Data for this study come from the Québec Longitudinal Study of Child Development (QLSCD) study, which follows a representative cohort of 2120 children born in the Canadian province of Québec in 1997–1998. To ensure geographic representation and minimize the effect of seasonality, participants were chosen through a random selection of children born throughout the year in each public health geographic area of the province. Twins and children with major diseases or handicaps at birth were excluded from the cohort. Selected children were first seen at 5 months of age and then once each year thereafter (follow-up assessments were conducted at 1½, 2½, 3½, 4½, 5, 6 and 8 years). Data on children and their parents were collected by trained interviewers through home interviews regularly conducted with the person most knowledgeable about the child (the mother in 98% of cases). Participating families gave written informed consent for the study at each assessment. The survey protocol was approved by the Quebec Institute of Statistics (Quebec City, Quebec, Canada) and the St-Justine Hospital Research Center (Montreal, Quebec, Canada) ethics committees. Informed consent for the study was obtained from parents or legal guardians.
The average response rate during the 8 years of data collection was 87.0% (range, 68%–100%) 
. The present analysis is based on 1682 children with available data on food insecurity as well as at least 2 measures of mental health symptoms. Compared to the original cohort, nonparticipants were more likely to be from families that were characterized by low income, low education, immigrant background, young maternal age, single-parenthood and maternal depression, but participants and nonparticipants did not differ with regard to children’s mental health symptoms.
Food insecurity was ascertained when the participating child was 1½ and 4½ years old. On those two occasions, mothers were asked: a) whether family members had eaten less than they should have because they had run out of food or money to buy food (1½ and 4½ years), b) whether family members had eaten the same foods several times because they did not have anything else and could not afford to buy other foods (4½ years only), c) whether the family could not afford to offer nutritious meals to the children (4½ years only), d) how often family members did not eat as much as they should have because they had run out of food or money to buy food (4½ years). These measures of food insecurity were previously shown to predict children’s overweight and obesity 
. Children whose families experienced any of these situations were considered to be exposed to food insecurity: (3.4% of the study population at age 1½ year, 3.6% at age 4½ years, 5.9% at 1½ or 4½ years of age).
Children’s Mental Health
Children’s mental health was assessed at 4½, 5, 6 and 8 years based on parental reports. Symptoms of depression/anxiety were assessed using 5 items adapted from the Preschool Behavior Questionnaire 
and the Child Behavioral Checklist 
: ‘nervous, high strung or tense’, ‘fearful or anxious’, ‘worried’, ‘not as happy as other children’, ‘has difficulty having fun’ 
. Symptoms of aggression were assessed using 5 items previously validated in this study: ‘hits’, ‘kicks’, ‘bites’, ‘fights’, ‘bullies others’ 
. Symptoms of hyperactivity-impulsivity and inattention were assessed through a combination of items from the Child Behavior Checklist 
, the Ontario Child Health Study Scales 
and the Preschool Behavior Questionnaire 
. Hyperactivity-impulsivity was assessed using 5 items: ‘can’t sit still, is restless’, ‘fidgets’, ‘can’t settle down to do anything for more than a few moments’, ‘is impulsive, acts without thinking’, ‘has difficulty waiting for turn in games’ 
. Inattention was assessed using 3 items: “can't concentrate, can't pay attention for long”, “is easily distracted, has trouble sticking to any activity”, “is inattentive”. All items pertaining to children’s mental health symptoms were scored 0 (‘never’), 1 (‘sometimes’) or 2 (‘often’) and then summed to range 0–10 
Based on the four measures of children’s psychological symptoms between ages 4½ and 8 years which were available to us, we used semiparametric mixture models 
to calculate longitudinal symptom trajectories. This approach makes it possible to identify groups with distinct longitudinal symptom patterns empirically rather than using a set cut off. As such, this method provides a description of the ‘natural’ course of the evolution of mental health symptoms over time. Additionally, the reliance on multiple measures of symptoms as well as the grouping of children according to a trajectory pattern reduces the measurement in error related to a single assessment 
. For each symptom group, the model implemented using the PROC TRAJ procedure in SAS defined the shape of the trajectory and the proportion of participants in each group. The validity of the ‘best fitting” classification was confirmed using the Bayesian Information Criterion (BIC). Overall, we identified 3 groups of symptoms of depression/anxiety (low: 19.2%, moderate: 59.8%, high: 21.0%), 3 groups of symptoms of aggression (low: 23.8%, moderate/declining: 50.1%, high: 26.2%), and 4 groups of symptoms of hyperactivity/inattention, (low: 20.9%, low/intermediate: 38.3%, intermediate: 34.8%, high: 6.0%). Children’s symptoms were moderately correlated to one another (correlation coefficients at age 8 years: depression/anxiety and aggression: 0.16, p<0.0001; depression/anxiety and hyperactivity/inattention: 0.31, p<0.0001; aggression and hyperactivity/inattention: 0.32, p<0.0001).
Analyses were adjusted for the characteristics of children and their families, which can be associated with food insecurity and children’s mental health symptoms 
. Covariates were measured at age 5 months (prenatal tobacco exposure, maternal and paternal depressive symptoms and family functioning) or concomitantly to food insecurity. Demographics included the child’s sex (male vs. female), immigrant status (immigrant vs. non-immigrant), family structure (parents separated vs. two-parent family) and maternal age at child’s birth (<21 vs. >
21 years). Family income was calculated according to guidelines issued by Statistics Canada, taking into account the number of people in the household and the type of residence area (urban vs. rural based on population density); family income was coded as insufficient vs. sufficient. Maternal and paternal education was defined as <High school vs. >
High school. Prenatal tobacco exposure was defined as maternal consumption of >
1 cigarette/day (yes vs. no). Maternal and paternal depressive symptoms were assessed by the abbreviated version (12 items) of the Center for Epidemiologic.
Studies Depression (CESD) Scale 
. Parents reported the frequency of depressive symptoms in the previous week. Each item was coded on a 4-point scale. Total informant ratings were z-standardized. Family dysfunction was assessed with the McMaster Family Assessment, which includes 12 items measuring communication, showing and receiving affection, control of disruptive behaviour, and problem resolution in the family; each item was coded 0 (‘never’), 1 (‘sometimes’), or 2 (‘often’) and the overall score was z
. Negative parenting was assessed using the Parental Cognition and Conduct Toward the Infant Scale, which includes dimensions such as coercitive parenting (7 items) and overprotection (5 items), each rated on a scale ranging 0 to 10; overall scores were z-standardized 
To study the association between food insecurity and children’s mental health outcomes, we combined exposure to food insecurity when children were 1½ and 4½ years of age (ever food-insecure vs. never food-insecure) and tested associations with children’s probability of being on a ‘high’ behavioural trajectory group at ages 4½ to 8 years. First, we tested sex-adjusted associations, in order to account for sex-related differences in the prevalence of mental health symptoms in children. Second, we adjusted for covariates. In additional analyses we tested whether the association between food insecurity and long-term behavioural problems 1) was robust to statistical adjustment on behavioural problems prior to age 4½; 2) differed depending on the child’s sex. Analyses were carried out in a logistic regression framework in SAS (V9).