Housework Time from Middle Childhood through Adolescence: Links to Parental Work Hours and Youth Adjustment

Abstract

The developmental course, family correlates, and adjustment implications of youth housework participation from age 8–18 were examined. Mothers, fathers, and two siblings from 201 European American families provided questionnaire and/or daily diary data on six occasions across 7 years. Multilevel modeling within an accelerated longitudinal design revealed that girls spent more time on housework than did boys but that housework time of both girls and boys increased from middle childhood to mid-adolescence and leveled off thereafter. In years when mothers were employed for more hours than usual, girls, but not boys, spent more time on housework than usual. Housework time was linked to more depressive symptoms (at a between-person level) and predicted lower school grades (at a within-person level) for youth with low familism values. Housework time also predicted more depressive symptoms (at a within-person level) for youth with high parent-youth conflict about housework. Findings highlight the gendered nature of housework allocation and the importance of considering both individual and contextual factors when examining youth daily activities.

Housework is a daily activity for many youth in the U.S. (Raley, 2006). Youth are assigned household duties to build responsibility and self-reliance (Goodnow, 1988), but for many parents, such demands as labor force involvement mean that youth’s housework is critical to household maintenance and family well-being (Burton, 2007). Although studies have examined the development and correlates of youth housework participation, gaps remain in our understanding: There are few long-term longitudinal data on housework and its links to changing family demands. Findings on the adjustment implications of housework are also mixed.

Grounded in an ecological perspective that daily activities are both reflections of and influences on youth development (Bronfenbrenner & Crouter, 1983), this study explored the developmental course, family correlates, and adjustment implications of housework participation. Our first goal was threefold: to chart the development of youth housework time from middle childhood through adolescence, to examine whether parental work hours were linked to youth housework time, and to assess the role of youth gender in these processes. Our second goal was to test whether housework time predicted youth adjustment and whether youth familism values and parent-child conflict about housework moderated these links. We took advantage of a long-term longitudinal study, wherein six waves of data were collected from mothers, fathers, and firstborns and secondborns in a sample of predominantly European American, married-couple, dual-earner families. Though homogeneous in terms of ethnic composition and family structure, the sample provided detailed, repeated, multimodal measurement on numerous constructs, allowing us to extend prior work by focusing on longitudinal changes and within-person variation (Curran & Bauer, 2011). The accelerated longitudinal design, wherein two different-aged cohorts of youth (firstborns and secondborns) were repeatedly measured, further allowed us to capture a broad swath of development within a comparatively short period of time and increase our power to detect subtle, within-person associations (Duncan, Duncan, Hip, 1996).

Changes in Housework Time: The Roles of Youth Gender and Parental Work Hours

An ecological perspective highlights the roles of both individual and contextual factors in shaping youth daily activities (Bronfenbrenner & Crouter, 1983). For instance, although youth in middle-class, married-couple, dual-earner families typically perform only a small percentage of the overall housework (Ochs & Izquierdo, 2009), with age, youth contributions may increase in response to changing parental expectations (Goodnow, 1988). Corroborating studies documented cross-sectional age differences in housework participation, with adolescents devoting more time compared to preadolescents (Gager, Sanchez, & DeMaris, 2009; Raley, 2006). However, from mid to late adolescence, other activities, particularly peer engagement and paid work (Larson & Verma, 1999), may reduce youth’s availability for housework. Indeed, one longitudinal study showed decreases in youth participation in housework between grades 9 and 12 (Gager, Conney, & Call, 1999). Guided by prior work, we hypothesized that housework time would increase across childhood, peak in early adolescence, and decline thereafter.

Trajectories of housework time may differ for girls and boys. Many household tasks, such as cooking and cleaning, are seen as “women’s work” and “training for girls” (Bowes & Goodnow, 1996). In fact, children as young as five express gender-stereotypical ideas about housework (Schuette & Killen, 2009). Across the life course, women and girls also perform more housework than do men and boys (Lachance-Grzela & Bouchard, 2010). A gender intensification hypothesis predicts that societal pressures to conform to traditional gender roles increase across adolescence (Galambos, Almeida, & Petersen, 1990). As girls and boys mature, there may be larger gender disparities in housework. Few longitudinal studies have explored changes in housework across adolescence, but one cross-sectional study (Hilbrecht, Zuzanek, & Mannell, 2008) and one short-term longitudinal study (Gager et al., 1999) suggested that gender differences in housework participation increased with age. Therefore, we hypothesized that gender disparities in youth’s housework involvement would be more pronounced over time.

Youth housework time may also depend on contextual factors, such as parental employment conditions. Given the “feminine” nature of many household tasks (Bowes & Goodnow, 1996), when mothers experience heavy work demands, additional tasks may be allocated to daughters. Indeed, housework disparities favoring girls are largest in families with mothers who work full time and have heavy workloads (Crouter, Head, Bumpus, & McHale, 2001; Manke, Seery, Crouter, & McHale, 1994). Most prior research has examined between-person variation, however, and associations on this level may be caused by stable confounding factors that are not controlled in the analyses (Curran & Bauer, 2011). An exception was a study by Tsai, Telzer, Gonzales, and Fuligni (2013), which showed that, on days when mothers experienced more fatigue than usual (compared to their own cross-day averages), their younger sons were more likely to perform housework, perhaps because they were typically least likely to help and had more opportunities to increase their participation. Tsai et al. used a dichotomous measure (i.e., did or did not perform housework on a particular day), which might not have been sensitive enough to detect within-person variation in daughters’ generally high involvement in housework. A finer-grained measure (in our case, time spent on specific household tasks) may further illuminate how parents’ work hours matter for daughters’ and sons’ participation. Thus, we hypothesized that within-person variation in mothers’ work hours would be positively linked to within-person variation in daughters’, but not sons’, housework time.

Adjustment Implications of Housework Time: The Roles of Familism Values and Conflict

An ecological perspective also conceptualizes daily activities as influences on youth development (Bronfenbrenner & Crouter, 1983). For instance, Telzer and Fuligni (2009a) showed that, on days when adolescents performed more housework than usual, they reported happier feelings than usual, supporting the idea that housework, as a form of contribution to the family, may provide youth with a sense of purpose. However, in another study, Telzer and Fuligni (2009b) found that, in years when Chinese and Mexican American adolescents spent more days helping out with housework than usual, they had lower school grades than usual, suggesting that some youth may have difficulty balancing family and school responsibilities. More generally, these findings indicated that housework can have both positive and negative implications: Research on moderators is needed to explain discrepant findings.

In this study, we examined familism values, that is, individual beliefs regarding family support, cohesion, and obligations (Fuligni, Tseng, & Lam, 1999), as a potential moderator. Familism is rooted in Hispanic cultural heritage, but research indicates that, although the average levels of familism values are higher in ethnic minorities than in European Americans, the measurement properties of this construct are equivalent across ethnic groups, supporting its applicability in diverse populations in the U.S. (Schwartz, 2007). Studying an ethnically diverse sample, Telzer and Fuligni (2009a) hypothesized that adolescents who did not value family obligations but had heavy household responsibilities would experience attitude-behavior incongruence and exhibit maladjustment. Their findings, however, revealed that familism values explained little variability in the links between assistance with household tasks (including cooking and cleaning, running errands, and assisting parents at their work) and daily feelings of happiness. In contrast, East and Weisner (1990) concluded that familism values may exacerbate the detrimental impact of more demanding kinds of tasks, based on the findings that the longitudinal link between caring for their sisters’ infants and maladjustment was stronger for Mexican American youth with higher familism values. In this study, we assessed youth’s time spent on four stereotypically feminine tasks (cooking, doing dishes, doing laundry, and cleaning the house) and a self-care task (cleaning their own rooms), because these tasks are some of the most frequent tasks that youth undertake (Bowes & Goodnow, 1996; Telzer & Fuligni, 2009a) and often need to be done on a daily basis (Coltrane, 2000). Focusing on this subset of tasks, we tested the hypothesis that housework time would predict maladjustment, as indexed by more depressive symptoms and lower school grades, especially for youth with low familism values. Parent-child conflict about housework also may moderate the effect of housework participation. According to Goodnow and Lawrence (2001), the implications of housework may depend on the style in which youth’s contributions are made (whether the tasks are voluntary or mandatory) and the degree of consensus (whether family members share the same views about who should do what).

Parent-child conflict about housework may reflect youth’s resistance to undertaking tasks and/or a lack of consensus about how assignments should be distributed. Few studies have formally tested parent-child conflict as a moderator. Yet, Grusec, Goodnow, and Cohen (1996) found that voluntary, but not mandatory, involvement in housework was positively linked to prosocial behaviors. Further, using ethnographic methods, Ochs and colleagues showed that disagreements about housework allocations, rather than actual amounts of housework, constituted the source of most family stress (Ochs & Kremer-Sadlik, 2013; Ochs & Izquierdo, 2009). In this study, we conceptualized conflict about housework as a proxy for the voluntary/consensual nature of youth housework participation and hypothesized that housework time would predict more depressive symptoms and lower school grades, especially for youth who had frequent conflict with their parents.

The Current Study

In sum, this study contrasted the trajectories of girls’ versus boys’ housework time, tested whether youth’s housework time fluctuated in response to parents’ work hours, and explored the moderating roles of familism values and parent-child conflict. Given their links to youth housework participation, we controlled for youth birth order, parental education, and family size in all analyses (Lachance-Grzela & Bouchard, 2010; Raley, 2006).

Method

Participants

Data came from a longitudinal study of family relationships. We used waves including either the predictor or the outcome variables of interest (Years 2, 3, 4, 6, 7, and 8), referred to as Times 1 through 6 hereafter. Recruitment letters were sent to families with 4^th and 5^th graders in 16 school districts of a northeastern state in the U.S. Due to the goals of the larger study, families were eligible if parents were married and both employed, and the firstborn was in the 4^th or 5^th grade with a secondborn sibling 1–4 years younger. A total of 203 families that contacted our office and were eligible initially participated. We excluded two families that dropped out after the first study wave and based our analyses on mothers (n = 201), fathers (n = 201), and youth (n = 402) in the remaining 201 families. Retention was high: At Time 6, 95% of parents and youth remained in the study. Reflecting the ethnic composition of the region (85% European American; U.S. Census Bureau, 2000), the sample was predominantly European American (two children were adopted from Asia). Reflecting the educational (> 80% of adults completed high school) and financial (median income = $55,714 for married-couple families) backgrounds of the targeted population, at Time 1, the average educational level was 14.63 years (SD = 2.11; range = 12–20) for mothers and 14.72 years (SD = 2.40; range = 10–20) for fathers, and the median family income was $58,050 (SD = 31,472; range = 16,000–224,000). Youth age at Time 1 averaged 11.83 years (SD = 0.55; range = 10.41–13.72) for firstborns and 9.22 years (SD = 0.93; range = 7.00–11.21) for secondborns. Sibling dyads were divided evenly by gender constellation.

Procedures

We collected data using two methods (Appendix A). First, at Times 1, 2, 4, 5, and 6, interviewers visited families to conduct home interviews with mothers, fathers, and youth. Parents and youth gave informed consent/assent, received honorariums, and completed questionnaires. Due to funding gaps, respondents completed a subset of the measures via mailed surveys at Time 3. Second, in the 2 to 3 weeks following the home interviews at Times 1, 2, 4, and 5, the years prior to the years when youth adjustment was measured, youth were interviewed by phone on 5 weekday and 2 weekend evenings about their daily time use.

Measures

Background characteristics measured in the home interviews with parents at Time 1 were youth age, gender, and birth order, parental education (averaged across mothers and fathers as one variable), and family size. Between Times 1 and 6, 17 families reported parental divorce (n = 12) or death (n = 5); a control variable was created to indicate these single-parent families.

Parents’ work hours were measured in the home interviews at Times 1, 2, 4, and 5. Mothers’ and fathers’ reports of the total hours they spent “at work,” “driving to and from work,” and “on work-related activities at home” per week were summed.

Youth’s time spent on household tasks was measured via the phone interviews at Times 1, 2, 4, and 5. Calls were made in the evenings, about an hour before bedtimes to obtain as much information as possible about youth activities on the call days. During each call, youth reported how much time (in minutes) they had spent on 70 specific activities during the day. The cued recall procedure was designed to limit definitional problems, memory demands, and social desirability pressures that may affect global self-reports of housework participation (Larson & Verma, 1999). We focused on four stereotypically feminine tasks (cooking, doing dishes, doing laundry, and cleaning the house) and a self-care task (cleaning one’s own room), given that these tasks are frequently performed by youth on a daily or almost daily basis (Bowes & Goodnow, 1996; Coltrane, 2000; Telzer & Fuligni, 2009a). Youth’s reports were summed across the five tasks and seven calls. At any given time point, only youth who completed all seven calls were included in the analyses. Compliance rate was high: Across time points, 95% of youth completed all seven calls. To assess whether youth were reliable reporters, we calculated the correlations between firstborns’ and secondborns’ reports of the time they spent with each other. Firstborns’ and secondborns’ reports, though made separately, were highly correlated (rs = .53, .67, .92, and .94 at Times 1, 2, 4, and 5, respectively), indicative of high inter-reporter reliability. To correct for skewness, housework time was square root transformed.

Youth’s depressive symptoms were measured in the home interviews at Times 2, 3, 5, and 6, with the 10-item Children’s Depression Inventory–Short Form (Kovacs, 1992). Youth chose one of three statements that best described their experiences, such as “I am sad once in a while,” “I am sad many times,” or “I am sad all of the time.” Ratings were summed; higher scores reflected more symptoms. Cronbach’s alphas were .64, .79, .82, and .83 at Times 2, 3, 5, and 6, respectively. To correct for skewness, depressive symptoms were log transformed.

Youth’s school performance was measured via grades in four subjects (English, math, science, and social studies), collected from youth’s report cards, at Times 2, 3, 5, and 6. Letter grades were converted into numerical scores (A = 4; B = 3; C = 2; D = 1; F = 0) and then averaged. Cronbach’s alphas were .87, .84, .84, and .84 at Times 2, 3, 5, and 6, respectively. To correct for skewness, school performance was square root transformed.

Youth’s familism values were measured in the home interviews at Time 4, with the 14-item Familism Scale, which tapped beliefs about family obligations, family support, and using family members as referents (Sabogal, Marín, Otero-Sabogal, Vanoss Marín, & Pérez-Stable, 1987). Youth used a 5-point scale to rate their agreement with such statements as “Relatives should help out when people have problems” and “The family should consult close relatives concerning important decisions.” Ratings were summed; higher scores reflected higher values. Cronbach’s alpha was .76. The average was 48.69 (SD = 6.21).

Parent-child conflict about housework was measured in the home interviews at Times 1, 2, 4, and 5 with a single item. Youth used a 6-point scale to rate, separately for each parent, “How often do you have arguments or disagreements with your mother/father about chores. This means problems about tasks, such as keeping your room clean, doing the dishes, shoveling snow, or setting the table.” Reports for mothers and fathers were moderately correlated (rs = .40, .50, .43, and .49 at Times 1, 2, 4, and 5, respectively) and were averaged at each time point.

Results

Multilevel Models

Three-level, multilevel models (Level 1 = within-individual; Level 2 = within family/between-sibling; Level 3 = between-family) were used to take into account the clustering of our data (time within child within family). By specifying a correlation matrix between the error residuals, multilevel models allowed us to treat the two children from the same family as individuals, instead of a dyad, and combine the longitudinal data from each child to estimate a common developmental course (Duncan et al., 1996; Raudenbush & Bryk, 2002). Multilevel models also adjusted for the invariant intervals between measurements (Singer & Willet, 2003) and effectively reduced estimation biases due to missing data (Schafer & Graham, 2002).

Changes in Housework Time: The Roles of Youth Gender and Parental Work Hours

Descriptive statistics for housework time, depressive symptoms, and school performance are shown in Tables 1 and 2. To address our first goal, we used questionnaire data from parents, and phone diary data from youth, all assessed at Times 1, 2, 4, and 5. We began by testing the effects of youth age on housework time (Model 1A). Significant linear and quadratic age effects indicated that housework time increased steadily from age 8 to about age 14 and then leveled off (Figure 1). Next, we controlled for youth birth order, parental education and divorce/death, and family size, and tested the interactions between age effects and gender (Model 2A). Results indicated that girls averaged more time on household tasks than did boys. The interactions between age effects and gender were not significant, however, suggesting that the gender difference did not change across adolescence. We then examined the links between parents’ work hours and youth’s housework time, and whether the links differed for girls versus boys (Model 3A). To distinguish within- from between-person associations, mothers’ and fathers’ work hours were each indicated by two variables (Singer & Willet, 2003): at Level 1, by a time-varying, group-mean centered (at each parent’s own cross-year average) variable; at Level 2, by the grand-mean centered (at the sample mean), cross-year average. The Level 1 variable captured how parents deviated from their own norms at each time point, indicating whether, controlling for the cross-year average (and thus any stable confounding factors, controlled or not controlled in the analyses), within-person variation in parents’ work hours was concurrently linked to within-person variation in youth’s housework time. The Level 2 variable captured how parents’ cross-year averages were different from the rest of the sample, indicating whether the cross-year average of parents’ work hours was linked to the cross-year average of their youth’s housework time. Model 3A revealed a significant Within-Person Mothers’ Work Hours x Gender interaction: In years when mothers worked more hours than usual, their daughters, γ = 0.03, SE = 0.01, p < .05, but not sons, γ = −0.01, SE = 0.02, n.s., did more housework than usual (Table 3).

Table 1.

Descriptive Statistics for Time Spent on Household Tasks across 7 Days for Firstborns (FB) and Secondborns (SB)

	Time 1		Time 2		Time 4		Time 5
	FB	SB	FB	SB	FB	SB	FB	SB
Means (in minutes)	96.44	82.52	97.54	78.94	112.53	95.78	98.62	102.97
Standard deviations	85.04	96.07	83.05	75.18	98.34	75.81	73.41	89.90
Ranges	0–625	0–730	0–412	0–545	0–455	0–425	0–385	0–727
Percentages of youth who reported zero housework participation	3%	4%	4%	7%	3%	3%	4%	4%

Table 2.

Descriptive Statistics for Depressive Symptoms and School Performance for Firstborns (FB) and Secondborns (SB)

	Time 2		Time 3		Time 5		Time 6
	FB	SB	FB	SB	FB	SB	FB	SB
Depressive symptoms
Means	1.26	1.37	1.89	1.19	2.20	2.01	1.99	2.22
Standard deviations	1.67	1.78	2.74	1.74	2.80	2.84	2.44	2.83
School Performance
Means	3.42	3.54	3.23	3.51	3.32	3.21	3.34	3.17
Standard deviations	0.74	0.61	0.73	0.62	0.70	0.76	0.67	0.82

Figure 1.

Predicted (solid markers) and observed (open markers) means of time spent on housework from middle childhood to late adolescence for girls and boys.

Table 3.

Coefficients (γ) and Standard Errors (SE) for Multilevel Models of Youth Housework Time

	Model 1A		Model 2A		Model 3A
	γ	SE	γ	SE	γ	SE
Intercept (γ000)	9.19**	0.21	10.04**	0.38	10.06**	0.38
Age (γ100)	0.12**	0.05	0.12*	0.05	0.13*	0.05
Age2 (γ200)	−0.04**	0.01	−0.04**	0.01	−0.04**	0.01
Gender (γ010)			−2.40**	0.26	−2.45**	0.26
Birth order (γ020)			−0.13	0.23	−0.05	0.23
Parental divorce or death (γ001)			1.42*	0.63	2.29**	0.69
Parental education (γ002)			0.03	0.09	0.04	0.09
Family size (γ003)			0.39	0.23	0.37	0.23
WP mothers’ work hours (γ300)					0.03*	0.02
BP mothers’ work hours (γ030)					0.02	0.01
Gender x WP mothers’ work hours (γ310)					−0.04*	0.02
WP fathers’ work hours (γ400)					0.01	0.01
BP fathers’ work hours (γ040)					−0.01	0.02

Note. BP = between-person; WP = within-person.

^*p < .05;

^**p < .01.

Adjustment Implications of Housework Time: The Roles of Familism Values and Conflict

To address our second goal, we used a lagged design to link housework time assessed by phone diaries at Times 1, 2, 4, and 5 to depressive symptoms (Model B) and school performance (Model C) assessed by questionnaires and school reports at Times 2, 3, 5, and 6. Controlling for youth age, gender, and birth order, parental education and divorce/death, and family size, we tested whether housework predicted adjustment and whether familism values and/or parent-child conflict moderated these associations. Like parents’ work hours in Model 3A, housework time was indicated by two variables. However, although the interpretation of its Level 2 version remained the same, its Level 1 version indicated whether, controlling for the cross-year average, within-person variation in housework time was longitudinally linked to within-person variation in youth adjustment, because youth adjustment was measured a year after each of the four assessments of housework time. Familism values were only measured at one time point and so included as a time-invariant, between-person moderator, but parent-child conflict about housework was measured at Times 1, 2, 4, and 5 and so included as a Level 2, time-invariant, between-person moderator and a Level 1, time-varying, within-person moderator.

Model B revealed a significant Between-Person Housework Participation x Familism interaction for depressive symptoms (Table 4). Follow-up tests indicated that, for youth with low (1 SD below the sample mean), γ = 0.02, SE = 0.01, p < .05, but not high (1 SD above the sample mean), γ = −0.01, SE = 0.01, n.s., familism values, the cross-year average of housework time was positively linked to the cross-year average of depressive symptoms (Figure 2). A Within-Person Housework Participation x Between-Person Parent-Child Conflict interaction was significant: For youth with high cross-year averages of parent-child conflict, in years when they did more housework than usual, they had more depressive symptoms than usual in the following year, γ = 0.02, SE = 0.01, p < .05. However, for youth with low cross-year averages of parent-child conflict, more housework than usual predicted fewer depressive symptoms than usual in the following year, γ = −0.17, SE = 0.01, p < .05 (Figure 3). Model C revealed a significant Within-Person Housework Participation x Familism interaction for school performance (Table 3): For youth with low, γ = −0.01, SE = 0.00, p < .01, but not high, γ = 0.00, SE = 0.00, n.s., familism values, more housework than usual predicted lower school grades than usual in the following year (Figure 4). Equations for all models are shown in Appendix B.

Table 4.

Coefficients (γ) and Standard Errors (SE) for Multilevel Models of Household Tasks Predicting Youth Depressive Symptoms (Model B) and School Performance (Model C)

	Model B		Model C
	γ	SE	γ	SE
Intercept (γ000)	0.925**	0.07	3.165**	0.05
Age (γ100)	0.099**	0.02	−0.054**	0.01
Age2 (γ200)	−0.006	0.00	0.001**	0.01
Age3 (γ300)	−0.001	0.00	0.001	0.00
Gender (γ010)	−0.277**	0.06	−0.114**	0.04
Gender x Age (γ110)	−0.102**	0.02	-	-
Gender x Age2 (γ210)	0.010*	0.00	-	-
Gender x Age3 (γ310)	0.001	0.00	-	-
Birth order (γ020)	0.087	0.05	−0.052	0.03
Parental divorce/death (γ001)	0.024	0.10	−0.156	0.09
Parental education (γ002)	−0.026	0.01	0.077**	0.01
Family size (γ003)	−0.078	0.04	0.065*	0.03
WP housework time (γ400)	−0.000	0.05	−0.006	0.00
BP housework time (γ030)	0.006	0.01	−0.003	0.01
Familism (γ040)	−0.006	0.00	−0.005	0.00
WP housework time x Familism (γ410)	-	-	0.001**	0.00
BP housework time x Familism (γ060)	−0.003*	0.00	-	-
WP PC conflict (γ500)	0.035	0.02	−0.020	0.01
BP PC conflict (γ050)	0.249**	0.04	−0.067*	0.03
WP housework time x BP PC conflict (γ410)	0.025**	0.01	-	-

Note. BP = between-person; WP = within-person; PC = parent-child.

^*p < .05;

^**p < .01.

Figure 2.

The between-person association between housework time and depressive symptoms for groups with high versus low familism values.

Figure 3.

The within-person association of housework time and depressive symptoms for persons with high versus low conflict about housework with their parents.

Figure 4.

The within-person associations of housework participation with school performance for persons with high versus low familism values.

Discussion

Limited longitudinal data and mixed results from prior work motivated our study’s focus on the development and correlates of youth housework and moderators of the links between housework and adjustment. Our results indicated that housework time increased from middle childhood through mid-adolescence and then leveled off. Although girls spent more time on household tasks than boys, there was no gender difference in the pattern of change. Consistent with an ecological perspective (Bronfenbrenner & Crouter, 1983), in years when mothers spent more hours in paid work than usual, daughters spent more time on housework than usual. With respect to youth adjustment, housework time was linked to more depressive symptoms and lower school grades, but only for youth with low familism values or high parent-child conflict.

Changes in Housework Time: The Roles of Youth Gender and Parental Work Hours

Toward illuminating factors that shape youth housework participation, we tested the roles of youth gender and parental work hours in longitudinal changes and within-person variation in youth housework time. Consistent with cross-sectional data (Gager et al., 2009; Raley, 2006), housework time increased from middle childhood to early adolescence. Yet, in contrast to prior reports of declines in housework participation across adolescence (Gager et al., 1999; Hilbrecht et al., 2008), housework time leveled off after mid-adolescence. These latter studies, however, relied on global self-reports of time spent on unspecified household tasks in “an average week” (Gager et al., 1999) and on cross-sectional data from older and younger adolescents (Hilbrecht et al., 2008). Our cued recall procedure, which focused on daily involvement in specific tasks, in the context of a long-term longitudinal design might provide for more accurate estimates of changes in youth activities over time (Larson & Verma, 1999).

As hypothesized, girls averaged more time on housework than did boys. This may not be surprising, given that most of the household tasks we focused on were stereotypically feminine (Bowes & Goodnow, 1996). However, contrary to a gender intensification hypothesis (Galambos et al., 1990) and some previous findings (Hilbrecht et al., 2008), the gender difference did not increase across adolescence. One possible explanation is that many stereotypically feminine tasks need to be done on a daily or almost daily basis (Coltrane, 2000). As youth’s housework can be critical to household maintenance and family well-being (Burton, 2007), adolescents who are responsible for these tasks may have to perform them, regardless of changes in other areas of their lives. Consistent with this interpretation, although Gager et al. (1999) reported an increasing gender difference in total housework, the gender difference in the kinds of housework we studied here did not increase. To our knowledge, ours is the first study to examine the development of youth housework time using long-term longitudinal data. If the age effects documented in our study are replicable, an important next step will be to explore how youth manage their time in the face of multiple obligatory and leisure activities. Directions for future research also include studying when gender differences in housework participation emerge and how such differences are linked to other domains of gender development, such as gendered interests and aspirations for adult roles.

Previous research demonstrated that daughters of mothers with longer work hours and heavier workloads spent more time on housework (Crouter et al., 2001; Manke et al., 1994). Expanding on an earlier study of the role of mothers’ fatigue in daily variation in youth’s housework (Tsai et al., 2013), we used a finer-grained analysis to show that, in years when mothers worked more hours than usual, their daughters, but not sons, spent more time on housework than usual. These within-person associations, emerging even after fathers’ work hours were controlled, provided strong support for the cultural construal of housework as “women’s work” and “training for girls” (Bowes & Goodnow, 1996). A direction for future research is to investigate the long-term implications of these patterns: Are women’s choices about work and family roles better predicted by their own gendered activities in childhood and adolescence, or the work and family roles of their mothers? Fathers’ work hours were unrelated to their children’s housework participation, possibly because fathers are relatively uninvolved in stereotypically feminine household tasks (Lachance-Grzela & Bouchard, 2010). Other employment conditions (e.g., work stress) and individual characteristics (e.g., gender role attitudes) of fathers may be more tightly linked to their sons’ and daughters’ housework involvement. More generally, our findings underscore the importance of considering both individual and contextual factors in understanding youth’s daily activities.

Adjustment Implications of Housework Time: The Roles of Familism Values and Conflict

Mixed findings on the implications of housework participation led us to examine familism values and parent-child conflict as potential moderators. Consistent with the idea that youth who do not value family obligations yet are heavily involved in housework may experience attitude-behavior incongruence and exhibit maladjustment (Telzer & Fuligni, 2009a), for youth with low familism values, the cross-year average of housework time was positively related to the cross-year average of depressive symptoms. Also, in years when youth did more housework than usual, they had lower school grades than usual in the following year. Familism values have often been studied in ethnic minorities; studies of European Americans have focused on between-group differences in familism values (Schwartz, 2007). Our study extended this work by illustrating that, even for a group with generally weaker familism values, individual differences in familism values explained the associations between housework involvement and youth adjustment. Practically, when assigning household duties, parents should acknowledge their children’s contributions to the family and highlight the importance of family support. However, given the mixed findings in prior studies (East & Weisner, 2009; Telzer & Fuligni, 2009a), our results require replication, especially with samples characterized by differing levels of familism values and family demands.

In keeping with Goodnow and Lawrence’s (2001) conceptual framework that draws attention to the style in which youth get involved in household duties and the degree of consensus, we found that, at a within-person level, housework time predicted more depressive symptoms in the following year for youth with high parent-child conflict, but fewer depressive symptoms in the following year for youth with low parent-child conflict. Prior researchers have demonstrated that voluntary, but not mandatory, housework contributions are linked to youth adjustment (Grusec et al., 1996) and that family disagreements about housework arrangements, rather than actual amounts of housework participation, lead to family stress (Ochs & Kremer-Sadlik, 2013; Ochs & Izquierdo, 2009). Our study added to this small yet important body of work by documenting the role of parent-child conflict about housework in these processes. Future researchers should directly measure the voluntary and consensual nature of youth housework participation, and formally test whether it moderates the associations between housework and adjustment. On a practical level, however, parents may preempt conflict by praising their children’s voluntary contributions to housework and adopting a consensus-building approach to assigning household tasks.

Limitations and Conclusions

Our study is not without limitations. First, our sample was demographically homogenous, limiting the generalizability of our results, which should be replicated in samples that are more diverse with respect to ethnic composition and family structure. In addition, although we measured most constructs repeatedly, familism values were measured at only one time point. Given previous research showing that familism declines across adolescence (Tsai, Telzer, & Fuligni, 2013), additional studies are needed to capture whether changing familism values may differentially moderate the influence of housework at different points of development. Further, despite the methodological strengths of our study, conclusions about causal relations cannot be made based on correlational data (Curran & Bauer, 2011). Intervention studies that use randomized designs to manipulate youth housework involvement are needed to illuminate whether housework actually causes changes in adjustment. Finally, we focused on stereotypically feminine and self-care tasks because they tend to require regular involvement on the part of youth (Bowes & Goodnow, 1996; Coltrane, 2000; Telzer & Fuligni, 2009a). These tasks may differ in their development and correlates in comparison to others, such as home repair, helping siblings with homework, and assisting parents at their work. The longitudinal changes and within-person variation of different kinds of tasks await future investigation. Importantly, the particular features of tasks, such as the extent to which they engender positive versus negative affect, are perceived as stressful versus manageable, or are experienced as stimulating versus onerous, should be directly measured and formally tested as moderators.

Despite these limitations, our use of multiple-wave, daily diary data and focus on within-person variation allowed us to contribute new insights about the developmental course, family correlates, and adjustment implications of youth housework participation. More generally, our findings highlight the gendered nature of housework allocation and the importance of considering both contextual and individual factors in understanding youth daily activities.

Appendix A

Constructs Assessed via Different Methods at Different Time Points

To address our first goal, examining the development of housework time and the roles of youth gender and parental work hours in youth housework participation, we used questionnaire data from mothers and fathers, and phone diary data from firstborns and secondborns, all assessed at Times 1, 2, 4, and 5. Youth housework time and parental work hours were assessed at the same time points, because we were interested in the concurrent associations between parental work hours and youth housework participation. To address our second goal, examining whether youth’s housework participation predicted their depressive symptoms and school performance, we used a lagged design. As with our first goal, housework time was assessed via phone diaries at Times 1, 2, 4, and 5, but youth adjustment was assessed via questionnaires and report cards at Times 2, 3, 5, and 6 in order to test the longitudinal associations between housework participation and youth adjustment:

Constructs (assessment methods)	Years of data collection in the larger study
	2	3	4	5	6	7	8
	Time points included in the current study
	1	2	3		4	5	6
Parents’ work hours (questionnaires)	X	X			X	X
Youth’s housework time (phone diaries)	X	X			X	X
Youth’s depressive symptoms (questionnaires)		X	X			X	X
Youth’s school performance (report cards)		X	X			X	X
Youth’s familism values (questionnaires)					X
Youth’s conflict with parents (questionnaires)	X	X			X	X

Appendix B

Equations for Multilevel Models of Housework Time

Model 1A

Level 1 equation

$$\text{Housework}{\text{Time}}_{\text{ijk}}={\mathrm{\pi }}_{0\text{jk}}+{\mathrm{\pi }}_{1\text{jk}}\times \text{Age}+{\mathrm{\pi }}_{2\text{jk}}\times {\text{Age}}^2+e_{\text{ijk}}$$

Level 2 equations

$$\begin{array}{l}{\mathrm{\pi }}_{0\text{jk}}={\mathrm{\beta }}_{00\mathrm{k}}+u_{0\text{jk}}\\ {\mathrm{\pi }}_{1\text{jk}}={\mathrm{\beta }}_{10\mathrm{k}}+u_{1\text{jk}}\\ {\mathrm{\pi }}_{2\text{jk}}={\mathrm{\beta }}_{20\mathrm{k}}\end{array}$$

where $\left(\begin{array}{c}{u}_{0jk}\\ u_{1jk}\end{array}\right)~N\left[\left(\begin{array}{c}0\\ 0\end{array}\right),\left(\begin{array}{cc}{\tau }_{00k}& {\tau }_{01k}\\ {\tau }_{10k}& {\tau }_{11k}\end{array}\right)\right]$

Level 3 equations

$$\begin{array}{l}{\mathrm{\beta }}_{00\mathrm{k}}={\mathrm{\gamma }}_{000}+u_{00\mathrm{k}}\\ {\mathrm{\beta }}_{10\mathrm{k}}={\mathrm{\gamma }}_{100}\\ {\mathrm{\beta }}_{20\mathrm{k}}={\mathrm{\gamma }}_{200}\end{array}$$

where u_00k ~ N (0, τ₀₀₀)

Model 2A

Level 1 equation

$$\text{Housework}{\text{Time}}_{\text{ijk}}={\mathrm{\pi }}_{0\text{jk}}+{\mathrm{\pi }}_{1\text{jk}}\times \text{Age}+{\mathrm{\pi }}_{2\text{jk}}\times {\text{Age}}^2+e_{\text{ijk}}$$

Level 2 equations

$$\begin{array}{l}{\mathrm{\pi }}_{0\text{jk}}={\mathrm{\beta }}_{00\mathrm{k}}+{\mathrm{\beta }}_{01\mathrm{k}}\times \text{Gender}+{\mathrm{\beta }}_{02\mathrm{k}}\times \text{Birth}\text{Order}+u_{0\text{jk}}\\ {\mathrm{\pi }}_{1\text{jk}}={\mathrm{\beta }}_{10\mathrm{k}}+u_{1\text{jk}}\\ {\mathrm{\pi }}_{2\text{jk}}={\mathrm{\beta }}_{20\mathrm{k}}\end{array}$$

where $\left(\begin{array}{c}{u}_{0jk}\\ u_{1jk}\end{array}\right)~N\left[\left(\begin{array}{c}0\\ 0\end{array}\right),\left(\begin{array}{cc}{\tau }_{00k}& {\tau }_{01k}\\ {\tau }_{10k}& {\tau }_{11k}\end{array}\right)\right]$

Level 3 equations

$$\begin{array}{l}{\mathrm{\beta }}_{00\mathrm{k}}={\mathrm{\gamma }}_{000}+{\mathrm{\gamma }}_{001}\times \text{Parental}\text{Divorce}\text{or}\text{Death}+{\mathrm{\gamma }}_{002}\times \text{Parental}\text{Education}+{\mathrm{\gamma }}_{003}\times \text{Family}\text{Size}+u_{00\mathrm{k}}\\ {\mathrm{\beta }}_{01\mathrm{k}}={\mathrm{\gamma }}_{010}\\ {\mathrm{\beta }}_{02\mathrm{k}}={\mathrm{\gamma }}_{020}\\ {\mathrm{\beta }}_{10\mathrm{k}}={\mathrm{\gamma }}_{100}\\ {\mathrm{\beta }}_{20\mathrm{k}}={\mathrm{\gamma }}_{200}\end{array}$$

where u_00k ~ N (0, τ₀₀₀)

Model 3A

Level 1 equation

$$\text{Housework}{\text{Time}}_{\text{ijk}}={\mathrm{\pi }}_{0\text{jk}}+{\mathrm{\pi }}_{0\text{jk}}\times \text{Age}+{\mathrm{\pi }}_{2\text{jk}}\times {\text{Age}}^2+{\mathrm{\pi }}_{3\text{jk}}\times \text{WP}\text{Mothers}’\text{Work}\text{Hours}+{\mathrm{\pi }}_{4\text{jk}}\times \text{WP}\text{Fathers}’\text{Work}\text{Hours}+e_{\text{ijk}}$$

Level 2 equations

$$\begin{array}{l}{\mathrm{\pi }}_{0\text{jk}}={\mathrm{\beta }}_{00\mathrm{k}}+{\mathrm{\beta }}_{01\mathrm{k}}\times \text{Gender}+{\mathrm{\beta }}_{02\mathrm{k}}\times \text{Birth}\text{Order}+{\mathrm{\beta }}_{03\mathrm{k}}\times \text{BP}\text{Mothers}’\text{Work}\text{Hours}+{\mathrm{\beta }}_{04\mathrm{k}}\times \text{BP}\text{Fathers}’\text{Work}\text{Hours}+u_{0\text{jk}}\\ {\mathrm{\pi }}_{1\text{jk}}={\mathrm{\beta }}_{10\mathrm{k}}+u_{1\text{jk}}\\ {\mathrm{\pi }}_{2\text{jk}}={\mathrm{\beta }}_{20\mathrm{k}}\\ {\mathrm{\pi }}_{3\text{jk}}={\mathrm{\beta }}_{30\mathrm{k}}+{\mathrm{\beta }}_{31\mathrm{k}}\times \text{Gender}\\ {\mathrm{\pi }}_{4\text{jk}}={\mathrm{\beta }}_{40\mathrm{k}}\end{array}$$

where $\left(\begin{array}{c}{u}_{0jk}\\ u_{1jk}\end{array}\right)~N\left[\left(\begin{array}{c}0\\ 0\end{array}\right),\left(\begin{array}{cc}{\tau }_{00k}& {\tau }_{01k}\\ {\tau }_{10k}& {\tau }_{11k}\end{array}\right)\right]$

Level 3 equations

$$\begin{array}{l}{\mathrm{\beta }}_{00\mathrm{k}}={\mathrm{\gamma }}_{000}+{\mathrm{\gamma }}_{001}\times \text{Parental}\text{Divorce}\text{or}\text{Death}+{\mathrm{\gamma }}_{002}\times \text{Parental}\text{Education}+{\mathrm{\gamma }}_{003}\times \text{Family}\text{Size}+u_{00\mathrm{k}}\\ {\mathrm{\beta }}_{01\mathrm{k}}={\mathrm{\gamma }}_{010}\\ {\mathrm{\beta }}_{02\mathrm{k}}={\mathrm{\gamma }}_{020}\\ {\mathrm{\beta }}_{03\mathrm{k}}={\mathrm{\gamma }}_{030}\\ {\mathrm{\beta }}_{04\mathrm{k}}={\mathrm{\gamma }}_{040}\\ {\mathrm{\beta }}_{10\mathrm{k}}={\mathrm{\gamma }}_{100}\\ {\mathrm{\beta }}_{20\mathrm{k}}={\mathrm{\gamma }}_{200}\\ {\mathrm{\beta }}_{30\mathrm{k}}={\mathrm{\gamma }}_{300}\\ {\mathrm{\beta }}_{31\mathrm{k}}={\mathrm{\gamma }}_{310}\\ {\mathrm{\beta }}_{40\mathrm{k}}={\mathrm{\gamma }}_{400}\end{array}$$

where u_00k ~ N (0, τ₀₀₀)

Note. BP = between-person; WP = within-person.

Subscripts i indicates occasions within individual j in family k, j indicates individuals within family k, and k indicates families.

Equations for Multilevel Model of Depressive Symptoms

Model B

Level 1 equation

$$\begin{array}{l}\text{Depressive}{\text{Symptoms}}_{\text{ijk}}={\mathrm{\pi }}_{0\text{jk}}+{\mathrm{\pi }}_{\text{1jk}}\times \text{Age}+{\mathrm{\pi }}_{2\text{jk}}\times {\text{Age}}^2+{\mathrm{\pi }}_{3\text{jk}}\times {\text{Age}}^3+{\mathrm{\pi }}_{4\text{jk}}\times \text{WP}\text{Housework}\\ \text{Participation}+{\mathrm{\pi }}_{5\text{jk}}\times \text{WP}\text{Parent-Child}\text{Conflict}+e_{\text{ijk}}\end{array}$$

Level 2 equations

$$\begin{array}{l}{\mathrm{\pi }}_{0\text{jk}}={\mathrm{\beta }}_{00\mathrm{k}}+{\mathrm{\beta }}_{01\mathrm{k}}\times \text{Gender}+{\mathrm{\beta }}_{02\mathrm{k}}\times \text{Birth}\text{Order}+{\mathrm{\beta }}_{03\mathrm{k}}\times \text{BP}\text{Housework}\text{Participation}+{\mathrm{\beta }}_{04\mathrm{k}}\times \\ \text{Familism}+{\mathrm{\beta }}_{05\mathrm{k}}\times \text{BP}\text{Housework}\text{Participation}\times \text{Familism}+{\mathrm{\beta }}_{06\mathrm{k}}\times \text{BP}\text{Parent-Child}\text{Conflict}+u_{0\text{jk}}\\ {\mathrm{\pi }}_{1\text{jk}}={\mathrm{\beta }}_{10\mathrm{k}}+{\mathrm{\beta }}_{11\mathrm{k}}\times \text{Gender}+u_{1\text{jk}}\\ {\mathrm{\pi }}_{\text{2jk}}={\mathrm{\beta }}_{20\mathrm{k}}+{\mathrm{\beta }}_{21\mathrm{k}}\times \text{Gender}\\ {\mathrm{\pi }}_{\text{3jk}}={\mathrm{\beta }}_{30\mathrm{k}}+{\mathrm{\beta }}_{31\mathrm{k}}\times \text{Gender}\\ {\mathrm{\pi }}_{\text{4jk}}={\mathrm{\beta }}_{40\mathrm{k}}+{\mathrm{\beta }}_{41\mathrm{k}}\times \text{BP}\text{Parent-Child}\text{Conflict}\\ {\mathrm{\pi }}_{\text{5jk}}={\mathrm{\beta }}_{50\mathrm{k}}\\ {\mathrm{\pi }}_{\text{5jk}}={\mathrm{\beta }}_{50\mathrm{k}}\\ {\mathrm{\pi }}_{\text{6jk}}={\mathrm{\beta }}_{60\mathrm{k}}\end{array}$$

where $\left(\begin{array}{c}{u}_{0jk}\\ u_{1jk}\end{array}\right)~N\left[\left(\begin{array}{c}0\\ 0\end{array}\right),\left(\begin{array}{cc}{\tau }_{00k}& {\tau }_{01k}\\ {\tau }_{10k}& {\tau }_{11k}\end{array}\right)\right]$

Level 3 equations

$$\begin{array}{l}{\mathrm{\beta }}_{00\mathrm{k}}={\mathrm{\gamma }}_{000}+{\mathrm{\gamma }}_{001}\times \text{Parental}\text{Divorce}\text{or}\text{Death}+{\mathrm{\gamma }}_{002}\times \text{Parental}\text{Education}+{\mathrm{\gamma }}_{003}\times \text{Family}\text{Size}+u_{00\mathrm{k}}\\ {\mathrm{\beta }}_{01\mathrm{k}}={\mathrm{\gamma }}_{010}\\ {\mathrm{\beta }}_{02\mathrm{k}}={\mathrm{\gamma }}_{020}\\ {\mathrm{\beta }}_{03\mathrm{k}}={\mathrm{\gamma }}_{030}\\ {\mathrm{\beta }}_{04\mathrm{k}}={\mathrm{\gamma }}_{040}\\ {\mathrm{\beta }}_{05\mathrm{k}}={\mathrm{\gamma }}_{050}\\ {\mathrm{\beta }}_{06\mathrm{k}}={\mathrm{\gamma }}_{060}\\ {\mathrm{\beta }}_{10\mathrm{k}}={\mathrm{\gamma }}_{100}\\ {\mathrm{\beta }}_{11\mathrm{k}}={\mathrm{\gamma }}_{110}\\ {\mathrm{\beta }}_{20\mathrm{k}}={\mathrm{\gamma }}_{200}\\ {\mathrm{\beta }}_{\text{21k}}={\mathrm{\gamma }}_{210}\\ {\mathrm{\beta }}_{30\mathrm{k}}={\mathrm{\gamma }}_{300}\\ {\mathrm{\beta }}_{31\mathrm{k}}={\mathrm{\gamma }}_{310}\\ {\mathrm{\beta }}_{40\mathrm{k}}={\mathrm{\gamma }}_{400}\\ {\mathrm{\beta }}_{41\mathrm{k}}={\mathrm{\gamma }}_{410}\\ {\mathrm{\beta }}_{50\mathrm{k}}={\mathrm{\gamma }}_{500}\end{array}$$

where u_00k ~ N (0, τ₀₀₀)

Note. BP = between-person; WP = within-person.

Subscripts i indicates occasions within individual j in family k, j indicates individuals within family k, and k indicates families.

Equations for Multilevel Model of School Performance

Model C

Level 1 equation

$$\begin{array}{l}\text{School}{\text{Performance}}_{\text{ijk}}={\mathrm{\pi }}_{0\text{jk}}+{\mathrm{\pi }}_{\text{1jk}}\times \text{Age}+{\mathrm{\pi }}_{2\text{jk}}\times {\text{Age}}^2+{\mathrm{\pi }}_{3\text{jk}}\times {\text{Age}}^3+{\mathrm{\pi }}_{4\text{jk}}\times \text{WP}\text{Housework}\\ \text{Participation}+{\mathrm{\pi }}_{5\text{jk}}\times \text{WP}\text{Parent-Child}\text{Conflicts}+e_{\text{ijk}}\end{array}$$

Level 2 equations

$$\begin{array}{l}{\mathrm{\pi }}_{0\text{jk}}={\mathrm{\beta }}_{00\mathrm{k}}+{\mathrm{\beta }}_{01\mathrm{k}}\times \text{Gender}+{\mathrm{\beta }}_{02\mathrm{k}}\times \text{Birth}\text{Order}+{\mathrm{\beta }}_{03\mathrm{k}}\times \text{BP}\text{Housework}\text{Participation}+{\mathrm{\beta }}_{04\mathrm{k}}\times \\ \text{Familism}+{\mathrm{\beta }}_{05\mathrm{k}}\times \text{BP}\text{Parent-Child}\text{Conflict}+u_{0\text{jk}}\\ {\mathrm{\pi }}_{1\text{jk}}={\mathrm{\beta }}_{10\mathrm{k}}+u_{1\text{jk}}\\ {\mathrm{\pi }}_{\text{2jk}}={\mathrm{\beta }}_{20\mathrm{k}}\\ {\mathrm{\pi }}_{\text{3jk}}={\mathrm{\beta }}_{30\mathrm{k}}\\ {\mathrm{\pi }}_{\text{4jk}}={\mathrm{\beta }}_{40\mathrm{k}}+{\mathrm{\beta }}_{41\mathrm{k}}\times \text{Familism}\\ {\mathrm{\pi }}_{\text{5jk}}={\mathrm{\beta }}_{50\mathrm{k}}\end{array}$$

where $\left(\begin{array}{c}{u}_{0jk}\\ u_{1jk}\end{array}\right)~N\left[\left(\begin{array}{c}0\\ 0\end{array}\right),\left(\begin{array}{cc}{\tau }_{00k}& {\tau }_{01k}\\ {\tau }_{10k}& {\tau }_{11k}\end{array}\right)\right]$

Level 3 equations

$$\begin{array}{l}{\mathrm{\beta }}_{00\mathrm{k}}={\mathrm{\gamma }}_{000}+{\mathrm{\gamma }}_{001}\times \text{Parental}\text{Divorce}\text{or}\text{Death}+{\mathrm{\gamma }}_{002}\times \text{Parental}\text{Education}+{\mathrm{\gamma }}_{003}\times \text{Family}\text{Size}+u_{00\mathrm{k}}\\ {\mathrm{\beta }}_{01\mathrm{k}}={\mathrm{\gamma }}_{010}\\ {\mathrm{\beta }}_{02\mathrm{k}}={\mathrm{\gamma }}_{020}\\ {\mathrm{\beta }}_{03\mathrm{k}}={\mathrm{\gamma }}_{030}\\ {\mathrm{\beta }}_{04\mathrm{k}}={\mathrm{\gamma }}_{040}\\ {\mathrm{\beta }}_{05\mathrm{k}}={\mathrm{\gamma }}_{050}\\ {\mathrm{\beta }}_{10\mathrm{k}}={\mathrm{\gamma }}_{100}\\ {\mathrm{\beta }}_{20\mathrm{k}}={\mathrm{\gamma }}_{200}\\ {\mathrm{\beta }}_{30\mathrm{k}}={\mathrm{\gamma }}_{300}\\ {\mathrm{\beta }}_{40\mathrm{k}}={\mathrm{\gamma }}_{400}\\ {\mathrm{\beta }}_{41\mathrm{k}}={\mathrm{\gamma }}_{410}\\ {\mathrm{\beta }}_{50\mathrm{k}}={\mathrm{\gamma }}_{500}\end{array}$$

where u_00k ~ N (0, τ₀₀₀)

Note. BP = between-person; WP = within-person.

Subscripts i indicates occasions within individual j in family k, j indicates individuals within family k, and k indicates families.