, and SAP rating. While the number of occupants livingin a dwelling is shown to have the largest magnitude of effect, floorarea and household income are also substantial drivers. In addition,we show there is strong mediation between causal variables. Forinstance, household income and the number of occupants living ina dwelling are both strongly mediated by dwelling floor area. Inother words, households occupied by more people or have higherincomes live in larger houses and therefore consume more energy.

Possibly the most important discovery of this research is thefinding of a statistically significant reciprocal relationship betweenSAP and residential energy consumption. This is the first time sucha relationship has been empirically identified and may haveimportant consequences for the development of new policy aimingto dramatically cut energy consumption from the residential sector.This finding shows that homes with a propensity to consume moreenergy already have relatively higher SAP rates and thereforesuggests the scope for additional savings through the imple-mentation of energy efficiency technologies may be limited. Whatis more, this finding implies that homes with a propensity toconsume more energy will be more expensive to decarbonise dueto the law of diminishing returns. On the other hand, if we focus onhomes with a propensity to consume less energy, it can be shownthat these homes already have relatively lower SAP rates and aretherefore in general less efficient. However, these homes tend to bemore poorly heated with lower overall internal temperatures. Inaddition, improving the energy performance of these homesthrough the implementation of energy efficiency technologies maycontribute to the rebound effect acting to increase the averageinternal temperature rather than decrease energy consumption.These findings suggest the presence of a residential energy effi-ciency barrier that must be overcome before any real savings fromthe residential sector can start to accrue. This result may explainwhy several Government supported projects in the UK aimed atreducing residential energy consumption have not realised theirtargets. With this purpose in mind, a dual policy approach mayhave the most effect. Homes with a propensity to consume moreenergy should be targeted using behavioural strategies combinedwith economic penalties and incentives. On the other hand, homes

with low SAP rates should be targeted for whole home efficiencyupgrades in order to break through the energy efficiency barrier.

Acknowledgements

Dr Michael Pollitt and Professor Douglas Crawford-Brown areacknowledged for their feedback and support for putting togetherthis paper.

Appendix. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.energy.2011.07.009.

References

[1] WWF. WWF Building Stock Report. Available at: http://assets.wwf.org.uk/downloads/how_low_report.pdf; 2007 [Accessed April 14, 2009].

[2] UK Government. Climate Change Act. Available at: http://www.opsi.gov.uk/acts/acts2008/ukpga_20080027_en_1; 2008 [Accessed May 12, 2009].

[3] Communities and Local Government. Building a greener future: towards zerocarbon development - consultation - planning, building and the environment -communities and local government. Available at: http://www.communities.gov.uk/archived/publications/planningandbuilding/buildinggreener; 2006 [AccessedApril 1, 2009].

[4] DECC. Heat and energy saving strategy consultation. Available at: http://hes.decc.gov.uk/; 2009 [Accessed March 26, 2009].

[5] Energy Efficiency Partnership. An assessment of the size of the UK householdenergy efficiency market. Element Energy Ltd. Available at: http://www.eeph.org.uk/uploads/documents/partnership/Assessment%20of%20the%20UK%20household%20energy%20efficiency%20market_171108.pdf; 2008 [AccessedMay 6, 2009].

[6] Department for Communities and Local Government. Building a greenerfuture. London: Dept. for Communities and Local Government; 2007.

[7] McKinsey. Sustainable urban infrastructure study - LondonEditiona view to 2025.London. Available at: http://w1.siemens.com/entry/cc/features/sustainablecities/all/pdf/SustainableUrbanInfrastructure-StudyLondon.pdf; 2008.

[8] McKinsey. Pathways to a low-carbon economy. Available at: file:///D:/Scotts%20Stuff/PhD%20Material/Litterature/Reports/MCkinsey/PathwayToLowCarbonEconomy_FullReportA.pdf; 2009 [Accessed May 5, 2009].

[9] Centre for alternative technologies. Zero Carbon Britain. Available at: http://www.cat.org.uk/news/news_release.tmpl?command¼search&db¼news.db&eqSKUdatarq¼37990&home¼0; 2007.

[10] ECI. 40% house. Environmental Change Institute. Available at: http://www.eci.ox.ac.uk/research/energy/downloads/40house/40house.pdf; 2005 [AccessedMay 17, 2009].

[11] Levine M, Urge-Vorsatz D. Chapter 6-Resdiential and commercial buildings.Available at: http://www.ipcc.ch/pdf/assessment-report/ar4/wg3/ar4-wg3-chapter6.pdf; 2008 [Accessed April 20, 2009].

[12] World Business Council for Sustainable Development. Energy efficiency inbuildings - transforming the market. Available at: http://62.50.73.69/transformingthemarket.pdf; 2009 [Accessed April 27, 2009].

[13] Kavgic M, Mavrogianni A, Mumovic D, Summerfield A, Stevanovic Z, Djurovic-PetrovicM.A reviewofbottom-upbuilding stockmodels for energyconsumptionin the residential sector. Building and Environment 2010;45(7):1683e97.Available at: doi:10.1016/j.buildenv.2010.01.021 [Accessed July 7, 2010].

[14] Tso GKF, Yau KKW. Predicting electricity energy consumption: a comparison ofregression analysis, decision tree and neural networks. Energy 2007;32(9):1761e8. Available at: doi:10.1016/j.energy.2006.11.010 [Accessed June 21, 2010].

[15] Swan LG, Ugursal VI. Modeling of end-use energy consumption in the resi-dential sector: A review of modeling techniques. Renewable and SustainableEnergy Reviews 2009;13(8):1819e35. Available at: doi:16/j.rser.2008.09.033[Accessed August 1, 2011].

[16] Strachan N, Kannan R. Hybrid modelling of long-term carbon reductionscenarios for the UK. Energy Economics 2008;30(6):2947e63. Available at:doi:10.1016/j.eneco.2008.04.009 [Accessed July 14, 2009].

[17] McFarland JR, Reilly JM, Herzog HJ. Representing energy technologies in top-down economic models using bottom-up information. Energy Economics2004;26(4):685e707. Available at: doi:10.1016/j.eneco.2004.04.026[Accessed May 17, 2009].

[18] Jebaraj S, Iniyan S. A review of energy models. Renewable and SustainableEnergy Reviews 2006;10(4):281e311. Available at: doi:10.1016/j.rser.2004.09.004 [Accessed May 13, 2010].

[19] Aydinalp-Koksal M, Ugursal VI. Comparison of neural network, conditionaldemand analysis, and engineering approaches for modeling end-useenergy consumption in the residential sector. Applied Energy 2008;85(4):271e96. Available at: doi:10.1016/j.apenergy.2006.09.012 [AccessedMay 13, 2010].

[20] Böhringer C, Rutherford TF. Integrated assessment of energy policies:decomposing top-down and bottom-up. Journal of Economic Dynamics and

S. Kelly / Energy 36 (2011) 5610e56205620

Control 2009;33(9):1648e61. Available at: doi:10.1016/j.jedc.2008.12.007[Accessed July 12, 2010].

[21] Tuladhar SD, Yuan M, Bernstein P, Montgomery WD, Smith A. A top-downbottom-up modeling approach to climate change policy analysis. EnergyEconomics 2009;31(Suppl. 2):S223e34. Available at: doi:10.1016/j.eneco.2009.07.007 [Accessed July 12, 2010].

[22] Summerfield AJ, Lowe RJ, Oreszczyn T. Two models for benchmarking UK -domestic delivered energy. Building Research & Information 2010;38(1):12.Available at: doi:10.1080/09613210903399025 [Accessed June 9, 2010].

[23] Shorrock L. A detailed analysis of the historical role of energy efficiency inreducing carbon emissions from theUKhousing stock. Ecee. Available at: http://www.bre.co.uk/filelibrary/rpts/eng_fact_file/Shorrock.pdf; 2003 [AccessedMay 21, 2009].

[24] Azadeh A, Saberi M, Seraj O. An integrated fuzzy regression algorithm forenergy consumption estimation with non-stationary data: a case study ofIran. Energy 2010;35(6):2351e66. Available at: doi:10.1016/j.energy.2009.12.023 [Accessed May 13, 2010].

[25] Rylatt R, Gadsden S, Lomas K. Methods of predicting urban domestic energydemand with reduced datasets: a review and a new GIS-based approach.Building Services Engineering Research & Technology 2003;24(2):93e102.Available at: doi:10.1191/0143624403bt061oa [Accessed March 30, 2010].

[26] Aydinalp M, Ugursal VI, Fung AS. Modelling of residential energy consumptionat the national level. International Journal of Energy Research 2003;27(4):441e53. Available at: doi:10.1002/er.887 [Accessed December 31, 2009].

[27] Hitchcock G. An integrated framework for energy use and behaviour in thedomestic sector. Energy and Buildings 1993;20(2):151e7. Available at: doi:10.1016/0378-7788(93)90006-G [Accessed May 13, 2010].

[28] Hoogwijk M, van Vuuren DP, Scrieciu S. Sectoral emission mitigationpotentials: comparing bottom up and top down approaches. Available at:http://www.env.go.jp/press/file_view.php?serial¼12478&hou_id¼10316;2008 [Accessed May 15, 2009].

[29] Johnston DA. Physically based energy and carbon dioxide emission model ofthe UK housing stock. Available at: http://www.leedsmet.ac.uk/as/cebe/assets/djthesis.pdf; 2003 [Accessed May 15, 2009].

[30] Douthitt RA. An economic analysis of the demand for residential space heating fuelin Canada. Energy 1989;14(4):187e97. Available at: http://www.scopus.com/inward/record.url?eid¼2-s2.0-0024649550&partnerID¼40&md5¼77d021c33d3bd3ef9f2de3e5b00cdd88 [Accessed December 15, 2010].

[31] BRE. The governments standard assessment procedure for energy rating ofdwellings. Available at: http://www.bre.co.uk/filelibrary/SAP/2009/SAP-2009_9-90.pdf; 2005 [Accessed December 10, 2009].

[32] DEFRA. BREDEM-12 model description. Available at: http://circa.europa.eu/Public/irc/dsis/chpwg/library?l¼/consumption_households/bredem_descriptionpdf/_EN_1.0_&a¼d; 2001 [Accessed May 26, 2009].

[33] Cambridge Architectural Research. Modelling greenhouse gas emissions fromScottish housing: manual and model. Available at: http://www.scotland.gov.uk/Publications/2010/01/27160142/1; 2009 [Accessed February 23, 2010].

[34] Cheng V, Steemers K. Modelling domestic energy consumption at districtscale: A tool to support national and local energy policies. EnvironmentalModelling & Software 2011;26(10):1186e98. Available at: doi:16/j.envsoft.2011.04.005 [Accessed August 1, 2011].

[35] Baker P, Blundell R, Micklewright J. Modelling household energy expendituresusing micro-data. The Economic Journal 1989;99(397):720e38. Available at:http://www.jstor.org/stable/2233767 [Accessed July 14, 2010].

[36] Baker KJ, Rylatt RM. Improving the prediction of UK domestic energy-demandusing annual consumption-data. Applied Energy 2008;85(6):475e82. Avail-able at: doi:10.1016/j.apenergy.2007.09.004 [Accessed July 14, 2010].

[37] DETR. English house condition survey: user guide. Available at: http://www.communities.gov.uk/housing/housingresearch/housingsurveys/englishhousecondition/; 1996 [Accessed March 10, 2010].

[38] Communities and Local Government. English housing survey (EHS) - housing- communities and local government. Available at: http://www.communities.gov.uk/housing/housingresearch/housingsurveys/englishhousingsurvey/;2010 [Accessed August 23, 2010].

[39] Dresner S, Ekins P. Economic instruments to improve UK home energy effi-ciency without negative social impacts*. Fiscal Studies 2006;27(1):47e74.Available at: doi:10.1111/j.1475-5890.2006.00027.x [Accessed March 30,2011].

[40] Shorrock L, Dunster J. The physically-based model BREHOMES and its use inderiving scenarios for the energy use and carbon dioxide emissions of the UKhousing stock. Energy Policy 1997;25(12):1027e37. Available at: doi:10.1016/S0301-4215(97)00130-4 [Accessed May 15, 2009].

[41] Firth SK, Lomas KJ, Wright AJ. Targeting household energy-efficiency measuresusing sensitivity analysis. Building Research & Information 2010;38(1):25.Available at: doi:10.1080/09613210903236706 [Accessed April 29, 2010].

[42] Communities and Local Government. EHCS technical report. Available at: http://www.communities.gov.uk/documents/housing/pdf/ehcstrp05.pdf; 2005.

[43] Summerfield AJ, Lowe RJ, Oreszczyn T. Two models for benchmarking UK -domestic delivered energy. Building Research & Information 2010;38(1):12.Available at: doi:10.1080/09613210903399025 [Accessed April 29, 2010].

[44] Hunt LC, Judge G, Ninomiya Y. Underlying trends and seasonality in UK energydemand: a sectoral analysis. Energy Economics 2003;25(1):93e118. Availableat: doi:10.1016/S0140-9883(02)00072-5 [Accessed March 29, 2011].

[45] Micklewright J. Towards a household model of UK domestic energy demand.Energy Policy 1989;17(3):264e76. Available at: doi:10.1016/0301-4215(89)90051-7 [Accessed July 14, 2010].

[46] Fouquet R. The impact of VAT introduction on UK residential energy demand:an investigation using the cointegration approach. Energy Economics 1995;17(3):237e47. Available at: doi:10.1016/0140-9883(95)00015-M [AccessedJuly 14, 2010].

[47] Boonekamp PGM. Price elasticities, policy measures and actual developmentsin household energy consumption - A bottom up analysis for the Netherlands.Energy Economics 2007;29(2):133e57. Available at: doi:10.1016/j.eneco.2005.09.010 [Accessed May 5, 2010].

[48] Lijesen MG. The real-time price elasticity of electricity. Energy Economics2007;29(2):249e58. Available at: doi:10.1016/j.eneco.2006.08.008 [AccessedMay 5, 2010].

[49] Lee S- Y. Structural equation modeling: a Bayesian approach. Chichester:Wiley; 2007.

[50] Tabachnick BG. Using multivariate statistics. Boston [Mass.]: Pearson/A&B;2007.

[51] Kline RB. Principles and practice of structural equation modeling. New York,NY: Guilford Press; 2005.

[52] Rubin DB. Inference and missing data. Biometrika 1976;63(3):581e92.Available at: http://www.jstor.org/stable/2335739 [Accessed July 21, 2010].

[53] Schumacker RE, Marcoulides GA, editors. Full information estimation in thepresence of incomplete data. in: Advanced structural equation modeling:issues and techniques. L. Erlbaum Associates, 1996.

[54] Dorofeev S. Statistics for real-life sample surveys: non-simple-randomsamples and weighted data. Cambridge: Cambridge University Press; 2006.

[55] Keith T.Multiple regression and beyond. Boston:Mass: Pearson Education; 2006.[56] Vernon T. Personality and individual differences. CO2 2007;42(5). Available at:

doi:10.1016/S0191-8869(07)00013-X [Accessed August 16, 2010].[57] Steemers K, Yun GY. Household energy consumption: a study of the role of occu-

pants. Building Research and Information 2009;37(5e6):625e37. Available at:http://www.scopus.com/inward/record.url?eid¼2-s2.0-70349645107&partner-ID¼40&md5¼e23de27f03f528d3de09b508af5040e2 [Accessed June 29, 2011].

[58] Baker KJ, Rylatt RM. Improving the prediction of UK domestic energy-demandusing annual consumption-data. Applied Energy 2008;85(6):475e82. Avail-able at: doi:10.1016/j.apenergy.2007.09.004 [Accessed December 16, 2010].

[59] Herring H. Energy efficiencyea critical view. Energy 2006;31(1):10e20.Available at: doi:10.1016/j.energy.2004.04.055 [Accessed March 29, 2011].

[60] Sorrell S. The rebound effect. Available at: file:///C:/Documents%20and%20Settings/sjk64/Desktop/0710ReboundEffectReport.pdf; 2007 [AccessedJune 15, 2009].

[61] Madlener R, Alcott B. Energy rebound and economic growth: a review of themain issues and research needs. Energy 2009;34(3):370e6. Available at: doi:10.1016/j.energy.2008.10.011 [Accessed March 29, 2011].