Sandrine Monnery Patris

Natalie Rigal

Audrey Peteuil

Claire Chabanet

Sylvie Issanchou

Dr Sandrine Monnery-Patris
email: sandrine.monnery-patris@inra.fr

Development of a new questionnaire to assess the links between children's self-regulation of eating and related parental feeding practices

Keywords: self-regulation of eating, food as reward, feeding on a schedule, body mass index, responsive feeding

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Infants have an innate ability to self-regulate their food intake, as intake is primarily driven by responses to hunger and satiation cues [START_REF] Birch | Caloric compensation and sensory specific satiety: evidence for self-regulation of food intake by young children[END_REF][START_REF] Birch | The variability of young children's energy intake[END_REF][START_REF] Johnson | Conditioned preferences: Young children prefer flavors associated with high dietary fat[END_REF]. However, it has been shown that this innate ability decreases with age [START_REF] Fomon | Infant nutrition[END_REF][START_REF] Fox | Relationship between Portion Size and Energy Intake among Infants and Toddlers: Evidence of Self-Regulation[END_REF][START_REF] Taveras | Association of breastfeeding with maternal control of infant feeding at age 1 year[END_REF]. As foods become more easily available, children, even from an early age, are often faced with challenging situations where overeating may occur [START_REF] Fox | Relationship between Portion Size and Energy Intake among Infants and Toddlers: Evidence of Self-Regulation[END_REF][START_REF] Rolls | Serving portion size influences 5-year-old but not 3-year-old children's food intakes[END_REF][START_REF] Savage | Parental influence on eating behavior: Conception to adolescence[END_REF][START_REF] Taveras | Association of breastfeeding with maternal control of infant feeding at age 1 year[END_REF]. As children age, their ability to selfregulate their food intake becomes influenced by the external environment (Birch, Fischer & Davidson, 2003), for instance, by portion sizes [START_REF] Fisher | Portion size effects on daily energy intake in low-income Hispanic and African American children and their mothers[END_REF][START_REF] Fisher | Super-size me. Portion size effects on young children's eating[END_REF] or by parental control in feeding (Faith, Scanlon, Birch, Francis, & Sherry, 2004;Fisher & Birch, 1999;Frankel et al., 2016). These environmental influences could lead children to focus their attention on external cues rather than on internal cues to self-regulate their eating (Fisher & Birch, 1999). Children with poor self-regulation of eating are at an increased risk for developing obesity [START_REF] Francis | Self-regulation and rapid weight gain in children from age 3 to 12 years[END_REF]. The present study focused on the following two behaviors that are potentially related to overeating in that they have been shown to be linked with childhood adiposity: eating in the absence of hunger and eating compensation ability [START_REF] Kral | Caloric compensation and eating in the absence of hunger in 5-to 12-y-old weight-discordant siblings[END_REF]. Eating in the absence of hunger refers to a child's susceptibility to eating palatable foods even when satiated [START_REF] Shunk | Girls at risk for overweight at age 5 are at risk for dietary restraint, disinhibited overeating, weight concerns, and greater weight gain from 5 to 9 years[END_REF]Tanofsky-Kraff et al., 2008;[START_REF] Hughes | Satiety and the self-regulation of food take in children: A potential role for gene-environment interplay[END_REF]. Eating compensation refers to the ability to adjust food intake between successive eating occasions [START_REF] Birch | Caloric compensation and sensory specific satiety: evidence for self-regulation of food intake by young children[END_REF].

To date, there are limited data regarding eating in the absence of hunger and poor caloric compensation in young children, and most of the existing data are based on laboratory paradigms. In these laboratory settings, eating in the absence of hunger is measured directly by determining a child's actual ad libitum food intake after the child has consumed a meal and reports that he/she is full (Fisher & Birch, 2002;Hughes & Frazier-Wood, 2014). The caloric compensation ability is reflected by a decrease in food intake after having eaten a high energy preload compared to a low energy preload [START_REF] Birch | Caloric compensation and sensory specific satiety: evidence for self-regulation of food intake by young children[END_REF]Hughes and Frazier-Wood, 2014;[START_REF] Remy | Impact of adiposity, age, sex and maternal feeding practices on eating in the absence of hunger and caloric compensation in preschool children[END_REF]. These experimental paradigms cannot be used on very large samples, and their implementation in longitudinal studies is difficult. Thus, a validated questionnaire would be useful for assessing a child's susceptibility to self-regulation of eating (eating in the absence of hunger, eating compensation ability) in large-scale and/or longitudinal studies. Only a few readily available self-report questionnaires on eating in the absence of hunger in 8-to 12-year-old Anglophone children have been validated [START_REF] Madowitz | Concurrent and convergent validity of the eating in the absence of hunger questionnaire and behavioral paradigm in overweight children[END_REF]) and 14-year-old children (Tanofsky-Kraff et al., 2008). To the best of our knowledge, no questionnaire has been developed that assesses both eating in the absence of hunger and eating compensation ability in young children. However, the existing evidence indicates that eating behaviors are quite consistent from childhood to adolescence [START_REF] Madruga | Tracking of dietary patterns from childhood to adolescence[END_REF][START_REF] Nicklaus | Early origins of overeating: Tracking between early food habits and later eating patterns[END_REF], highlighting the need for validated tools that evaluate eating behaviors of children that may potentially be related to being overweight.

Previous cross-sectional studies using eating in the absence of hunger or caloric compensation paradigms have suggested that the ability to regulate food intake decreases with age; compared to younger children, older children ate more in the absence of hunger (see [START_REF] Lansigan | Understanding eating in the absence of hunger among young children: A systematic review of existing studies[END_REF] for a review) and showed poorer caloric compensation [START_REF] Birch | Caloric compensation and sensory specific satiety: evidence for self-regulation of food intake by young children[END_REF][START_REF] Cecil | Energy intakes of children after preloads: Adjustment, not compensation[END_REF][START_REF] Hetherington | Response to energy dilution in the short term: Evidence of nutritional wisdom in young children?[END_REF][START_REF] Zandstra | Short-term regulation of food intake in children, young adults and the elderly[END_REF]. [START_REF] Rolls | Serving portion size influences 5-year-old but not 3-year-old children's food intakes[END_REF] observed that a larger portion size induced a higher food intake in 5-year-old children but not in 3-year-old children, confirming the decrease in the ability of self-regulation that occurs with age. However, only a few studies have offered insight regarding the specific early age that the ability to regulate energy intake begins to decrease. [START_REF] Fox | Relationship between Portion Size and Energy Intake among Infants and Toddlers: Evidence of Self-Regulation[END_REF] reported the existence of a negative association between energy density and average portion size in 6-to 11-month-old children but not in toddlers; this suggests that the mechanisms that drive the self-regulation of eating are diminished in toddlers. Thus, it seems particularly important to explore both eating in the absence of hunger and eating compensation behaviors from this early age.

The ability to self-regulate tends to decrease as eating becomes affected more by external cues, such as palatability and portion size, and by parental influence (Faith, Scanlon, Birch, Francis, & Sherry, 2004;Fisher et al., 2007;Fisher & Birch, 1999;[START_REF] Fisher | Super-size me. Portion size effects on young children's eating[END_REF][START_REF] Fomon | Infant nutrition[END_REF][START_REF] Fox | Relationship between Portion Size and Energy Intake among Infants and Toddlers: Evidence of Self-Regulation[END_REF]Frankel et al., 2016;[START_REF] Taveras | Association of breastfeeding with maternal control of infant feeding at age 1 year[END_REF][START_REF] Wardle | Food and activity preferences in children of lean and obese parents[END_REF][START_REF] Wardle | Development of the children's eating behaviour questionnaire[END_REF]). The influence of parental feeding practices and styles on a child's eating behavior, intake and subsequent weight status has been demonstrated in many studies (see [START_REF] Ventura | Does parenting affect children's eating and weight status[END_REF], for a review). Some parental feeding practices, such as feeding when an infant is not hungry, seem to promote overeating in children by impairing an infant's response to his or her internal states of hunger and satiation (DiSantis, [START_REF] Disantis | The role of responsive feeding in overweight during infancy and toddlerhood: A systematic review[END_REF][START_REF] Shunk | Girls at risk for overweight at age 5 are at risk for dietary restraint, disinhibited overeating, weight concerns, and greater weight gain from 5 to 9 years[END_REF]Tanofsky-Kraff et al., 2008).

Thus, the ability to measure children's self-regulation of eating and related parental feeding practices outside of a laboratory setting is an important contribution. Using validated questionnaires, Frankel et al. (2016) examined the relationships between parental feeding styles as assessed by the Caregiver's Feeding Styles Questionnaire (CFSQ, Hugues, Power, Fisher, Mueller & Nicklas, 2005) and preschool children's self-regulatory abilities as assessed by the Child Eating Behavior Questionnaire (CEBQ, [START_REF] Wardle | Development of the children's eating behaviour questionnaire[END_REF]. This study involved low-income Hispanic and black parents and their children.

Interestingly, Frankel et al. found that indulgent feeding styles (feeding characterized by low levels of demandingness or expectations for children's food intake behaviors and high levels of responsiveness or the warmth and sensitivity of parents' reactions to children's cues of hunger/satiety) were associated with children's lower satiety responsiveness and higher food enjoyment. Satiety responsiveness refers to a child's sensitivity to and consumption in response to feelings of fullness and hunger, whereas enjoyment of food describes how a child is responsive to external food cues [START_REF] Carnell | Measuring behavioural susceptibility to obesity. Validation of the child eating behaviour questionnaire[END_REF][START_REF] Gustafson | Psychometric properties of a new questionnaire to assess eating in the absence of hunger in children and adolescents[END_REF]. These behaviors are components of the self-regulation of eating and have been shown to mediate the links between parental feeding styles and children's body mass index [START_REF] Carnell | Measuring behavioural susceptibility to obesity. Validation of the child eating behaviour questionnaire[END_REF][START_REF] Gustafson | Psychometric properties of a new questionnaire to assess eating in the absence of hunger in children and adolescents[END_REF].

Until now, the assessment of the relationships between parental feeding practices/styles and children's self-regulation of eating has been examined mainly with Anglo-Saxon samples and/or with low-income parents [START_REF] Carnell | Measuring behavioural susceptibility to obesity. Validation of the child eating behaviour questionnaire[END_REF][START_REF] Gustafson | Psychometric properties of a new questionnaire to assess eating in the absence of hunger in children and adolescents[END_REF][START_REF] Hodges | Development of the responsiveness to child feeding cues scale[END_REF]Hughes & Frazier-Wood, 2014;Johnson, 2000;[START_REF] Johnson | Conditioned preferences: Young children prefer flavors associated with high dietary fat[END_REF][START_REF] Musher-Eizenman | Comprehensive Feeding Practices Questionnaire: validation of a new measure of parental feeding practices[END_REF]. No questionnaire has been validated in France, despite the country's cultural specificities (Rozin, Fischler, Imada, Sarubin, & Wrzesniewshi, 1999;Rozin, Kurzer, & Cohen, 2002). According to these authors, French culture is more attached to food-pleasureoriented eating values than to food-health-oriented ones, in comparison to American cultures, for instance; this could, in turn, lead French parents to favor very different feeding practices than Anglo-Saxon parents, as shown by [START_REF] Schwartz | Complementary feeding and "donner les bases du goût" (providing the foundation of taste). A qualitative approach to understand weaning practices, attitudes and experiences by French mothers[END_REF]. These authors have shown that for French mothers, pleasure and taste development are considered of primary importance from infancy. They observed that for French mothers, complementary feeding lays the foundations of taste early in life. In this study, thematic analysis of transcribed focus groups and interviews revealed the perceived importance of flavor exposure and taste discovery in educating the palate of infants with a variety of different foods beyond mere nutrition.

The objective of the first part of the present study was to develop a self-report questionnaire suitable for French samples that assesses different dimensions of children's self-regulation of eating and related parental feeding practices. Given the importance of establishing healthy eating habits in early childhood [START_REF] Birch | Preventing childhood obesity: What works?[END_REF][START_REF] Kelder | Longitudinal tracking of adolescent smoking, physical activity, and food choice behaviors[END_REF], we focused on the period from 1 to 5 years of age. Our aim was to combine into the same instrument both behaviors involved in children's self-regulation of eating: eating in the absence of hunger, which may reflect responses to external cues, and eating compensation ability, which may reflect responses to internal cues [START_REF] Almiron-Roig | Factors that determine energy compensation: a systematic review of preload studies[END_REF][START_REF] Remy | Impact of adiposity, age, sex and maternal feeding practices on eating in the absence of hunger and caloric compensation in preschool children[END_REF]. The originality of our approach is that we based the development of our questionnaire on input from French parents' perceptions collected during interviews since French parents may have a very different approach to feeding than families in Anglo-Saxon households do.

The objective of the second part of our study was to validate the questionnaire and then to assess the relationships between children's self-regulation of eating and a broad range of behaviors that French parents may engage in when managing their child's eating regulation and the relationships between children's self-regulation and children's body mass index. We sought to identify which parental feeding practices could be considered effective or ineffective for French parents regarding children's self-regulation of eating. Moreover, we hypothesized a relationship between children's self-regulation of eating and children's body mass index.

General study design

The current study relies on two parts. In the first part, semi-structured interviews were conducted to create a self-report questionnaire suitable for French samples by assessing dimensions of children's self-regulation of eating and dimensions of related parental feeding practices. Then, input from parents and the literature on parental feeding practices were used to develop a new instrument that more adequately assessed parental perception of children's self-regulation of eating and parental feeding practices that parents may engage in when managing children's eating behaviors. An initial version of the parental self-report questionnaire was then constructed.

In the second part, this questionnaire was distributed to another sample of participants. The questionnaire was then validated, and the selected items were used to examine the links between parental feeding practices, children's self-regulation abilities and children's body mass index.

Written informed consent was obtained from both parents of all the children. The protocol was reviewed and approved by the local ethical committee, CPP Est I Burgundy (ID RCB: 2012-A00187-36). We certify that all the applicable institutional and governmental regulations concerning the ethical use of human volunteers were followed during this research study.

Part 1: Development and validation of the questionnaire

Methods

Participants

Forty-five French mothers of children aged from 12 to 60 months were recruited for the interviews (mean age mother = 33.50). Some mothers were unemployed (10.0%); low, intermediate and high occupational status represented 28.0%, 36.9% and 25.1%, respectively.

The mothers were all native French speakers.

Interviews

During the interviews conducted at home by a psychologist, the mothers were first asked to describe their child's eating behavior in terms of hunger and satiety cues and in terms of selfregulation. The very first question was 'How do you know whether your child is hungry or not hungry?' The second question was 'When is your child hungry/not hungry?' The third question was 'How do you react when your child says that s/he is hungry/not hungry?' Finally, the mothers were asked 'Do you think that your child is able to regulate/to compensate food intake? In which situations can the behavior of "caloric/energy compensation" be (or not be) observed? In other words, in which situations your child is able (or not able) to compensate food intake?'

To explore parental practices that could impede a child's self-regulation, the mothers were then asked, 'How do you manage your child when s/he says that s/he is still hungry-for instance, just after a meal?', 'How do you manage your child when s/he is hungry and has difficulty in waiting for eating?', and 'Do you use foods as a reward to regulate your child's mood?'

Analysis of the interviews

The analysis of the interviews relied on the analysis of the thematic content, which was conducted by three psychologists among the study investigators. Many descriptions spontaneously emerged from these interviews. These descriptions were first simply listed and then categorized into different thematic contents as follows.

Maternal perception of children's self-regulation of eating. Some mothers described their children as having poor self-regulation abilities in terms of eating compensation ('If my child has a snack just before mealtime, he eats as usual during mealtime, even if he had received a snack just before'). They also reported different situations in which their children would eat in the absence of hunger ('After a mealtime, if candies are available, he will eat some, even if I am sure that he is not hungry anymore').

Parental awareness of children's internal cues. It appeared that difficulties in coping with a child's hunger (or lack of hunger at a mealtime) were very common in the mothers ('My child has a big appetite!'). For some mothers, it was relatively difficult to know whether their children were hungry or not ('Well, it is not easy to know when my child is hungry. What is sure is that he always prefers to play than to eat!'). Other mothers seemed very aware of their children's cues, especially of hunger cues ('As soon as he becomes agitated, as soon as he

wriggles, I know what that means!').

Parental feeding practices used to manage children's self-regulation of eating. It is noteworthy that most of the mothers who reported that their children ate in the absence of hunger also described their use of food as a reward ('X is congratulated when she eats all the food in her plate'; 'I am so proud when the plate is clean!') and, to a lesser extent, their use of food for emotional regulation ('I sometimes give him a piece of bread or a candy for waiting').

The other types of situations spontaneously described by the mothers were linked to structuring feeding habits related to their organization of meal times ('The hours for meal times are very regular, even on the weekend') or to their feeding practices ('My child is allowed to snack between meal times'). For the mothers, these eating aspects (regularity of meal times and 'snacking') were evoked in association with a child's ability to compensate for his or her food intake ('It is easier to regulate behavior when the meal times are regular').

Item selection

The items of the dimensions that were included in the questionnaire were selected mainly from the following two sources: i) mother's accounts during the interviews; ii) evaluation of the existing validated questionnaires, since it appears that some spontaneous responses that were related to parental feeding practices were very similar to items of existing validated scales: the Comprehensive Feeding Practices Questionnaire (CFPQ, Musher & Holub, 2007) and the Infant Feeding Questionnaire (IFQ, [START_REF] Baughcum | Maternal feeding practices and beliefs and their relationships to overweight in early childhood[END_REF].

Results

An initial version of the questionnaire with 28 items was constructed. The selected items are summarized in Table 1, which describes the source of the selected items (from the mothers' interviews or from the existing validated scales) and the corresponding scale for each answer.

For the sake of clarity, only the 21 items from the dimensions retained for the structural equation modeling (see below) are presented in this Table .       Insert Table 1 about here Table 1. Twenty-one items of the self-report questionnaire were categorized by dimension

with their corresponding answer modalities and the source (interviews or existing scales).

Only items retained for the SEM analysis are reported. IFQ [START_REF] Baughcum | Maternal feeding practices and beliefs and their relationships to overweight in early childhood[END_REF]) During the weekend, do you make him/her eat at set times? 5-point scale ranging from "Never" to "Always" IFQ [START_REF] Baughcum | Maternal feeding practices and beliefs and their relationships to overweight in early childhood[END_REF] When my child is hungry before a meal time, I make him/her wait. Interview 1 The corresponding scores ranged from 1 (S/he does not want it) to 4 (S/he eats it up). 2 The corresponding scores ranged from 1 (S/he does not take any) to 4 (S/he takes a lot).

It should be noted that the items related to the dimension of eating in the absence of hunger ('After s/he has finished his meal, if candies are available and I let him/her…') could be closely related to the dimensions of the Child Eating Behavior Questionnaire (CEBQ, Wardle et al., 2001), especially the dimension of the enjoyment of food, which refers to how responsive a child is to external food cues [START_REF] Carnell | Measuring behavioural susceptibility to obesity. Validation of the child eating behaviour questionnaire[END_REF]Wardle et al., 2001), and the dimension of food responsiveness, which describes how responsive a child is to food and eating (Wardle et al., 2001). In the same vein, it should be noted that the items related to the dimension of children's eating compensation ability ('My child eats less at meal times when s/he has eaten something before the meals') are very close to those of the satiety responsiveness dimension of the CEBQ, since this dimension refers to a child's sensitivity to and consumption in response to hunger and fullness internal cues. These existing relevant scales were not used a priori in the current study because (i) we favored the mothers' verbatim responses to fully adapt the questionnaire to French participants and (ii) they concerned other age ranges that did not strictly correspond to the age group of children of the present study. The items that were spontaneously reported clearly evoked concrete and idiosyncratic situations that may be culturally determined, which may, in turn, allow participants to more fully engage while they complete the questionnaire.

Concerning the parental feeding practices, most of the items were selected from existing questionnaires, as reported in Table 1. The items that belong to the dimension 'parental awareness of child's cues' and those belonging to the dimension 'feeding on a schedule' were selected from the Infant Feeding Questionnaire [START_REF] Baughcum | Maternal feeding practices and beliefs and their relationships to overweight in early childhood[END_REF] because they mostly matched the mothers' verbatim responses. Three items from the dimension 'use of food as reward' were selected from the Comprehensive Feeding Practices Questionnaire [START_REF] Musher-Eizenman | Comprehensive Feeding Practices Questionnaire: validation of a new measure of parental feeding practices[END_REF], as they spontaneously emerged during the interviews with the mothers.

A new dimension entitled 'Snacking/eating flexibility' was constructed and included items from the interviews with the mothers. This dimension described situations in which the child was allowed to eat between the main meals ('At home, I allow my child to help him/herself to biscuits and sweets/chocolates'; 'When we are out for shopping, my child is allowed to have something to eat') and relied on concrete situations spontaneously described by the mothers.

Finally, two of the three items of the dimension 'emotional regulation' of the CFPQ questionnaire of Musher-Eizenman and Holub (2007) were selected ('Do you give this child something to eat or drink if s/he is bored even if you think s/he is not hungry?' 'Do you give this child something to eat or drink if s/he is upset even if you think s/he is not hungry?'), as they emerged, though to a lesser extent, during the interviews.

Participants

Parents of pupils in 6 daycare centers and in 7 kindergarten schools in Dijon and Paris were invited to participate in the study via leaflets. All parents who agreed to participate in the study were recruited. Parents of premature children (born before 37 weeks of gestation) were excluded from the analysis. A total of 932 questionnaires were distributed. Ultimately, 793 parents of pupils in the daycare centers (mean age mother=34.00 [min-max=22-46]; mean age father=35.92 [min-max=22-39]) and kindergarten schools (mean age mother=35.09 [min-max=23-46]; mean age father=37.50 [min-max=24-46]) participated in the study (response rate of 85%). The parents of the children aged approximately 1 to 3 years old were recruited from daycare centers (n=247), while the parents of children aged 3 to 6 years old were recruited from kindergartens (n=546) (see Table 2). [START_REF] Rolland-Cachera | Body Mass Index variations: centiles from birth to 87 years[END_REF].

Insert Table 2 about here

*** Within a line, means with the same letter were not significantly different (p>0.05).

Note. Level 1 corresponds to youth training, a BTEC First Diploma, a GNVQ Foundation, or no diploma.

Level 2 corresponds to A level or a high-school diploma/degree. Level 3 corresponds to a diploma of higher education or 12 th grade. Level 4 corresponds to a three-year university degree. Level 5 corresponds to a

Master's degree or a Master 2, and level 6 corresponds to higher than a Master 2 (PhD).

It should be noted that mothers with a low level of education were more represented in the kindergarten group than in the daycare centers (Chi² (5) = 035, p<0.001). This may be because the mothers with jobs used the daycare system for their children. In contrast, the number of years of education of the fathers was not significantly different between the daycare centers and the kindergartens (p = 0.49).

Questionnaire completion

The questionnaires were anonymous and took less than 10 minutes to complete. They were filled out at the participants' homes and were returned in sealed envelopes. Questions concerning the child's age and gender, the parent's age, and some demographic characteristics were asked. The parents were also asked for their children's heights and weights from weighing records measured by a pediatrician and reported in the 'health notebook'. The 'health notebook' is a very common tool in France that records health information for each child (height, weight, vaccination, diseases, growth, etc.). This tool has to be brought by the parents to each compulsory medical examination of their children so that the pediatrician can record the children's health information. From these data, the child's body mass index (BMI) was calculated (kg/m 2 ) and converted into a standardized z-score based on the French norms (Rolland-Cachera et al., 2002;[START_REF] Rolland-Cachera | Body Mass Index variations: centiles from birth to 87 years[END_REF].

Statistical Analysis

Confirmatory factor analysis (CFA): Validation of each dimension of the questionnaire

The questionnaire was validated using a structural equation modeling (SEM) approach [START_REF] Bollen | Structural equations with latent variables[END_REF][START_REF] Kaur | Confirmatory factor analysis of the child-feeding questionnaire among parents of adolescents[END_REF]. To validate the internal consistency of the questionnaire, a confirmatory factor analysis (CFA) was conducted in three steps. First, a measurement model was fitted for the dimensions linked to children's self-regulation of eating (eating in the absence of hunger and poor eating compensation); second, another measurement model was fitted for the dimensions related to parental feeding practices (use of food as reward, awareness of child's cues, feeding on a schedule, and snacking). Third, a measurement model was fitted for all dimensions together. In each measurement model, all constructs were allowed to correlate with each other. Finally, modification indices were considered to suggest fit improvement.

Structural equation modeling: Assessments of the links between parental feeding practices,

children's self-regulation abilities and children's BMI

To assess the structure between the dimensions related to parental feeding practices (use of food as reward, awareness of child's cues, feeding on a schedule, and snacking), the dimensions related to children's self-regulation of food intake (eating in the absence of hunger, and eating compensation ability) and child's BMI, a structural equation modeling analysis was conducted. First, the model defined by regression effects of the four dimensions related to parental feeding practices on the two dimensions related to child's self-regulation of eating (eating in the absence of hunger and eating compensation ability) was estimated. Then, non-significant regression links were removed. Finally, the child's BMI was added with regression links between the two dimensions related to the child's self-regulation of eating and the child's BMI.

All CFA and SEM analyses were conducted using the R package lavaan 0.5-23.1097 [START_REF] Rosseel | lavaan: An R Package for Structural Equation Modeling and more. Version 0.5-12 (BETA)[END_REF]. Missing data (< 7% for the items of the questionnaires; < 10% regarding child's BMI) were removed using a listwise deletion procedure. As a result, 557 observations of the original 793 remained for the estimation. All items except child's z-BMI were declared as ordered, and a diagonally weighted least squares estimator (DWLS) was used to estimate model parameters. Each model fit was assessed using the root mean square error of approximation (RMSEA), the comparative fit index (CFI) and the Tucker-Lewis Index (TLI).

The objective was to obtain a small RMSEA and high CFI and TLI indices. The usual cut-offs equal to 0.05 for RMSEA and 0.90 for CFI and TLI were considered guidelines, although it has been shown that such values are easily reached in the case of ordered items [START_REF] Xia | RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods[END_REF]. To the best of our knowledge, no cut-off has ever been proposed regarding fit indices when analyzing ordered categorical variables.

Results

Descriptive analysis.

A descriptive analysis was conducted to check the relevance and understanding of the items by the participants. Two points were raised. First, some items were almost never used by our participants. On average, 94% of the participants declared that they never use food to calm their child or used this practice rarely. For this reason, the two items related to emotional regulation practices were not included in the SEM analysis. Second, the analysis of the answers revealed that five items were not fully understood by the participants. It appeared that the wording was ambiguous or that the response modality was not suitable, leading to missing answers in a large proportion and/or to annotations, which led us to exclude these items. In particular, the excluded items were formulated as follows: "My child eats less when…", and the participants were invited to assess the probability of occurrence (from "never" to "always") of each proposal: "s/he is ill", "does not like the offered food", "eats something before a mealtime", "has eaten a lot during the previous meal", "is tired", "is angry". The instructions were not clearly understood, as some participants selected only one proposal from the list by circling it without specifying its frequency as expected, whereas other participants rated the frequency of each proposal. It appeared that the list of proposals intrinsically mixed activities that were too disparate to be fully understood by the participants. Therefore, these 1.

Confirmatory factor analysis (CFA): Validation of each dimension of the questionnaire

The items belonging to the child's self-regulation of food intake (eating in the absence of hunger and eating compensation ability) and to the dimensions related to parental feeding practices (use of food as reward, awareness of child's cues, feeding on a schedule, and snacking) were submitted to CFA analyses. The analysis performed on 21 items (Table 3) Insert Table 3 about here In the preliminary step, two models were considered, one for the child's self-regulation abilities and another for the parental feeding practices. In contrast, all dimensions were included in the same final model.

indicated
of eating (eating in the absence of hunger and poor eating compensation) was not significant (standardized estimate = -0.11, p = 0.06), suggesting that these two behaviors are distinct.

Structural equation modeling: Links between parental feeding practices, child's selfregulation of food intake and child's BMI

The model with all the parental constructs and the child's self-regulation constructs were evaluated in the same measurement model. The model showed a good fit (DWLS = 537, df = 193, p < 0.001, RMSEA = 0.057 [0.051,0.062]; CFI = 0.94; TLI = 0.93). For the sake of clarity, Figure 1 represents only significant regressions between latent variables. All regression and covariance parameters are reported in Table 4.

Insert Table 4 and Figure 1 about here As shown in Figure 1, the model showed a negative association between the parental awareness of the child's internal cues and the child's eating in the absence of hunger (standardized estimate = -.20; p = 0.02), meaning that the lower the awareness that parents declared about their children's internal cues, the more the children were perceived as being at risk of eating in the absence of hunger. This practice was also negatively associated with children's poor eating compensation ability (standardized estimate = -.17; p = 0.005), suggesting that the lower the awareness that they declared about their children's internal cues, the more the children were described as having poor compensation abilities. Moreover, a positive association between the use of food as reward dimension and children's eating in the absence of hunger was reported (standardized estimate = 0.31; p < 0.001); the more the parents used food in a non-eating context, the more the child was described as eating in the absence of hunger. Interestingly, significant positive relationships were observed between eating in the absence of hunger and children's z-BMI (standardized estimate = 0.17, p = 0.003) and between poor eating compensation and children's z-BMI (standardized estimate = 0.17, p < 0.001).

General discussion

The first aim of the present study was to examine the development and the initial validation of a new self-reported questionnaire for use in large-scale French studies to assess two children's behaviors involved in challenging eating situations (eating in the absence of hunger and poor eating compensation ability) and related feeding practices that are supposed to be used by parents while coping children's eating behaviors.

The results of the confirmatory factor analysis allow us to confirm the relevance of the child's constructs (eating in the absence of hunger and poor eating compensation ability) and the parental feeding practices' constructs (food as reward, parental awareness of child's cues, snaking, and feeding on a schedule) of the new self-report questionnaire. Concerning the child's constructs, the results validated the internal consistency of the two dimensions and confirmed that eating in the absence of hunger and poor eating compensation ability are two relatively independent behaviors, as shown in a study using experimental paradigms [START_REF] Remy | Impact of adiposity, age, sex and maternal feeding practices on eating in the absence of hunger and caloric compensation in preschool children[END_REF]. Thus, it could be argued that the eating in the absence scale offers insights regarding whether a child may initiate eating when not hungry, whereas the poor eating compensation scale offers insights regarding whether a child may adjust his/her intake during a meal depending on what s/he has eaten before the meal [START_REF] Hughes | Satiety and the self-regulation of food take in children: A potential role for gene-environment interplay[END_REF].

The present results suggested that eating in the absence of hunger and poor eating compensation ability reflect different alterations in self-regulation of eating that are already present in 1-5-year-old French children. The hypothesis that eating in the absence of hunger may reflect responses to external cues and eating compensation to internal cues could explain this non-significant link [START_REF] Almiron-Roig | Factors that determine energy compensation: a systematic review of preload studies[END_REF][START_REF] Remy | Impact of adiposity, age, sex and maternal feeding practices on eating in the absence of hunger and caloric compensation in preschool children[END_REF].

Concerning the parental constructs, the current study corroborated the use of different feeding practices by French parents, especially the use of food as reward (CFPQ, Musher & Holub, 2007), the parental awareness of children's cues and the dimension of feeding on a schedule (IFQ, Baughcum et al., 2001). Our study also offered an initial validation of a new subscale dedicated to snaking/flexibility in eating constructed from the mothers' verbatim responses obtained during the interviews.

The second aim of the current study was to assess i) the relationships between children's selfregulation of eating and parental feeding practices that parents may engage when managing their children's self-regulation of eating and ii) the relationships between children's selfregulation and children's body mass index. Using a structural equation modeling approach, our results revealed that the lower the awareness that parents declared about their children's internal cues, the more a child was perceived to be at risk of eating in the absence of hunger.

In the same vein, the lower the awareness that parents declared about their children's internal cues, the more a child is described as having poor eating compensation abilities. These relationships reinforced the hypothesis that caregiver feeding patterns that are unresponsive to child hunger and/or fullness cues may contribute to over intake by promoting eating in the absence of hunger or eating beyond fullness [START_REF] Costanzo | Domain specific parenting styles and their impact on the child's development of particular deviance. The example of obesity[END_REF][START_REF] Disantis | The role of responsive feeding in overweight during infancy and toddlerhood: A systematic review[END_REF][START_REF] Frankel | Parents' perceptions of preschool children's ability to regulate eating. Feeding style differences[END_REF][START_REF] Hodges | Development of the responsiveness to child feeding cues scale[END_REF]. The present results may suggest that a childcentered feeding approach that is responsive to the child's hunger and satiety cues is likely to respect the child's behaviors that are driven by internal biological cues or sensations when eating.

Moreover, a relationship between the use of food as reward and children's eating in the absence of hunger has been reported, suggesting that the more a parent uses food in a non-eating context, the more a child is described as eating in the absence of hunger. This association is consistent with previous data that has shown that the use of food as reward is associated with higher consumption of unhealthy foods in children [START_REF] Kröller | Maternal feeding strategies and child's food intake: Considering weight and demographic influences using structural equation modeling[END_REF][START_REF] Remy | Impact of adiposity, age, sex and maternal feeding practices on eating in the absence of hunger and caloric compensation in preschool children[END_REF]. A narrative review of the literature highlights the point that the effects of the use of food as reward could lead to mixed results, depending on the type of measured outcome (liking vs food refusal) and the initial level of liking of the food [START_REF] Cooke | Facilitating or undermining? The effect of reward on food acceptance: A narrative review[END_REF]. The authors pointed out that in some conditions, non-food rewards (e.g., stickers, praise) can be highly effective in encouraging children to taste new or less-liked foods to benefit from the 'mere exposure' effect. The beneficial effect of receiving a reward upon acceptance of a disliked vegetable, over and above the effect of mere exposure alone, has also been described with no evidence of any decrease in acceptance, either in the short term or up to three months after rewards were withdrawn (Cooke et al., 2011b).

However, there seems to be a consensus on the fact that offering food as a reward appeared to be universally ineffective (Cooke et al., 2011a). In the current study, the items of the dimension of use of food as reward clearly referred to situations in which parents offered food as a reward in exchange for good behavior. Thus, the relationships between this instrumental practice and children's eating in the absence of hunger clearly supported previous literature on the negative impact of instrumental feeding, such as using food as reward [START_REF] Birch | Effects of instrumental consumption on children's food preference[END_REF][START_REF] Birch | Eating as the means activity in a contingency. Effects on young children's food preference[END_REF][START_REF] Newman | Effect of a means-end contingency on young children's food preferences[END_REF][START_REF] Rigal | Links between maternal feeding practices and children's eating difficulties. Validation of French tools[END_REF] or using food to soothe infants or toddlers [START_REF] Stifter | Parent use of food to soothe infant/toddler distress and child weight status. An exploratory study[END_REF][START_REF] Stifter | Understanding and measuring parent use of food to soothe infant and toddler distress: A longitudinal study from 6 to 18 months of age[END_REF].

Finally, no relationship was reported between feeding on a schedule and children's selfregulation of eating. One could argue that this structuring habit may be effective, since the regularity of meal times could help children attend to internal, biologically driven cues or sensations of hunger between meal times. Previous studies have shown that an increased frequency of family meals was associated with healthier consumption [START_REF] Davis | Recommendations for Prevention of Childhood Obesity[END_REF].

The present results failed to demonstrate that the regularity of meal times could favor a child's developmental regulation of food intake. Similarly, no relationship was reported between snacking and children's self-regulation of eating. Further studies are needed to fully understand the potential role of this factor on children's eating self-regulation.

Interestingly, both significant positive relationships were observed between eating in the absence of hunger and the child's body mass index and between poor eating compensation ability and the child's body mass index. These results suggest that these two constructs reflect children's difficulties in self-regulation of eating, which could lead to over-consumption with adverse impacts on children's body mass index. These results are very close to those of the literature on children's emotional and external eating. It has been shown that higher emotional and external eating behaviors lead to over-eating in response to emotions or food-related stimuli, regardless of the internal states of hunger and satiety, in overweight rather than in normal-weight children or adolescents [START_REF] Braet | Differences in eating style between overweight and normal-weight youngsters[END_REF][START_REF] Braet | Assessment of emotional, externally induced and restrained eating behaviour in nine to twelve-year-old obese and non-obese children[END_REF][START_REF] Kral | Caloric compensation and eating in the absence of hunger in 5-to 12-y-old weight-discordant siblings[END_REF][START_REF] Webber | Associations between child weight and maternal feeding styles are mediated by maternal perceptions and concerns[END_REF]. Thus, the observed relationships between children's eating in the absence of hunger/poor eating compensation ability and children's body mass index confirmed previous findings and reinforced the relevance of the model. It can be concluded that an impaired ability to regulate short-term food intake may represent a behavior for being at risk of being overweight in young children. The fact that relationships have been found between parental feeding practices and children's selfregulation abilities and between children's self-regulation abilities and children's body mass index could offer initial evidence of the validity of the questionnaire.

Strengths and limits

Even if it is not possible, strictly speaking, to validate a questionnaire in a single study, the current research was undertaken to provide initial evidence of the validity of a new instrument dedicated to children's self-regulation of eating and related parental feeding practices in French parents of 1-5-year-old children. The advantage of the self-report questionnaire, in comparison with the other experimental protocols that are commonly conducted to assess selfregulation in young children, is that it can be used easily in large-scale studies. Moreover, for the assessment of the a child's eating compensation ability and eating in the absence of hunger, one could argue that an approach based on a questionnaire may be more relevant than a laboratory setting, since it allows the parent to take into account not only the adjustment of intake during one meal (i.e., short-term compensation), as in the experimental settings, but also the pattern over a time period that is longer than just one meal. The present study suggested that the parents were aware of their children's regulation abilities. One limit of this declarative approach, however, could be the effect of social desirability. In previous studies, it has been shown that the parents' perception of feeding practices can be influenced by their own dietary restraints, their perceptions of their children's risk of being overweight [START_REF] Birch | Mothers' child-feeding practices influence daughters' eating and weight[END_REF], their own weight history (Saelens et al., 2000), and their concern for their children's weight [START_REF] Gray | Factors associated with parental use of restrictive feeding practices to control their children's food intake[END_REF]. A limitation of our study is that no information on breast-feeding and formula-fed practices has been collected, despite the documented differences in self-regulation among breast and formula-fed infants.

Further investigations that include this information are needed. Another limitation may be linked to the use of cross-sectional data, which impede speculation on the directionality and dynamic of the reported effects. It seems that similar caution is warranted here since parental assessments of eating in the absence of hunger and eating compensation may also be responsive to/stem from child weight. Even if the current study did not validate the instrument against the gold-standard laboratory studies already in use, it offered an initial validation of a questionnaire based on both a qualitative analysis of the mothers' verbatim responses that emerged from the interviews and a structural equation modeling approach used to confirm the different parental and child's constructs. Contrary to previous studies that targeted lowincome parents (for instance, see [START_REF] Frankel | Parents' perceptions of preschool children's ability to regulate eating. Feeding style differences[END_REF], the present research involved a quite large sample of French parents from different socio-economic statuses, as observed in previous French studies (see, for instance, [START_REF] Rigal | Links between maternal feeding practices and children's eating difficulties. Validation of French tools[END_REF]. This allowed us to identify deleterious feeding practices regarding children's self-regulation of food intake and a significant relationship between children's self-regulation of eating and children's body mass index, even if the study did not exclusively target families with disadvantaged socioeconomic statuses.

Conclusions and perspectives

It appears that eating in the absence of hunger and poor eating compensation ability are two relatively independent behaviors that are linked to children's body mass index and that are impacted by different parental factors. What can be concluded from this study? The more parents use food as reward, the more their children are perceived as being at risk of eating in the absence of hunger (which makes it an ineffective practice). The more parents pay attention to their children's hunger and satiety cues, the less their children are perceived as being at risk of eating in the absence of hunger, and the less they are perceived as being unable to selfregulate food intake (effective practices). More research is needed to understand the complex motivations underlying these parental behaviors so that appropriate interventions can be developed and to take into account this particular developmental period (ages 1-5), given the stark differences in fine and gross motor skill capacities (grasping, gripping, pincer-grip, etc.), nutritional needs/norms, and daily routines. Addressing these questions is especially challenging because attention to these cues can help children focus on internal signals, which

  good fit indices (DWLS = 487, df = 173, p < 0.001, RMSEA = 0.054 [0.049-0.060]; CFI = 0.95; TLI = 0.94).

Figure 1 .

 1 Figure 1. Structural model for the association between the parental constructs, the child's self-

Selected items and related dimensions Answer modality Sources Child's self-regulation abilities dimensions Eating in the absence of hunger

	If my child is no longer hungry and I offer him	S/he does not want it (1)	Interviews
	something s/he particularly likes… (Tick your	S/he asks if he can have it later
	answer)					S/he eats a few bites, just to taste it
						S/he eats it up
	After s/he has finished his meal, if candies are	S/he does not take any (2)	Interviews
	available and I let him/her… (Tick your answer)	S/he takes them in order to have them
						later
						S/he takes one or two just to taste
						them
						S/he takes a lot
	Poor eating compensation ability
	My child eats less at meal times when s/he has eaten	5-point scale ranging from "Never" to	Interviews
	something before the meals.			"Always"
	My child gets full before his/her meal is finished.	5-point scale	Interviews
	My child eats less at meal times when s/he has been	5-point scale	Interviews
	at a birthday party or snacked at a friend's house.
	If my child eats, let us say, a bun or a muffin, one	S/he is not hungry when it is time for	Interviews
	hour before the meal… (Tick your answer)		the meal (3)
						S/he is hungry when it is time for the
						meal but eats less than usual
						S/he eats as s/he usually eats
	Parental feeding practices dimensions
	Food as reward
	I offer sweets (candy, ice cream, cake, pastries) to my		CFPQ (Musher &
	child as a reward for good behavior.			Holub, 2007)
	I offer my child her/his favorite food in exchange for	5-point scale ranging from "Never" to	CFPQ (Musher &
	good behavior.				"Always"	Holub, 2007)
	I withhold sweets/dessert from my child in response		CFPQ (Musher &
	to bad behavior.					Holub, 2007)
	Parental awareness of child's cues
	I know when my child is hungry.				IFQ (Baughcum et
							al., 2001)
	I know when my child is full.			5-point scale ranging from "Never" to	IFQ (Baughcum et
						"Always"	al., 2001)
	I know when my child is not hungry during meal		IFQ (Baughcum et
	times.						al., 2001)
	Snacking/flexibility in eating
	At home, I allow my child to help him/herself to		Interviews
	biscuits and sweets/chocolates.
	When we are out shopping, my child is allowed to		Interviews
	have something to eat.
	After	being	physically	active	(walking,	5-point scale ranging from "Never" to	Interviews
	swimming…), my child has something to eat.	"Always"
	If my child is hungry, I allow him/her to eat.			Interviews
	My child has a snack between meals.			Interviews
	My child eats between meals.				Interviews
	Feeding on a schedule
	During the week, do you make him/her eat at set
	times?

Table 2 .

 2 Characteristics of the participants who completed the questionnaire.

	Daycare centers	Kindergartens

* Chi-squared test revealed that the distributions of the girls and boys in the daycare centers and in the kindergartens were not different (Chi ² (1) = 0.54, p = 0.45) ** Z-score of BMI based on French norms

Table 3 :

 3 CFA models with factor loadings

	Selected items and related dimensions	mean	Preliminary	Std.	Final	Std.
		(SD)	loading 3	error	loading 3	error
	Child's

self-regulation abilities dimensions Eating in the absence of hunger 1

		2.43	∝= .
		(0.79)
	If my child is no longer hungry and I offer him/her something s/he	2.47	0.36	0.30	0.47	0.07
	particularly likes. (Tick your answer)	(1)
	After s/he has finished his meal, if candies are available and I let	2.39	1.08	0.91	0.83	0.11
	him/her… (Tick your answer)	(0.96)
	My child eats less at meal times when s/he has eaten something				0.15	0.06
	before the meals. 2
	Poor eating compensation ability 1	3.15	∝= .
		(0.70)
	My child eats less at mealtimes when s/he has eaten something	2.23	0.51	0.04	0.49	0.04
	before the meals. 2	(0.62)
	R My child gets full before his/her meal is finished.	3.32	0.83	0.02	0.82	0.02
		(1.02)
	R My child eats less at meal times when s/he has been at a birthday	3.70	0.71	0.03	0.70	0.03
	party or snacked at a friend's house.	(0.95)
	If my child eats, let us say, a bun or a muffin, one hour before the	3.36	0.74	0.02	0.76	0.02
	meal… (Tick your answer)	(1.10)
	Parental feeding practices dimensions
	Food as reward	1.83	∝= .
		(0.79)
	I offer sweets (candy, ice cream, cake, pastries) to my child as a	1.81	0.89	0.03	0.88	0.03
	reward for good behavior.	(0.94)
	I offer my child her/his favorite food in exchange for good	1.74	0.71	0.03	0.71	0.03
	behavior.	(0.91)
	I withhold sweets/dessert from my child in response to bad	1.94	0.61	0.04	0.62	0.04
	behavior.	(1.16)
	Parental awareness of child's cues	3.97	∝= .54
		(0.58)
	I know when my child is hungry.	4.11	0.56	0.04	0.50	0.04
		(0.79)
	I know when my child is full.	4.09	0.65	0.04	0.62	0.04
		(0.76)
	I know when my child is not hungry during meal times.	3.70	0.64	0.04	0.70	0.05
		(0.87)
	Snacking/flexibility in eating	2.24	∝= .
		(0.62)
	At home, I allow my child to help him/herself to biscuits and	2.37	0.75	0.02	0.74	0.03
	sweets/chocolates.	(0.91)
	When we are out for shopping, my child is allowed to have	1.39	0.58	0.04	0.52	0.05
	something to eat.	(0.75)
	After being physically active (walking, swimming…), my child has	2.27	0.54	0.03	0.53	0.04
	something to eat.	(1.20)
	If my child is hungry, I allow him/her to eat.	2.26	0.74	0.03	0.73	0.03
		(0.91)
	My child has a snack between meals.	2.65	0.50	0.03	0.47	0.04
		(1.17)
	My child eats between meals.	2.49	0.48	0.04	0.48	0.04
		(0.99)
	Feeding on a schedule	4.20	∝= .48
		(0.55)
	During the week, do you make him/her eat at set times?	4.64	0.90	0.05	0.96	0.05
		(0.58)
	During the weekend, do you make him/her eat at set times?	4.19	0.69	0.04	0.66	0.04
		(0.78)
	When my child is hungry before a meal time, I make him/her wait.	3.77	0.41	0.04	0.39	0.05
		(0.95)

Table 4 :

 4 SEM model: parameter estimates, standard errors, p values and standardized estimates (i.e., completely standardized solutions) for regression parameters, and correlations between dimensions

	Structural regression coefficients	Estimate	Std. err	P value	Std. estimate
	Poor eating compensation ability
	Snacking/flexibility in eating	-0.12	0.07	0.077	-0.12
	Feeding on a schedule	-0.09	0.06	0.156	-0.09
	Food as reward	-0.11	0.06	0.054	-0.10
	Parental awareness of child's cues	-0.18	0.06	0.005	-0.17
	Eating in the absence of hunger
	Snacking/flexibility in eating	-0.02	0.09	0.866	-0.01
	Feeding on a schedule	0.03	0.09	0.739	0.03
	Food as reward	0.34	0.08	0.000	0.31
	Parental awareness of child's cues	-0.22	0.09	0.016	-0.20
	z-BMI
	Poor eating compensation ability	0.22	0.06	0.000	0.17
	Eating in the absence of hunger	0.21	0.07	0.003	0.17
	Latent variable correlations
		Food as reward	Parental awareness of child's cues	Snacking/ flexibility in eating	Feeding on a schedule
	Food as reward
	Parental awareness of child's cues	-0.09
	Snacking/flexibility in eating	0.26	0.17
	Feeding on a schedule	-0.16	0.18	-0.41

The corresponding scores ranged from 1 (S/he is not hungry when it is time for the meal) to 3 (S/he eats as s/he usually does).

For the child's eating in the absence of hunger dimension and for the poor eating compensation ability, the higher the score is, the less the child is able to self-regulate food intake.

This item loaded mainly on the construct 'Poor eating compensation ability' but also on the construct 'Eating in the absence of hunger'. This modification, which makes sense, was suggested by the modification indices and improved the model fit.

Loading and standardized loadings are equal. All the items have a p-value < 0.001 except the item 'My child eats less at meal times when s/he has eaten something before the meals', the p-value of which is 0.007.

The research leading to these results received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under the grant agreement n°245012-HabEat