François Trouilleux

A DESCRIPTION OF THE FRENCH NUCLEUS VP USING CO-OCCURRENCE CONSTRAINTS

 as a reference and show how requirement and exclusion properties may be implemented in NooJ, introducing a new type of constraint.

Introduction

In [START_REF] Bès | La phrase verbale noyau en français[END_REF], Gabriel G. Bès proposed a new formalism for syntactic description, called "Properties", which he exposed together with a description of the French nucleus verb phrase. Properties are a constraint system; we propose to describe with NooJ [START_REF] Silberztein | NooJ Manual[END_REF] a set of strings close to that of [START_REF] Bès | La phrase verbale noyau en français[END_REF], showing how the different Property types may be coded in NooJ. On this occasion, we introduce a new type of constraint in NooJ: co-occurrence constraints.

This introductory section sets the scene with an overview of the Properties formalism, an informal global definition of the language to be defined and an exposition of our adequacy criteria. We will then refine of our language definition in two steps: (i) by specifying word categories and linearity constraints, as well as optionality and uniqueness, and (ii) by specifying co-occurrence constraints.

Properties

The Properties formalism consists in a set of seven different types of formulas on categories ("properties"), which, interpreted as a conjunction, denote a language1 . As pointed out in [START_REF] Trouilleux | Note de lecture sur Philippe Blache, Les Grammaires de propriétés[END_REF], the Properties of [START_REF] Bès | La phrase verbale noyau en français[END_REF] 2 may be viewed as an extension of the decomposition of information initiated by the ID/LP (immediate dominance/linear precedence) GPSG formalism [START_REF] Gazdar | Generalized Phrase Structure Grammar[END_REF]. LP rules have a direct correspondence in so-called "linearity properties", while the information expressed by a set of ID rules will be expressed by five different property types:

the alphabet property specifies the set of categories which may occur in a string of the targeted language (henceforth S L ); the uniqueness property specifies which categories may only appear once in S L ; the obligation property specifies which categories are mandatory in S L , possibly disjunctively; requirement properties state that if some category appear in S L , then some other category must also be present; this property type includes agreement constraints; exclusion properties state that two categories may not co-occur in S L .

Targeted Language

We define the set of strings to be specified by our grammar in terms of the EASY annotation scheme [START_REF] Gendner | [END_REF], so that we will be able to test the grammar against the EASY corpus in future work. The targeted strings are the NV and PV constituents of the EASY scheme, extended to the right by the negation adverb or the past participle(s), and possible intermediate words, e.g. adverbs or pronouns tout or rien. Here are a few examples (targeted strings are underlined):

(1) Pierre ne le lui a pas donné. / Pierre did not give it to him/her.

(2) Ils ont tous été mangés hier. / They all have been eaten yesterday.

(3) Pierre dit à Marie de ne pas les revoir.

Pierre says to Marie not to see them again..

The combination of infinitives with support verbs or modal auxiliaries (e.g. il va venir, il la fait travailler) are not part of our targeted language. definition of languages as a sets of strings, but rather provide an annotation of the defined strings. Even though the NooJ variable system could presumably be used to code such dependencies, we do not address this issue in this paper. 2 Non French speaking readers may consult [START_REF] Blache | Property Grammars: a Fully Constraint-Based Theory[END_REF] for a description in English of the Property formalism.

Adequacy criteria

Our goal is simple descriptive adequacy: precisely specify the set of well-formed sequences, ruling out ill-formed ones. We add two restrictions to the definition of our targeted language: (i) our grammar does not deal with phonological or prosodic matters (e.g. the incorrect je aime and j'y irai will be specified as well as the correct j'aime and j'irai), and (ii) it does not account for the government of clitics by verbs: any clitic pronoun will combine with any verb, and no verb will require some specific pronoun. We leave this major issue for future work.

The major challenges in the language we intend to describe are the handling of clitic pronouns and anaphoric quantifiers (tous), the choice of the auxiliary verb depending on the past participle and reflexiveness, past participle agreement, and the co-occurrence of items which may be separated by several words (e.g. ne and pas in ne me l'a-t-il donc pas donné).

The treatment of French clitic pronouns has given rise to many articles, so that the constraints on these pronoun sequences are quite well known. A question which has been debated is whether French clitic pronouns should be dealt with lexically or post-lexically (cf. Heap and Roberge, 2001, §3.3.2). We chose to describe our language with a NooJ syntactic grammar. However, this does not mean that we took a strong position on the lexical/post-lexical issue, for two reasons: (i) our grammar is descriptive only, it is not intended to have cognitive adequacy and (ii) arguments in favour of the lexical treatment of French clitic pronouns are typically phonological and we set aside such matters. The choice of a syntactic grammar, however, is supported by the fact that, in compound tenses, the pronoun, while attached to the auxiliary verb, is governed by the past participle (e.g. in (4), l' is governed by lavé), and as [START_REF] Abeillé | La complémentation des auxiliaires français[END_REF] points out, "it is clear that compound tenses concern syntax more than morphology".

(4) Il ne l'a donc pas bien lavé.

He NEG it has thus not well washed. / He thus didn't wash it well. [START_REF] Miller | French clitic movement without clitics or movement[END_REF] proposed a lexical treatment of French clitic pronouns in HPSG. The system produces "cliticized words" from the composition of verbs with clitics, checking and reducing the verb's argument structure as clitics are added. To account for compound tenses, "the tense auxiliaries and their participle complements share arguments"; but they must do so at the syntactic level, so it is most likely that the system either requires multiple auxiliary verb entries (one for each possible type of past participle in terms of argument structure) or generates all possible clitic-auxiliary combinations. Such a treatment at the lexical level would be possible in NooJ; e.g. in (4), the sequence il ne l'a would be analysed as a kind of compound. However, one would need to record all the components of the il ne l'a compound using ad hoc features in order to correctly combine it with past participles and the negation adverb. We preferred to handle all combinatorial aspects at the same level.

Categories, Linearity, Obligation and Uniqueness

Let us go one step further in the description of our targeted language by specifying the alphabet of categories, linearity constraints, obligation and uniqueness properties. Word order is very much fixed in the sequences we are trying to describe, so that we will introduce categories together with linearity constraints. As for obligation, things are simple: there is only one mandatory category: one non past participle verb form, which we will refer to as VF.

It is customary to account for the rigid order of clitic pronouns to the left of VF using a table as Table 1 3 (see e.g. [START_REF] Bonami | French pronominal clitics and the design of Paradigm Function Morphology[END_REF]. Column headers give the non-terminal symbols used in the grammar for the corresponding items. Subject pronouns come first, followed by the negation particle ne, followed by the complement pronouns. Table 1 shows five different slots 4 for these pronouns: (i) the series me, te, se, nous, vous, which may either be accusative or dative and be reflexive or not, (ii) third person non reflexive accusative (le, la, les), (iii) third person 3 1: I sleep, 2: you NEG sleep, 3: he himself D it A buys, 4: you it A him D buys, 5: she them A them D there gives, 6: he you D them A from-there brings-back. 4 In addition to the five pronoun slots of Table 1, our grammar includes an additional slot for an ethical dative pronoun at the beginning of the pronoun sequence. non reflexive dative (lui, leur), (iv) pronoun y and (v) pronoun en. Word order is fixed, ignoring dialectal variations.

NOM NEG

ACC1r

Slots on the right-hand side of the verb are given in Table 2 5 . The first column recalls that these items may combine with items on the left-hand side of the verb. Two types of clitic pronouns in complementary distribution may appear to the right of the verb: complement pronouns with an imperative verb, and subject pronouns with other inflected verb forms. It must be noted that one may have only one subject pronoun, but possibly several complement pronouns, which the table does not indicate. After the pronoun(s) may come a negation adverb (PAS), a subject or object anaphoric plural quantifier(s) (TS) or the pronouns tout or rien. In final position comes the main past participle, which may be preceded by the past participles of avoir (eu) or être (été) in the double-compound tenses ("temps surcomposés") or in the passive voice. 1 must be completed by Table 3 6 . Column Prep introduces prepositions, column PAS introduces a 5 1: doesn't he like everything, 2: give it to me, 3: they all like everything, 4: has it not been given to him, 5: he is eaten, 6: he has had eaten, 7: they have all been loved, 8: he has had been loved. 6 1: in order not to buy them for us, 2: say nothing to him, 3: to all buy everything, 4: to all buy them for themselves.

cf. Tab

possible negation adverb before the infinitive verb and the next columns introduce the quantifier tous and pronouns tout and rien, which may combine with complement clitic pronouns. Subject pronouns (NOM) may not occur with infinitive or present participle verbs.

Adverbs may appear in between some columns, as (4) shows, and, as [START_REF] Abeillé | La complémentation des auxiliaires français[END_REF] points out with (5), long insertions are possible between the auxiliary verb and the past participle.

(5) Il a d'un seul coup, si l'on peut dire, changé de visage.

He has all at once, if one may say so, changed his face.

The grammar we present do not claim to account for such cases, except by allowing one optional adverb in some positions.

The information specified in Tables 1 to 3 may be represented by the NooJ graph in Fig. 1. This graph specifies the categories7 , in appropriate order, as well as optionality, i.e. the alphabet, linearity and obligation properties. We view this graph, with its train of categories and its bypasses marking optionality, as typical of a fixed word order language. K. Bogacki and E. Gwiazdecka's article, in this volume, shows how free word order can be dealt with in NooJ.

Fig. 1. Alphabet, linearity, obligation and uniqueness graph.

A series of NooJ <ONCE> constraints (cf. M. Silberztein's article in this volume), corresponding to uniqueness properties, reduces the set of possible combinations. They state that there is only one subject pronoun, one accusative pronoun, one dative pronoun, one adverbial pronoun and one pas negation adverb. Note that they automatically limit the number of clitic pronouns to three and determine their interpretation: for instance, if y and en co-occur, then en is an accusative (cf. il y en a, "there are some", it may otherwise have several non accusative functions), if le (ACC2) cooccurs with a slot 1 pronoun, then this pronoun is a dative, etc.

The graph also codes two co-occurrence constraints: (i) PAS before the verb may only occur with NEG (cf. top left corner) and (ii) the auxiliary past participles EU and ETE may only occur with VPP (cf. bottom right corner). Coding co-occurrence constraints between adjacent items as these is well done graphically. However, when there is a co-occurrence constraint between two items which are not necessarily adjacent, coding the constraint graphically will require duplicating the intermediate paths.

For instance, to specify graphically that PAS2 (bottom line) after the verb requires NEG (top line), one would have to duplicate everything that goes in between. We will show in the next section that we can save such node duplication using co-occurrence constraints.

Co-occurrence constraints

Tables 1 to 3 and the graph in Fig. 1 ignore co-occurrence constraints which do exist between some items. Our grammar then actually contains a variant of the Fig. 1 graph, annotated by a series of co-occurrence constraints. We cannot reproduce this graph here and invite the reader to download it from our web page8 . We will endeavour to give the reader all the necessary information to interpret the grammar: elements of NooJ syntax, a couple of examples and a complete specification, in natural language, of the implemented constraints.

Elements of NooJ Syntax

Variables. In NooJ, co-occurrence and agreement constraints are specified using variables. Variables are set as labelled parentheses around a node. They record the lexical feature information from the items that match the nodes and are then used in constraints specified in angle brackets along grammar paths to perform tests on the recorded information.

NooJ makes a distinction between global and local variables. To allow importation in larger grammars, our grammar only makes use of local variables. Access to local variables is limited: a constraint on a local variable in a graph G can only access variable values defined in or below G. To decide between possibly competing variable values, a breadth-first, left-to-right search procedure is used. Local variables are useful when constraints are limited to syntactic constituents. E.g. in ( 6), there are two occurrences of the subject-verb agreement constraint: Il pense and tu dors.

(6) Il pense que tu dors. / He thinks that you sleep. (7) ( P ( SN Il) ( SV pense ( PS que ( P ( SN tu) ( SV dors) *))) *).

Scope of this constraint is limited: dors should not agree with Il. With a classic constituent structure as in ( 7), and local variables on the subject pronoun and verb, the agreement constraint should be specified at the P level; the two instances of the constraint (marked by the stars in ( 7)) will each be evaluated with the appropriate set of values, thanks to the locality constraint for tu dors and thanks to the search procedure for Il pense.

Co-occurrence constraints. Formally, one may distinguish three types of co-occurrence constraints, summarized in Table 4. The third constraint type is new in NooJ and has been developed by Max Silberztein following our proposition at the NooJ Conference at INALCO, Paris. Co-occurrence constraints have negative counterparts thanks to the negation operator (!).

Syntax Semantics <$V1$N1=$V2$N2>

The value of attribute N1 recorded in variable V1 is equal to the value of attribute N2 recorded in variable V2. This is typically used for agreement constraints, with N1 and N2 identical.

<$V1$N1=Value>

The value of attribute N1 recorded in variable V1 is equal to the value Value. $N1 may be replaced by _ to denote the lemma recorded in V1.

<$V1>

The variable V1 is defined, i.e. it records some value(s). Table 4. Co-occurrence constraint types.

It must be noted that the first two constraint types are considered satisfied if any of the variable referred to is undefined. To avoid unnecessary constraint checking by NooJ and save computational time, agreement constraints should be set on the path of the less frequent of the two variables. In our grammar, pronoun-verb agreement constraints are thus specified on the pronoun paths: they are optional, while the verb is mandatory.

Constraints of the second type are all set on some optional item path and refer to a mandatory item.

Fig. 2. Two co-occurrence constraint examples.

Fig. 2 gives an example of co-occurrence constraints with the annotation of the two PAS occurrences. The first requires that VF be an infinitive (and requires NEG by graph design), the second requires that there is a negation particle ($NEG is defined in the NEG node), but sets no constraint on the verb. Dashed lines represent all the intermediate nodes it would be necessary to duplicate if the constraints were not available.

Co-occurrence constraints for the French nucleus verb phrase

Tables 5 to 7 list the co-occurrence and agreement constraints specified in the grammar, using an informal natural language formulation which documents the actual downloadable formal grammar. First columns refer back to annotations in the downloadable NooJ graph.

To correctly interpret the formulas, a few definitions are in order:

A reflexive pronoun is one of me, te, se, nous, vous, toi which agrees in number and person with the subject. Such pronouns are identified using agreement constraints9 ; a dedicated variable $REF is instantiated when the constraints are satisfied.

An auxiliary past participle is either eu or été when they are followed by another past participle (e.g. as in il a été mangé).

Sequences ending with a past participle (PP) fall into two categories: subject oriented or object oriented PP phrase, defined in Table 6.

The nice thing with properties is that each formula constrains the language on one very specific point, making it possible to illustrate the constraint with specific examples and counter-examples. Tables 5

Conclusion

.Our goal in this paper was twofold: demonstrating the coding of cooccurrence constraints in NooJ and specifying a fully operational grammar. Looking at our large graph, the reader might wonder what is the point in this style of coding. The point is modularity. The graph is large because it is made of an accumulation of observations, but most of these observations are fairly simple and it is easy to add or remove constraints.

The grammar should be primarily evaluated against its "contract", i.e. a set of strings marked as grammatical and ungrammatical, designed, as seen in Tables 5 to 7, to illustrate each constraint to be satisfied. In that sense, the grammar is not only a formal description of a set of strings, but also a test suite for the French nucleus verb phrase. Prior to evaluating the grammar against running text, bear in mind that the specified language is a purist's version of the standard modern French nucleus verb phrase-not appropriate for all uses. Tests on corpus showed some strings were not identified because they were ungrammatical (e.g. *je vous ait dit). This is good for error detection, bad for information extraction. We also found a few strings where word order is not the one our grammar allows: pour n'y plus revenir, sans lui rien apprendre. However, these are from XIX th century literature and sound outdated; modern word order would be pour ne plus y revenir, sans rien lui apprendre, which our grammar does recognize. The problem is an observation problem: what is the good set of strings to specify? [START_REF] Bès | La phrase verbale noyau en français[END_REF] showed that properties could easily accommodate variations in the observations; NooJ can now have this quality, with our transposition of properties into the NooJ formalism.

Table 1 . Clitic slots to the left of the mandatory verb form.

 1

		DAT1r ACC1	ACC2 DAT2 y	en ACC3	VF
		DAT1
	1 je					dors
	2 vous ne					dormez
	3 il	se	l'			achète
	4 tu		le	lui		achètes
	5 elle		les	leur	y	donne
	6 il	vous	les			en	rapporte

. 1 VF NOMi obj. pro.

				PAS	TS	TS	EU ETE	PP
						tout
	1 n'	aime	-t-il	pas		tout
	2	donne -le-moi
	3 ils	aiment			tous	tout
	4 ne lui	a	-t-il	pas			été	donné
	5 il	est					mangé
	6 il	a					eu	mangé
	7 elles	ont			toutes		été	aimées
	8 il	a					eu été	aimé

Table 2 . Slots to the right of the mandatory verb form. Prep NOM NEG PAS TS TS tout obj. pro. VF

 2

	1 pour	ne	pas	nous les acheter
	2	ne		rien lui	dire
	3 à		tous	tout	acheter
	4 de		toutes	se les	acheter

Table 3 . Additional options to the left of infinitive VFs.

 3

	If one considers infinitive verb forms, Table

Table 5 . Requirement and exclusion constraints.

 5 to 7 give such examples; see more examples in the grammar contract 10 . PP1 A subject oriented PP phrase is one where either VF is être, or été is present, and the PP verb either is marked as requiring être as an auxiliary or is marked as requiring avoir, is transitive and there is no reflexive pronoun (this is the passive voice).

	C1 A subject pronoun forbids that VF be an infinitive,	*il dormir
	present participle or imperative form.	*il dormant
		#*tu dors IP
	C2 A negation adverb before VF requires that VF be an	ne pas dormir
	infinitive.	*ne pas dort
	C3 A tous quantifier or a non clitic pronoun before VF	tout manger
	requires that VF be an infinitive.	#*tout OBJ mange
	C4 A tous quantifier either requires a plural subject or a	il les aime tous
	plural accusative pronoun, except en.	ils l'aiment tous
		*il l'aime tous
	C5 An ethical dative pronoun forbids that VF be a	il te lui donne
	second person form.	*tu te lui donnes
	C6 A slot 3 clitic pronoun forbids a slot 1 clitic pronoun.	*il se lui donne
		*il me leur donne
	C7 Clitic pronouns before VF either forbid that VF be an	ne le mange pas
	imperative, or require that VF is an imperative and	#*le mange IP
	there is a negation particle.
	C8 An auxiliary VF requires a past participle head verb.	il a dormi
	C9 A non auxiliary VF forbids a past participle.	*il part dormi
	C10 A slot 2 clitic pronoun to the right of an imperative	aime-moi
	may end the clitic sequence if it is not a marked	*aime-me
	unstressed form (me, te) and may be followed by a	donne-m'en
	slot 3 pronoun if it is not a marked stressed form	*donne-moi-en
	(moi, toi). (This is the purist's imperative.)
	C11 Complement clitic pronouns after VF require that VF	mange-le
	be an imperative and forbid there is a negation	*mangeait-le
	particle.	*ne mange-le
	C12 A negation adverb requires a negation particle	il ne mange pas
		*il mange pas
	C13 The auxiliary past participle eu requires a past	il a eu dormi
	participle head verb with feature Aux=a (assigned to	il s'est eu absenté
	verbs that require avoir as well as pronominal verbs).	*il est eu parti
	C14 The auxiliary past participle été requires avoir as VF.	il a été mangé
		*il est été mangé
	C15 The passive voice forbids an accusative pronoun.	*il l'est mangé

Table 6 . Properties of the past participle phrases.

 6

	A1 A subject pronoun agrees in person and number	*tu dort
	with VF.	*il dorment
	A2 A tous quantifier agrees in gender with the subject	ils sont tous partis
	or the direct object pronoun (see also C4, Table 5).	*elles sont tous partis
	A3 In a subject oriented PP phrase, the past participle	ils sont partis
	agrees in number with the subject 11 or it may be	*ils sont parti
	singular if the subject is second person plural.	vous êtes parti
	A4 In a subject oriented PP phrase, the past participle	elles sont parties
	agrees in gender with the subject.	*elles sont partis
	A5 In an object oriented PP phrase, if there is an	ils ont mangé
	accusative pronoun, the past participle agrees in	*ils ont mangés
	number and gender with the accusative pronoun,	il les a mangés
	otherwise it is masculine singular 12 .	*il les a mangé

Table 7 . Agreement constraints.

 7

(Trouilleux,

2007) shows that, ignoring fléchage ("arrowing") properties, a description in the properties formalism may be interpreted as the intersection (i.e. conjunction) of finite-state languages. The fléchage property type codes the dependencies between the words within the strings; it does not contribute to the

All nodes dominate only one terminal category, except PAS, ETE and VPP, which include optional adverbs. Initial prepositions are omitted for space reasons.

http://lrl.univ-bpclermont.fr/spip.php?rubrique48. The grammar is available as a NooJ project file or as a series of screen captures.

Additionally, we consider that reflexive pronouns agree in gender with the subject, even though none is overtly marked in gender. We consider that in elle s'est trompée, the past participle agrees with the object pronoun s'.

As the subject agrees in number and person with the verb, we code number or person agreement with the subject as an agreement with the verb.

The grammar does not deal with other cases of agreement with the direct object.


Fateh Belaid
email: fateh.belaid@cstb.fr

Thomas Garcia
email: garcia@gate.cnrs.fr

F Belaïd

Understanding the spectrum of residential energy-saving behaviours: French evidence using disaggregated data

Keywords: Energy-saving behaviours, Residential energy use, Econometric modelling, IRT, Lasso Q4, Q5, D19 Energy-saving behaviours, Residential energy use, Econometric modelling, IRT, Lasso JEL: Q4, Q5, D19

Analysing household energy-saving behaviours is crucial to improve energy consumption predictions and energy policy making. How should we quantitatively measure them? What are their determinants? This study explores the main factors influencing residential energy-saving behaviours based on a bottom-up multivariate statistical approach using data from the recent French PHEBUS survey. Firstly, we assess energy-saving behaviours on a one-dimension scale using IRT. Secondly, we use linear regression with an innovative variable selection method via adaptive lasso to tease out the effects of both macro and micro factors on the behavioural score. The results highlight the impact of five main attributes incentivizing energysaving behaviours based on cross-variable analyses: energy price, household income, education level, age of head of household and dwelling energy performance. In addition, our results suggest that the analysis of the inverted Ushape impact of age enables the expansion of the energy consumption life cycle theory to energy-saving behaviours.

Introduction

The building sector accounts for one of the major share of total primary energy consumption in most countries. Today, it is responsible for more than one-fifth of global energy consumption of delivered energy and as much as one-tenth of global greenhouse gas emissions, both in developed and developing countries. The amount of domestic energy used can vary widely within and across regions and countries. Various factors influence the ways in which energy is consumed by households, such as energy prices, household and dwelling characteristics, access to delivered energy, climate, home appliances types and effi-ciencies, energy sources and energy-related policies. Concerning the French case, the building sector is relatively intensive in energy as it was responsible for 30% of the total energy consumed and 20% of the CO 2 emissions produced in 2014. It is projected that with current policy settings residential energy demand will continue to grow and World residential energy consumption will increase by 57% from 2010 to 2040, mainly as a result of growing residential demand in the non-OECD countries (IEO, 2013). The residential sector has the largest potential for delivering longterm, significant and cost-effective reduction of greenhouse gas emissions. Therefore, making the housing stock as energy efficient as possible would bring multiple benefits to both the economy and the society.

While the impact of behaviours on energy consumption is fairly well apprehended, the factors influencing energy behaviours have not so far gotten much attention. It is essential to accurately assess energy behaviours to better define public policies' targets. Besides promoting energy efficient technologies and new energy resources development, changing occupants behaviour appears as a promising way of fostering energy efficiency in housings. In this context, our main objective is to provide further insight into how to improve the effectiveness and efficiency of energy policy making promoting more sustainable consumption patterns through a better identification of households involved in energy intensive behaviours.

For the lack of availability of disaggregated data on household energy usages, the majority of residential energy studies in this last decade have been dominated by the technical and physical research. More precisely, very few studies have focused on socio-economic energy-saving behaviours determinants [START_REF] Sardianou | Estimating energy conservation patterns of greek households[END_REF][START_REF] Sanquist | Lifestyle factors in us residential electricity consumption[END_REF][START_REF] Yue | Factors influencing energy-saving behavior of urban households in jiangsu province[END_REF]. To our knowledge, the present paper is the first to use microlevel data to investigate the impact of household characteristics, climate, physical and energy performance characteristics on domestic energysaving behaviour. It is based on PHEBUS 1 , a new data base containing information on the dwelling characteristics, the occupant's energy behaviours and their socio-demographic features combined with energy performance certificate (EPC). Starting by evaluating energy-saving behaviours on a one-dimension scale using Item Response Theory (IRT), we associate multivariate regression with adaptive lasso variable selection to identify the factors influencing energy-saving behaviours. Our results aim to contribute improving the understanding of the energy behaviours' black box.

The remainder of this paper is organised as follows: Section 2 gives a brief theoretical background on energy behaviours. Section 3 presents the conceptual framework and research hypotheses. Section 4 describes the data and the modelling approach. We report our empirical findings and discuss their implications in Section 5. Based on the results of the model, we draw conclusions and provide some policy implications in Section 6.

Theoretical background

Domestic energy consumption is a complex issue closely linked to the multitude of inter-related factors including direct factors such as technical attributes of the buildings, household characteristics and behaviour, energy systems, climate, equipment, but also indirect drivers such as fuel prices and inflation considered by macroeconomists [START_REF] Summerfield | Changes in energy demand from low-energy homes[END_REF]. Currently there is a lack of models or studies that include all of these factors. Since the late 1970s, in the aftermath of the oil crisis, concerns regarding residential energy use and conservation triggered a first wave of studies. Studies have varied in terms of approach (conceptual, methodological, and/or unit of analysis) and purpose (estimation, energy reduction, and/or energy conservation) [START_REF] Valenzuela | An analysis of monthly household energy consumption among single-family residences in texas[END_REF].This theme was particularly stimulated both by the increasing awareness of global warming, climate change, fossil fuel depletion and rising oil prices in recent years.

Broadly, as described by [START_REF] Swan | Modeling of end-use energy consumption in the residential sector: A review of modeling techniques[END_REF], there are two fundamental methods adopted to model and analyse various aspects of residential energy consumption: top-down and bottom-up approaches. Top-down models work at an aggregated level; usually using time series models to investigate inter-relationships between the energy sector and the economy. Bottom-up models are based on disaggregated views, they use high resolution data to estimate energy consumption and CO 2 emissions. Two classes of models can be identified within bottom-up models: engineering and statistical models. The approach proposed in this study corresponds to a bottom-up statistical model analysing the effects on household energy behaviours by using high resolution data containing technical, socio-demographic and behavioural data on households.

Over the last few years, empirical studies on residential energy consumption have received considerable attention.

For reasons of non-availability of disaggregated data, most of these studies use aggregated time series data, and only a few micro studies use the available householdlevel data [START_REF] Zhou | Estimation of urban residential electricity demand in china using household survey data[END_REF]. Furthermore, many of the current studies on energy consumption in the residential buildings and debates regarding energy efficiency in the housing stock focus on the physical and technical determinants of energy consumption, neglecting the role of the economic behaviours of resident households [START_REF] Brounen | Residential energy use and conservation: Economics and demographics[END_REF]. Previous studies in the USA and the Netherlands have determined that building characteristics explain from only 40% to 54% of the variation in energy use [START_REF] Guerra-Santin | Occupants' behaviour: determinants and effects on residential heating consumption[END_REF][START_REF] Sonderegger | Movers and stayers: the resident's contribution to variation across houses in energy consumption for space heating[END_REF]. Summerfield et al. ( 2010) stated that energy use in U.K. households may vary by up to three times in properties with similar physical attributes. Energy behaviours thus represent a significant potential for the increase of end-use energy efficiency in dwellings.

Conscious of the behaviours' large impact, some researches emphasise on the importance of analysing the factors influencing energy conservation behaviours [START_REF] Dwyer | Critical review of behavioral interventions to preserve the environment research since 1980[END_REF][START_REF] Abrahamse | A review of intervention studies aimed at household energy conservation[END_REF][START_REF] Darby | The effectiveness of feedback on energy consumption. A Review for DEFRA of the Literature on Metering[END_REF][START_REF] Allcott | Social norms and energy conservation[END_REF][START_REF] Ehrhardt-Martinez | Advanced metering initiatives and residential feedback programs: a meta-review for household electricity-saving opportunities[END_REF][START_REF] Yue | Factors influencing energy-saving behavior of urban households in jiangsu province[END_REF]. Most of these studies tackle the energy behaviours from a social sciences point of view and especially using environmental psychology [START_REF] Lopes | Energy behaviours as promoters of energy efficiency: A 21st century review[END_REF]. Recent literature on household energy use and energy-saving behaviours recognises that domestic energy use depends on factors such as energy price, climate, and building and household characteristics but also on the householders' energy-saving behaviours [START_REF] Barr | The household energy gap: examining the divide between habitual-and purchase-related conservation behaviours[END_REF][START_REF] Branco | Predicted versus observed heat consumption of a low energy multifamily complex in switzerland based on long-term experimental data[END_REF][START_REF] Lindén | Efficient and inefficient aspects of residential energy behaviour: What are the policy instruments for change?[END_REF][START_REF] Fabi | Occupants' window opening behaviour: A literature review of factors influencing occupant behaviour and models[END_REF][START_REF] Mizobuchi | The influences of financial and non-financial factors on energy-saving behaviour: A field experiment in japan[END_REF]. One of the most relevant study on residential energy behaviours is due to [START_REF] Steg | Encouraging proenvironmental behaviour: An integrative review and research agenda[END_REF]. The authors reviewed the contribution and the potential of environmental psychology for understanding and promoting pro-environmental behaviours. [START_REF] Lopes | Energy behaviours as promoters of energy efficiency: A 21st century review[END_REF] proposed a review of recent literature on energy behaviours exploring peer-reviewed publications in the field of energy behaviours, domestic end-use energy behaviours, and modelling behaviours approach. This study concludes that energy behaviours are highly complex, shaped by many factors both individual and contextual. Due to this complexity, they are usually studied using fragmented and disciplinary studies from a wide range of disciplinary areas such as sociology, psychology, economics and engineering. This section gives a brief overview of relevant studies that focus on the factors influencing households energy behaviours. [START_REF] Sardianou | Estimating energy conservation patterns of greek households[END_REF] developed an empirical model (latent trait model OLS regression) to investigate the main determinants of household energy conservation patterns in Greece using cross-section data based on an extensive survey of 586 Greek households. The study uses four subsets of variables: economic factors (private monthly income, electricity expenditures), demographic variables (age, sex and educational level of the respondent, marital status and family size), dwellings characteristics (homeownership, house type, number of rooms and size in m 2 ), information diffusion and attitudinal variables (individuals belief about their contribution to environmental problems). The results show that socio-economic variables such as consumers income and family size are suitable to explain differences in energy conservation preferences. In addition, the results suggest that electricity expenditures and age of the respondent are negatively associated with the number of energy conserving actions that a consumer is willing to adopt. [START_REF] Sanquist | Lifestyle factors in us residential electricity consumption[END_REF] investigated the role of lifestyle dimensions of residential electricity consumption using multivariate statistical approach namely factor analysis and multiple regression analysis. They used variables from the 2005 U.S. Residential Energy Consumption Survey (RECS). Their research shows that five lifestyle factors account for more than 40% of the variance in electricity consumption and income adds negligibly to predictive power (contributes 1% unique variance to the models).

Recently, [START_REF] Yue | Factors influencing energy-saving behavior of urban households in jiangsu province[END_REF] used a statistical analysis (descriptive statistical analysis, bivariate correlation, multiple and hierarchical linear regression) to explore factors influencing energy-saving behaviours of urban households by analysing the differences in households willingness to adopt three types of energy-saving behaviours in Jiangsu Province (China) and four dimensions of influencing factors: socio-demographics, energy-saving awareness, behavioural ability, and institutional factors. Their study is based on an internet survey that was sent out to 638 households. The results indicate that sociodemographic characteristics, including age, gender, income level, household structure, and educational background, are the most important factors influencing energy-saving behaviours.

Conceptual framework and research hypotheses

First of all, the concept of energy behaviours need to be tackled on a semantic point of view as the delimitation between behaviours and technical attributes of the building can be blurred. In its wider definition, this term is used in the literature to define the occupants' influence on the housing as well as general thinking and attitudes towards energy-saving [START_REF] Sardianou | Estimating energy conservation patterns of greek households[END_REF]. It can gather very different aspects such as the equipment level, some characteristics of the housing directly related to energy-saving theoretically modifiable by the occupants, ideological position on energy-saving or proselytism level of these opinions. Some of these characteristics make sense in a dynamic framework (technological improvements) when some others are to be analysed in a static one (given a technological level how do someone behave). Furthermore, it includes actions -what I do -as well as beliefs on these actions -what I think I do. In line with [START_REF] Lopes | Energy behaviours as promoters of energy efficiency: A 21st century review[END_REF], we choose to refer to energy-saving behaviours to express habits that are incorporated in the routine and repeated automatically. The fact that they are recurrent actions excludes purchasing behaviours that are discrete actions. They answer the question: to what extent is someone an energy-saver given the possibilities offered by his dwelling?

Adopting this conservative definition of energy-saving behaviours can appear as ambitious because establishing a link between technology in-dependent behaviours and characteristics is difficult. However, it enables us to best tackle the intrinsic meaning of behaviours and our conclusions not to be biased by the fact that all households do not have the same access to improvements (the housing occupation status playing, for example, a key role) and that they have moved in unequally equipped housings.

After their identification, energy-saving behaviours need to be accurately measured. Our data-base contains either self-reported behaviours or self-reported beliefs on behaviours. While actual behaviours and beliefs can be different because of a judgement bias, self-reports appear as more homogeneous. This is why we have included both kinds of information on energy-saving behaviours.

Based on the literature and on micro-economic theoretical insights, we aim to test the following set of hypotheses.

H 1. Energy-saving behaviours are positively affected by the energy price.

H 2. Energy-saving behaviours are negatively affected by the households' revenue.

H 3. Households living in highly energyconsuming buildings behave in a more energysaving manner.

H 4. Energy-saving behaviours are positively affected by the households' education level.

H 5. Energy-saving behaviours intensity follows an inverted U-shape curve with the age.

Hypothesis 1 is a price effect, Hypothesis 2 a revenue effect and Hypothesis 3 a cost per unit of service effect. Hypothesis 4 is motivated by the alignment of environmental behaviours and education level [START_REF] Hines | Analysis and synthesis of research on responsible environmental behavior: A meta-analysis[END_REF] while Hypothesis 5 matches the life-cycle theory of energy consumption [START_REF] Fritzsche | An analysis of energy consumption patterns by stage of family life cycle[END_REF].

Data and modelling approach

Data

This research is based on the 2014 PHEBUS2 new national household energy survey conducted by the Department of Observations and Statistics (SOeS) depending on the French Ministry of Ecology and Sustainable Development. In this study, we focused on 2,356 households in housing units statistically selected to represent 27 million housings in France. PHEBUS variables cover the household socio-demographic characteristics, the physical characteristics of the dwellings, appliance information, fuel types and related consumption. Furthermore, it contains data on housing energy performances coming from diagnosis lead by certified professionals.

Variables characterising energy-saving

behaviours Consistently with the previous definition of energy-saving behaviours, we have selected eight ordinal variables of interest in the PHEBUS database with their modalities ranked from the more energy-intensive to the more energy-saving behaviour. Six of them are binary variables. Concerning heating actions, we take into account selfimposed restrictions during winter (HR) as well as decreasing periodically the heating temperature in the night space (DSN) and elsewhere in the dwelling (DD). Beliefs regarding heating (HB), electricity (EB) and hot water (HWB) usages are evaluated by the preference between saving and comfort. The last actions in the scope of this paper take three modalities. The frequency of window opening per day during heating periods (WO) is considered either equal to more or less than 15 minutes a day by opposition to occasional opening. Regarding the heating temperature (HT), between 19 • C and 20 • C is considered as the average3 , a warmer heating or a colder one are defined accordingly.

The variables characterising the energysavings are very oriented towards non-intensive heating behaviours as six out of eight variables are related to heating behaviours. In comparison, the European residential building as 57% of the total final energy consumption is used for space heating, 25% for domestic hot water and 11% for electricity [START_REF] Chwieduk | Towards sustainable-energy buildings[END_REF].

To have a clear idea on the composition of the selected behaviour variables, we focus on their distribution (Table 1) and on their correlation factors (Figure 1). The observation numbers reveal the almost completeness of our database as no variables are missing more than 3% of answers.

All correlation coefficients are positive, supporting a global coherence in selected energysaving behaviours. However, window opening appears to be singular, as it is not significantly (at a 5% level) correlated with other variables than the heating temperature. The highest covariance is between the two temperature modulation behaviours as they are highly correlated with a similar characteristic: the fact of being equipped of a temperature modulator. Finally, we note that there are three times as many households overheating their dwelling than under-heating it which is in line with the fact that only one fifth of all households reports to apply heating restrictions. Regarding beliefs, households tend to prefer heating comfort over electricity comfort. The three kinds of belief are highly correlated (coefficients between 0.4 and 0.5). Modulating the temperature in the night-space is independent from ones' beliefs concerning hot water and electricity but, as expected, significantly correlated with heating beliefs. Only correlations between variables significantly correlated at a 5% level are given.

Variables explaining energy-saving behaviours

In order to correctly assess the potential factors influencing energy-saving behaviours, we need to evaluate these behaviours not only regarding individuals distinctiveness but also by analysing what is surrounding them. Obviously, individual features such as age, gender, or social background are expected to play a key role in explaining the energy-saving behaviours. However, households' behaviours are difficult to understand without apprehending the characteristics of what is surrounding them. At the least detailed level, geographic considerations such as the urban structure or the climate quality are to be studied. Regarding the physical discriminating factors two scopes can be distinguished, on the one hand the outside of the construction -the building -and on the other hand the inside -the indoor dwelling. The first set, preceding the second one on a macro to micro scale, includes the EPC or the proximity to other housings, while the second one is largely dedicated to equipment including heating equipment's characteristics.

The composition of the different levels of analysis are summarised in Figure 2. 3 give an extensive vision of respectively the quantitative and categorical characteristics in the scope of the study. Regarding the geographic area, the temperature index used is the Heating Degree Day (HDD) index. Based on the minimal and maximal daily outside temperature, it provides a simple metric for quantifying the amount of heating that buildings, in a particular location, need. The higher the HDD is, the more heating is needed. We have separated Paris conurbation from the other urban areas of more than 200,000 inhabitants to be able to take into account the specific role played by Paris in the French system. The EPC is based on both outside and inside dwelling characteristics. It is highly related with the construction year, the isolation performance or the roofing and, for part of the residential buildings, the diagnosis has been based on a collective approach. Therefore, we have chosen to include it among the building characteristics. The delimitation of the indoor dwelling group is closely related to our definition of energy-saving behaviours. We have excluded from the behavioural set all characteristics related to equipment or dwelling improvement, however they can be use-full in explaining these behaviours. For the equipment intensity, we have ranked households in four classes according to the number of small electric equipment as oven, washing machine, computers or television sets owned. As for house refurbishment, it indicates if works have been undertaken in the dwelling in the past few years. Finally, the energy price is computed ex-post based on total energy spending and energy consumption which explains its high variance. Individual characteristics correspond to the person self-determined as being the reference person for the household except for the earnings. This choice was driven by the necessity to have a bijection between individuals' and households' characteristics. Males being more than twice as represented as females, it reveals the fact that they have a higher propensity to self-declare as reference person for the household. Nationality splits the sample between French-born individuals and others. Earnings are based on declarations and correspond to monthly income for the whole household. We have chosen to split the age variable in four classes to be able to assess Hypothesis 4. While the current professional status is given by occupation, the socio-occupational categories correspond to either former or actual occupation in order to control for a hypothetical time-availability effect.

Unit N Mean St. Dev.

Geographic area

Temperature index

Modelling approach

An accurate measurement of energy-saving behaviours' need to overcome two features of ecological behaviours: i) the inconsistency from one behaviour to another, ii) the unequal difficulty of all behaviours [START_REF] Kaiser | A general measure of ecological behavior1[END_REF].

Influenced by social and cultural conditions as well as by the power of habits, individuals may behave ecologically in one domain but not in another [START_REF] Pickett | Is there a general conserving consumer? a public policy concern[END_REF]. In order to draw robust conclusions on a global energy-saving scale, it is important to smooth these inconsistencies by establishing an agglomerate measurement. For this purpose, the unequal difficulty of each behaviour can be an obstacle. As an example, self-imposed heating restrictions are more constraining than heating modulation while out of the dwelling. The IRT gives an adequate solution as it enables us to compare each household on a unique energysaving scale which takes into account the respective difficulty of each behaviour. IRT is a modelbased approach establishing a latent ability characteristic from answers to a questionnaire. As the set of energy-saving behaviours is composed of ordinal polytomous data, the underlying modelisation used is the Graded Response Model (GRM) introduced by [START_REF] Samejima | Estimation of latent ability using a response pattern of graded scores[END_REF]. Considering x im the ordinal manifest variable, z m the latent ability, α i the discrimination parameter and β ik the extremity parameters. GRM postulates that the probability of the m th subject to endorse the k th response of the i th item is expressed using a logistic function:

P(x im ≤ k|z m ) = exp(α i (z m -β ik )) 1 + exp(α i (z m -β ik )) P(x im = k|z m ) = f (w ik ) -f (w i,k+1 ) where w ik = α i (z m -β ik ), f (w) = exp(w) 1 + exp(w) ,
and

β 1 < β 2 < ... < β K
Then, we estimate the model using the MMLE maximization method [START_REF] Baker | Item response theory: Parameter estimation techniques[END_REF]) and the households' latent abilities with the maximum aposteriori approach.

In order to evaluate the impact of each characteristic on the latent ability level we use a three steps approach. i) we regress the previously described explanatory variables on the latent ability vector. We use a multivariate linear regression specifying the score and the categorical variables in level and the explicative quantitative variables in logarithm (exception made of the number of people). ii) to increase the interpretability of our model, we implement an adaptive lasso method (ALASSO) -an innovative variable selection method for regression [START_REF] Zou | The adaptive lasso and its oracle properties[END_REF], iii) we run the final regression with the selected explanatory variables.

Besides prediction accuracy another important criterion of robustness and goodness of the fitted underlying model is sparsity or parsimony. Variable selection might be an attempt to identify the best subset of important predictors among many variables to include in a model. This selection aims to improve the estimation accuracy and enhance the model interpretability with parsimonious representation. It is particularly important to high dimensional regression modeling. ALASSO is one among numerous subset selection automated procedure based either on sequential multi-variable evaluations or parameters shrinkage. It has several features that distinguish it from other traditional techniques of variables selection. The chief advantages of adaptive lasso over other methods [START_REF] Zou | The adaptive lasso and its oracle properties[END_REF] is:

• The ALASSO enjoys the oracle properties in the sense of [START_REF] Fan | Nonconcave penalized likelihood with a diverging number of parameters[END_REF] by utilizing the adaptively weighted l 1 -penalty even when the number of covariates is much larger than the sample size.

• The ALASSO shrinkage leads to a nearminimax optimal estimator even in the case of heteroskedastic data [START_REF] Caner | A near minimax risk bound: adaptive lasso with heteroskedastic data in instrumental variable selection[END_REF].

• The ALASSO is computationally efficient compared to the smoothly clipped absolute deviation and bridge methods, i.e., ALASSO estimate is a convex optimization problem.

ALASSO method shown to be both consistent in variable selection and asymptotically normal in coefficient estimation. However, ALASSO not only helps to improve the prediction accuracy when dealing with multicolinearity data, but also carries several properties such as interpretability and numerical stability.

Regarding the other methods some main drawbacks have been identified arguing in favour of the superiority of the ALASSO. As an example, stepwise methods suffer from high variability regarding the order of selection or data changes [START_REF] Breiman | Better subset regression using the nonnegative garrote[END_REF] while ridge regressions does not enable to shrink coefficients to zero. Moreover, [START_REF] Fan | Variable selection via nonconcave penalized likelihood and its oracle properties[END_REF] show that for large coefficients the lasso shrinkage [START_REF] Tibshirani | Regression shrinkage and selection via the lasso[END_REF] produces bias. Formally, the ALASSO is based on the following minimisation problem. Considering λ the amount of shrinkage, y the vector of responses and X = (x 1 , ..., x p ) the matrix composed of the p linearly independent predictor vectors, the adaptive lasso solves the OLS regression problem adding a weighted l 1 -norm penalty on the coefficients:

β(adaptive lasso) = arg min β ||y - p i=1 x i β i || 2 + λ p i=1 ŵi |β i | where ŵ = 1/| β |
Then, are selected for the final regression only the non-zero coefficient variables.

Results

Latent ability

We first estimate the item difficulty, i.e. the probability of exhibiting each behaviour composing the score (P(x im = k)) as function of the ability level (Figure 3). In line with the relative independence between the window opening observed in Subsection 4.2 and the other energy-saving behaviours, we notice that this behaviour has only a low influence on the latent ability. Apart from WO, for an increasing level of ability, one household has strictly increasing odds to behave in a more energy-saving way. The point at which one modality becomes more likely than another is related to the proportion of households involved in each one of them. For example, only households with an ability greater than three are more likely to heat their housing at a temperature lower than 19 • C as only 11% of the sample behave in such a manner. The sharpness of the curves is function of the correlation with other variables. In the set of ability determinant variables, DNS is the only one not correlated with all other variables, unsurprisingly it is for this variable that we note the smaller influence of a deviation from the point of equal likelihood. The heating belief is strongly correlated with the other behaviours, therefore it has the highest first derivative (in absolute value) in a neighbourhood of the point of equal likelihood. The latent ability vector obtained is statistically described in Table A.5, its kernel density has a three-bump shape (Figure A.4).

Hypotheses testing and discussion

The hypotheses testing is discussed based on the results of the linear multivariate regression with only the variables selected by the adaptive lasso (Table 4). The adaptive lasso shrinkage pattern is described in Appendix B.

Firstly, we observe a price effect as the energy price is one of the three significant effects at a 1% level, confirming Hypothesis 1. The more expensive energy intensive behaviours are, the less households consume them. Having a shared central heating system also a highly significant effect on the latent ability (p-value<0.01) which is negative. It strengthens the previous result as a shared central heating system often goes with a miss-information upon pooled energy expenses. It denotes that not only the price is important but also the feed-backs on this price, which has been identified as one of the most effective way of action of energy-efficiency policies [START_REF] Lopes | Energy behaviours as promoters of energy efficiency: A 21st century review[END_REF][START_REF] Mizobuchi | The influences of financial and non-financial factors on energy-saving behaviour: A field experiment in japan[END_REF]. It is also related with the fact that when possessing a shared heating system individuals have less possibilities to regulate the temperature and may thus have to engage in energy-wasting behaviours such as opening windows during a heating period to control the inside temperature. We fail to demonstrate a revenue effect (Hypothesis 2). Energysaving behaviours do not seem to be normal goods as their demand is independent from the revenue level. It can be explained by the fact that households do not feel any gain in over-consuming energy. Households with good energy-behaviours will not change their habits due to a higher income. The impact of revenue and price on behaviours is to be put in relation with their effect on energy consumption. It has been in the scope of several studies such as [START_REF] Labandeira | A residential energy demand system for spain[END_REF] regarding prices; [START_REF] Cayla | From practices to behaviors: Estimating the impact of household behavior on space heating energy consumption[END_REF] or [START_REF] Cayla | The role of income in energy consumption behaviour: Evidence from french households data[END_REF] regarding revenues; and [START_REF] Parti | The total and appliancespecific conditional demand for electricity in the household sector[END_REF], [START_REF] Dubin | An econometric analysis of residential electric appliance holdings and consumption[END_REF], [START_REF] Baker | Modelling household energy expenditures using micro-data[END_REF], [START_REF] Nesbakken | Energy consumption for space heating: a discrete-continuous approach[END_REF], [START_REF] Bernard | Quebec residential electricity demand: a microeconometric approach[END_REF] or [START_REF] Branch | Short run income elasticity of demand for residential electricity using consumer expenditure survey data[END_REF] for cross analysis. As reviewed by [START_REF] Risch | What matters in residential energy consumption? evidence from france[END_REF], the energy price elasticity estimations vary from -0.2 to -1.14 while the energy income elasticity is estimated to be lower, ranging between 0.01 and 0.13. Therefore our findings on price and revenue effect on energysaving behaviours are consistent with the important difference between energy price and energy income elasticities.

Hypothesis 3 is largely confirmed by our results as most building characteristics related to high energy consumption are also linked with more energy-saving behaviours. Households living in shared buildings have lower latent abilities than those living in isolated or semi-detached houses. In multi-households dwellings, there are synergies between the different heating actions of all households occupying the same building. It is easier for the occupants to be well heated and they have less to invest to find energy-comfort.

The effect of EPC is in line with this statement, households living in dwellings ranked at the bottom of the energy-performance scale are the ones with the better energy behaviours. In F or G EPC ranked dwellings, it is important to modulate the heating temperature while away because of the heat loss or to favour economy over comfort as the price of comfort can be really expensive. Additionally, the temperature index is the last clue regarding the veracity of Hypothesis 3 as the colder the outside temperature is, the more households show energy-saving behaviours. Once again, the impact of these behaviours is higher in colder regions as the cost of having a high heating temperature or to seek for heating comfort is higher. The size effect is the only result not supporting Hypothesis 3 as in a larger dwelling, energy-saving behaviours have more impact. However, it could lays within the fact that, in a smaller dwelling, an energy-saving way of life may be easier to undertake and less time consuming. To sum up, a household living in a building having a propensity to consume a high amount of energy behaves as energy-savers because of an important leverage effect of each of their actions on the energy consumption level. The confirmation of Hypothesis 3 is to be analysed in the light of the rebound effect literature. The rebound effect theory enables to assess energy-behaviours based on a comparison between expected consumption predicted by engineers and the actual consumption. When a household moves into a more efficient dwelling, the cost per unit of service of the equipment falls. Therefore, households adapt to a more energyintensive way of behaving, decreasing the potential impact of the improved performances of their new dwelling [START_REF] Berkhout | Defining the rebound effect[END_REF]. Based on a survey from [START_REF] Greening | Energy efficiency and consumptionthe rebound effecta survey[END_REF], the rebound effect is expected to range from 10% to 30% regarding space heating and 10% to 40% in water heating 4 . Even if we do not observe the education level a cross-analyses of the variables related to the profession gives results that cannot support Hypothesis 4. In opposition to highly educated socioprofessional categories -mainly top managerial and intellectual professions -, socio-professional categories with an average level of educationemployees, workers, or intermediate professionsexhibit more energy-saving behaviours. In addition, the relatively low educated farmers do not have worst behaviours. It is in line, with the neg-ative effect of being employed compared to being unemployed or to have a professional occupation status not mentioned 5 as a high educational level and intellectual background is positively correlated with the fact of being employed. This result cannot be interpreted only as a time availability effect otherwise retired people should behave more like energy-savers revealing that a social class mechanism could be in action. Sociooccupational categories correspond to different social classes which directly influence social status [START_REF] Bourdieu | Distinction: A social critique of the judgement of taste[END_REF]. A higher social status may incentivise more energy consuming behaviours through a preference for comfort over savings or a tendency not to stand for heating restrictions. The non-validation of Hypothesis 4 establishes a gap with the environmental literature as environmental behaviours are known to be positively correlated with the education level [START_REF] Hines | Analysis and synthesis of research on responsible environmental behavior: A meta-analysis[END_REF]. Households with a higher education level have been found to be more receptive to environmental friendly ideas or to be better informed about issues related to global warming, exhibiting better behaviours. However when it comes to energy-saving behaviours this impact is overcome by what we have interpreted as being a social status effect.

The inverted U-shape distribution of latent ability as a function of the age (Hypothesis 5) is supported by the results as one of the middle age classes is more energy-saver. The explanation of these results stands in the composition of the under 45 years old class. Only 8% of individuals belonging to this class are under 28 which is the average age at first childbearing in France 6 . Therefore, it is mainly composed of parents with young children 7 . To have a young child in the dwelling may explain the fact that individuals do not be-5 Individual with a occupation status not mentioned are either student, housewife/husband or having another kind of inactivity 6 Data from INSEE (French National Institute of Statistics and Economic Studies).

7 78% of all households with a child under 10 years old are in the less than 45 years old class and 56% of the previously mentioned class have a child under 10 years old.

have as energy-savers and choose to favour comfort of their child against savings. Once their children are older, parents can shift their behaviours to more environmental ones. Finally, when getting older people tend to seek for more energy comfort, but this time for themselves. In addition, the age has been shown to have a negative impact on environmental behaviours which strengthens the difference in behaviour between the middleage class and the oldest ones. This effect can be explained by a higher behavioural inertia from older individuals [START_REF] Hines | Analysis and synthesis of research on responsible environmental behavior: A meta-analysis[END_REF]. Hypothesis 5 expands the energy consumption life cycle theory to energy-saving behaviours. Regarding energy consumption, the life cycle theory identifies an inverted U-shape curve explained by an increased energy consumption through the child raising years, followed by a decline due to children leaving home [START_REF] Fritzsche | An analysis of energy consumption patterns by stage of family life cycle[END_REF]). An inverted U-shape has also been obtained by [START_REF] Hirst | Residential energy use: analysis of disaggregate data[END_REF] concerning the relationship between the number of conservative behaviours and age, but this time caused by individual motivations and not households composition. When it comes to energy-saving behaviours, the explanation of the inverted U-curve is two-fold. The birth of children is a key feature in explaining the left hand side of the inverted U-shape, while individual aspirations are explaining the right hand side.

The impact of being a tenant is ambiguous as two opposite effects can be highlighted [START_REF] Gillingham | Split incentives in residential energy consumption[END_REF]. Tenants live in less energyefficient houses as landlords tend to invest less to improve the performance of rented houses [START_REF] Black | Personal and contextual influences on househould energy adaptations[END_REF][START_REF] Barr | The household energy gap: examining the divide between habitual-and purchase-related conservation behaviours[END_REF], which induce energy-saving behaviours (Hypothesis 3). On the other hand, the financial impact of consuming energy is not always bear by the tenant as bills can be included in the renting price. This second effect would have a negative impact on the latent ability (Hypothesis 1). We find that the first effect dominates the second, this conclusion is driven from the fact that tenants impose to themselves more heating restrictions than owners. By going beyond the duality of the previous analysis, the positive impact of being tenant may also be related to a hidden revenue effect. In fact, for a same level of earnings an owner has generally more disposable income. Failing to prove Hypothesis 2, we can only speculate on the fact that this revenue effect is adding-up to the energyefficiency impact.

To explain the impacts of the heating system and living in a social housing, we need to look deeper in the correlation between these characteristics and individual energy behaviours. Households living in gas equipped housing modulate less their heating temperature8 . This behaviour is surprising as modulating temperature seems easier with electrical heating equipment, but it explains the negative impact on energy behaviours. Households living in social housing tend to favour savings over comfort for heating, hot water and electricity consumption. It matches the fact that, once controlled by the revenue which is the main selection criterion, the decision of living in a social housing can be interpreted as a prime of saving upon comfort. In fact, living in this kind of dwelling enables to decrease the rent [START_REF] Le Blanc | The effect of public social housing on households' consumption in france[END_REF].

Additionally, we note that being a male has a negative influence on behaviours but we need to stay cautious regarding the potential deductions from this result. In fact, this variable is an indication upon the gender of the individual declared as the reference person and gender is associated to a lot more intra-household volatility than previous variables. Unsurprisingly, the lowest equipment intensity goes with good energy-saving behaviours.

When comparing our results with Sardianou (2007), we find slightly different conclusions. While in line with Hypothesis 1 and Hypothesis 3, their conclusions support as well Hypothesis 2 and a neutrality of the education level. These differences lay within the fact that they chose to include in the definition of energy-saving behaviours (refer as energy conserving behaviours in their work) the attitude towards energy efficiency investments. As these investments are incentivised

Conclusion

An extensive understanding of residential energy consumption is decisive to influence efficiently positive energy consumption patterns and measure accurately the potential effects on the climate. Analyses on energy consumption in residential buildings and debates regarding energy efficiency in the housing stock are dominated by physical and technical studies due to the complexity of the energy behaviours problematic and the lack of information on domestic energy usages. Statistical bottom-up studies focusing on determinant factors of household energy-saving behaviours are thus rather limited. The targeting of efforts towards the productive system and the technical attributes of the buildings is not sufficient to achieve a substantial reduction in domestic energy consumption. The lifestyles and behaviours of households leading to end-use energy consumption are also drivers of the evaluation and then foster energy efficiency. In this context, energy behaviours are a major missing element between the technological progress and the energy consumption.

This work explores the influencing factors of domestic energy-saving behaviours in France. The study is based on a detailed survey combining several information about dwelling attributes, occupant characteristics and behavioural variables. Starting with the idea that individual behaviours are not to be analysed without assessing the environment in which they are expressed, the PHE-BUS survey has enabled us to evaluate the impact of a set of factors on energy-saving behaviours. This set is ranging from highly macro features such as the outdoor temperature to intrinsic micro individual characteristics, including exclusive information such as the EPC. Combining the IRT to quantitatively measure each household's ability to behave as energy-saver associated with the adaptive lasso method, we have highlighted five main vectors incentivising energy-saving behaviours based on cross-variable analysis. The identification of a positive price effect as well as a positive cost per unit of service effect are comforting expected tendencies, while the independence regarding revenue and especially the negative effect of education go upstream. The analysis of the inverted U-shape impact of the age on energysaving behaviours confirms the possible expansion of the energy consumption life cycle theory to energy-saving behaviours.

This research does not evaluate particular energy conservation policy but it suggests ways through which we can begin to think about how we value and integrate energy behaviours in the design of the future incentive energy policies to encourage energy-saving in the residential sector. The results should be useful to energy policymakers seeking to promote household energy efficiency and conservation to consider the importance of behavioural factors. Moreover, they enrich our understanding of energy behaviours' potential savings and suggest ways to develop new energy behaviours modelling strategies.

The use of micro level data can provide richer sources of information and opportunities to develop a deeper understanding of the factors affecting household energy-saving behaviours. In fact, the presented approach offers a new perspective to further researches which requires the collection and analysis of additional data. First of all, more detailed data on occupant behaviours and especially an observability of the behaviours in order not to be potentially victim of a report bias [START_REF] Olsen | Consumers' attitudes toward energy conservation[END_REF] would strengthen the energy-saving behaviours evaluation. Regarding the potential factors of influence, information on the price exante or a direct observation of the education level could be a first step potentially improving the strength of our results. A second one would be to analyse detailed information on all family members in a household to disentangle the direct effect of age linked to change in preferences from an indirect effect linked to the household composition. Finally information on households energy consumption before and after comprehensive thermal retrofits would enable to go from static analyses to dynamic ones and thus to obtain a direct measure of the rebound effect.

Figure 1 :

 1 Figure 1: Covariance matrix of energy behaviour variables Reading note: in the lowest part of the diagram is represented the intensity of the correlation using pies filled on the right side for positive correlations and on the left side for negative ones. The upper part gives the numeric values. Only correlations between variables significantly correlated at a 5% level are given.

Figure 2 :

 2 Figure 2: Representation of the different levels of analysis on a macro to micro scale

Figure 3 :

 3 Figure 3: Item difficulty estimation

Table 1 :

 1 Statistical description of energy behaviours

						Density
		N	Mean St. Dev.	1	2	3
	Actions
	WO	2,356 1.584	0.720	55% 31% 14%
	HT	2,333 1.817	0.616	30% 59% 11%
	DD	2,356 1.447	0.497	55% 45%
	DSN	2,356 1.498	0.500	50% 50%
	HR	2,356 1.219	0.414	78% 22%
	Beliefs
	HB	2,306 1.415	0.493	59% 41%
	EB	2,328 1.579	0.494	42% 58%
	HWB 2,334 1.446	0.497	55% 45%

Table 2 and

 2 Table

Table 2 :

 2 Statistic description of quantitative variables

		• C×day 2,168	2,490	386.605
	Indoor dwelling
	Size	m 2	2,352 105.281	45.021
	Energy price	e/kWh	2,356	0.109	0.035
	Individual
	Number of people	nbr	2,356	2.543	1.323
	Earnings	e/month 2,203	3,392	6,531

Table 3 :

 3 Statistic description of categorical variables

	Variable	Modality	N
	Geographic area
	Urban structure	Paris conurbation	319
		Rural commune	595
		From 2,000 to 20,000 inhabitants	434
		From 20,000 to 200,000 inhabitants	428
		More than 200,000 inhabitants	580
	Building
	Proximity to other households Shared building	663
		Isolated individual house	1189
		Semi-detached house	504
	EPC	A-B-C	369
		D	633
		E	691
		F-G	635
	Indoor dwelling
	Heating system	Shared central	226
		Individual central	1809
		Other	321
	Heating energy	Electricity	816
		Gas	862
		Other	678
	House refurbishment	Yes	1176
		No	1180
	Equipment intensity	Very low	588
		Low	707
		High	560
		Very high	501
	Individual
	Age	Less than 44	614
		From 45 to 56	604
		From 57 to 66	565
		More than 67	573
	Dwelling occupancy status	Owner	1751
		Tenant	605
	Social housing	No	2100
		Yes	256
	Socio-occupational category	Top managerial and intellectual profession 427
		Employee	536
		Worker	612
		Intermediate profession	539
		Artisan, shopkeepers, heads of businesses	49
		Farmer	40
		Other	40
	Professional occupation	Employed	1217
		Unemployed	105
		Retired	916
		Other	118
	Gender	Female	738
		Male	1617
	Nationality	French	2144
		Other	212

Table 4 :

 4 Multivariate regression of the latent abilities on the potential explaining factors selected by the adaptive lasso

			Latent Ability
		Coefficient	Variance
	Intercept	-0.448	0.773
	Geographic area
	Temperature index	0.202 * *	0.096
	Rural commune	-0.081 *	0.040
	Building
	Isolated individual house	0.117 * *	0.057
	Semi-detached house	0.112 * *	0.056
	EPC: F-G	0.067 *	0.038
	Indoor dwelling
	Size	-0.097 *	0.051
	Energy price	0.139 * * *	0.037
	Shared central heating system	-0.458 * * *	0.086
	Individual heating system	-0.051	0.048
	Electrical heating system	-0.090 * *	0.042
	Gas heating system	-0.065	0.044
	Low equipment intensity	-0.080 *	0.043
	High equipment intensity	-0.109 * *	0.048
	Very high equipment intensity	-0.095 *	0.051
	Individual
	Earnings	-0.018	0.012
	From 45 to 56 years old	0.096 * *	0.042
	From 57 to 66 years old	0.045	0.041
	Tenant	0.092 *	0.049
	Social housing	0.131 *	0.068
	Farmer	0.090	0.113
	Employee	0.116 * *	0.050
	Worker	0.125 * * *	0.046
	Intermediate profession	0.113 * *	0.045
	Employed	-0.118 *	0.060
	Retired	-0.050	0.064
	Male	-0.069 *	0.040
	French	-0.122 * *	0.059
	Note:		* p<0.1; * * p<0.05; * * * p<0.01

Access to data can be gained from the Service of Observations and Statistics (SOeS) attached to the French Ministry of ecology, Sustainable Development and Ecology, subject to the prior agreement of the Committee on Statistical Confidentiality.

The recommendation of the "Agence de l'environnement et de la maîtrise de l'énergie" (ADEME) is to heat at 19 • C which appears as a low reference level. We have added households heating their dwelling at 20 • C to the reference class to have a more balanced ranking.

A rebound effect of X% means that X% of the potential gain in consumption vanishes in behaviour adaptation.

Concerning households using only electrical heating, 45% of them modulate heating temperature in the dwelling and 49% in the night space. For households using gas it goes up to, respectively, 50% and 55%. by a higher level of education or by higher financial resources, it explains the difference in conclusions.

.5 presents the coefficient shrinkage using adaptive lasso after a 10-fold crossvalidation. In order to keep the appropriate variables, we have selected λ as to minimise the mean cross-validated error. It is important to note that in the adaptive lasso, as well as in the lasso, factorial variables are considered as being independently evaluated enabling to keep only the relevant clusters for one characteristic. It explains the multitude of coefficients plotted which prevent us from displaying the associated variable for all of them. Only the name of the five last selected variables are indicated. The socio-professional categories worker and employee, the fact of being tenant and the energy prices having a positive effect on energy-saving behaviours while a shared heating system have the opposite effect.