Triadic Family Structures and Their Day-to-Day Dynamics From an Adolescent Perspective: A Multilevel Latent Profile Analysis

Abstract

Relationship structure (patterns of relative closeness among multiple family members) and dynamics (changes in relationship structures over time) are two main aspects of family-system functioning, yet empirical tests of these concepts lag behind theory. Recent growth in advanced methods for complex data structures make it possible to empirically capture structures and dynamics within multiple family relationships over time. To answer how relationship structure may fluctuate from day to day, this study used multilevel latent profile analysis (MLPA) as an innovative and feasible method to capture mother-father-adolescent (MFA) relationship structures and dynamics on a daily basis. Using daily adolescent reports of mother-father (MF), mother-adolescent (MA), and father-adolescent (FA) closeness from 144 two-parent families for up to 21 days, we identified six day-level MFA structures: Cohesive (33% of days; three close dyads), Mother-Centered (9%; closer MF, average MA, less close FA), Adolescent-Centered (4%; less close MF, closer MA and FA), MA-Coalition (3%; closer MA, less close MF and FA), Disengaged (23%; three less close dyads), and Average (28%; three approximately average dyads). We identified five types of MFA dynamics at the family level: Stable Cohesive (35% of families; exhibited Cohesive structure most days), Stable Disengaged (20%; Disengaged structure most days), Stable MA-Coalition (3%; MA-Coalition structure most days), Stable Average (24%; Average structure most days), and Variable (17%; varied among multiple structures). Methodologically, daily diary designs and MLPA can be useful tools to empirically examine concrete hypotheses of complex, non-linear processes in family systems. Substantive and methodological implications are discussed.

Family relationships—including parent-adolescent and interparental relationships—have profound influences on adolescent development and long-term adjustment (e.g., Fosco & Feinberg, 2015; Laursen & Collins, 2009). Adolescents satisfy their basic psychological needs of relatedness and belonging by having strong, enduring bonds with parents (Baumeister & Leary, 1995; Ryan & Deci, 2001), and they strengthen their sense of emotional security through exposure to warm and affectionate interparental relationships (Cox et al., 2001; Davies & Cummings, 1994). Need satisfaction and sense of security both promote adolescent flourishing and reduce risk for maladjustment (e.g., Feldman et al., 1997; Leidy et al., 2009). Although close parent-adolescent and inteparental relationships have been identified as important for adolescent development, they are typically evaluated separately or as unique predictors. Holistic methods of evaluating family relationships would offer a more complete picture of family system functioning and how that impacts adolescent adjustment (Cox & Paley, 1997; Minuchin, 1985).

The Organization of Mother-Father-Adolescent (MFA) Relationships in Family Systems

Family systems theory emphasizes that families are comprised of interdependent subsystems; when the system is reduced to separate dyadic relationships, it yields an incomplete picture of the family context of individual development (Cox & Paley, 1997; Minuchin, 1985). Family organization, referring to the overall level of closeness and patterns of relative closeness across the mother-father (MF), mother-adolescent (MA), and father-adolescent (FA) dyads, provides valuable information about family systems functioning as a whole beyond each dyadic subsystem (Nichols & Everett, 1986). Considerable attention has been given to cohesive and disengaged patterns of family organizations, where all dyads tend to be emotionally close (i.e. cohesive) or distant (i.e. disengaged) (e.g., Kerig, 1995; Olson, 2000). However, patterns of relative closeness across multiple dyads can be diverse (e.g., Bowen, 1978; Minuchin, 1974), calling for greater nuance in conceptualizing organizations of multiple family relationships.

Structural family systems theorists (e.g., Minuchin, 1974; Minuchin et al., 1978) have argued that patterns evident in the relative emotional closeness among multiple dyads in a family may offer a window into the health of the family and its members. Kerig (1995) identified a number of family configurations that reflect unique patterns of overall and relative closeness among members, including cohesive, triangulated (containing 3 distinct structures), detouring, and separate. In this study, we build on this theoretical foundation, and extend this perspective to include additional potential structures that may emerge in daily life, comprised of eight different combinations of absolute and relative closeness in MF, MA, and FA dyads (see Figure 1). In what follows, we describe the proposed family structural classifications originated from prior work (e.g., Bell et al., 2001, Kerig, 1995, Minuchin 1974; Minuchin et al., 1978).

Figure 1.

Eight Different MFA Relationship Structures

The Cohesive family structure (1) is characterized by balanced, close dyadic relationship among all family members (Bell et al., 2001; Kerig, 1995; Olson, 2000). At the other extreme, the Disengaged structure (8) is characterized by emotional distance in all three dyadic relationships, where individuals often are highly independent and maximize their separated space and time apart (Olson, 2000). Between these two extreme forms, are six family structures that are characterized imbalanced (i.e., uneven) patterns of relationship closeness among the three dyads. Multiple studies, using diverse methodologies have identified these family forms (e.g., Davies et al., 2004; Olson, 2000; Xia et al., 2020), suggesting they may be prevalent family structures.

In some families, one person may play a central role in maintaining family affective bonds by being emotionally close to other family members, which is similar to processes in which children serve as “mediators” of interparental discord in distressed families (Bell et al. 2001). We conceptualize these three potential forms: Mother-Centered (2), Father-Centered (3), and Adolescent-Centered (4). These three structures are similar in that they are unbalanced in their relationships and are characterized by two close dyadic relationships and one emotionally distant relationship. Different from mother-centered and father-centered families in which the interparental relationship is close, adolescent-centered families may indicate a different family process where the adolescent is close to both parents, and greater distance is found in the interparental relationship (Bell et al., 2001; Xia et al., 2020).

Another broad pattern of organization may be found in family coalitions where one dyad is particularly close, while the third member is emotionally distant from the other two family members. Prior work underscores cross-generational coalitions, such as MA-Coalition (5) and FA-Coalition (6) families (Bell et al, 2001; Buchanan & Waizenhofer, 2001) where the adolescent is close to their mother or father, and the third member is emotionally distant from the others. Similarly, the couple relationship may be the focus of the coalition, termed a MF-Coalition (7), which corresponds to detouring process in interparental conflict scenarios where couples are especially close, effectively “pushing” the adolescent out (Bell et al. 2001; Kerig, 1995). These family structures are evident in studies focusing on both interparental conflict (Bell et al, 2001; Buchanan & Waizenhofer, 2001) and general family relationship structures (Kerig, 1995), suggesting these may be particularly robust forms of family relationships.

A Dynamic Perspective of MFA Relationships

Although structure and dynamics are both critical aspects of family functioning, the day-to-day changes in family structures are often overlooked (Cox & Paley, 1997; Granic & Hollenstein, 2003). Some MFA relationships may be cohesive most of the time with minor fluctuations on stressful days, some may switch between MA-Coalition and FA-Coalition structures on a daily basis, and other families may change unpredictably among different structures (Kerig, 1995; Buchanan & Waizenhofer, 2001; Olson, 2000). Capturing these MFA dynamics in representations of family functioning may offer greater insights than assessments that imply MFA relationship structures are static.

Little is known about MFA dynamics in daily life. Family systems theorists have postulated that families may differ in how stable or variable the nature of these relationships are from day to day (e.g., consistently stable cohesion, fluctuating from cohesive to alliances) (Minuchin, 1974; Olson, 2000). For example, some families have shifting alliances, where the adolescent is sometimes closer to their mother, sometimes closer to their father, and sometimes in the middle between their two parents (Kerig, 1995; Buchanan & Waizenhofer, 2001; Bell et al., 2001). Other possible dynamics may include, but are not limited to, stable alliance dynamics (i.e., the child is consistently closer to one parent) and variable dynamics (i.e., the relationship structures among the three family members frequently changing from day to day).

Leveraging Daily Diary Designs to Capture Family Dynamics

Daily diary designs, which use repeated assessments of ongoing experiences, offer the opportunity to capture changes in family life from day to day (Bolger et al., 2003; Repetti et al., 2015). Such designs directly assess same-day family processes in a natural setting, which maximizes ecological validity and minimizes retrospective report bias (Bolger et al., 2003; Repetti et al., 2015). Moreover, by tracking within-family interactions on a daily basis, diary methods capture micro-level processes in the family and inspire family researchers to look at system dynamics in order to move beyond static structures. This approach is also able to disentangle within-family dynamics from between-family differences (e.g., Gates & Liu, 2016; Fosco & Lydon-Staley, 2020) by analyzing data under a multilevel modeling framework (Bolger & Laurenceau, 2013; Larson & Almeida, 1999).

Using daily data to capture rich information in family systems is not without challenges. Although many models can analyze repeated measures within persons or dyads (e.g., Actor-Partner-Interdependence Model; Kenny et al., 2006), they often cannot accommodate multiple family relationships beyond a single dyad. Moreover, most multilevel modeling analytic approaches take a variable-centered approach (i.e., focusing on associations among multiple family variables instead of using them as indicators of an integrative family system), which cannot fully capture the nonlinear complexity in family systems. To the extent that family systems function as an integrative whole beyond each individual dyad (Minuchin, 1985) and families differences in relationship structures and dynamics reflect their unique functioning (Brinberg et al., 2017), family studies need to consider person-centered approaches that can include multiple dyads simultaneously to reflect different constellations of family functioning.

A Person-Centered Approach to Studying Family Systems

Latent profile analysis (LPA) is a type of finite mixture model that can be used to identify mutually exclusive and exhaustive latent subgroups of families with similar means on two or more continuous indicators from a person-centered perspective (Lazarsfeld & Henry, 1968). LPA complements traditional diary data methods (e.g., multilevel modeling) in family studies: it describes co-occurrence of indicators across multiple subsystems beyond one dyad at a time, which provides a more holistic perspective of the family system and a way to answer more comprehensive system-oriented research questions (Maughan & Cicchetti, 2002; Sturge-Apple et al., 2014). In single-level data, LPA can be used to identify unique family subgroups based on their similarity in structure, instead of estimating average associations among different variables. LPA also can be used to answer research questions about unique implications of different family structures on adolescent development (e.g., Sturge-Apple et al., 2014; Xia et al., 2020).

Although traditional LPA can capture subgroup differences in family structures, it is not designed to analyze nested data (e.g., day-level nested within family-level) and separate within-family heterogeneity from between-family heterogeneity, and thus it cannot capture variability in family structures over time inherent in dynamic process questions. Traditional LPA assumes that all data records are independent (Vermunt, 2003). This assumption is violated with daily diary data when observations from all families and all days are pooled for analysis. Although robust standard errors that adjust for non-independence of records can be applied to a traditional LPA, this does not provide a way to parse family structures from dynamics. A more flexible approach is needed to use daily observations from each family to examine family dynamics. Therefore, family-system studies call for an approach that maintains the benefits of person-centered analysis and the benefits of multilevel modeling in order to handle daily data nested within families.

Multilevel Latent Profile Analysis and Family Systems Dynamics

We suggest multilevel latent profile analysis (MLPA) as an innovative and feasible technique to model family structures from a person-centered perspective and to capitalize on the well-established multilevel modeling framework for daily data to model family dynamics. MLPA extends traditional LPA to accommodate data with a hierarchical structure by allowing Level-1 latent profile prevalences to vary across Level-2 subgroups (e.g., Henry & Muthén, 2010; Vermunt, 2003). This provides a way to model within-family process (time-level as Level-1) nested in between-family differences (family-level as Level-2).

MLPA advances our ability to empirically test specific hypotheses about the complex family system and provides potential to add new insights to theory by additionally considering the dynamic aspect of family systems. Specifically, MLPA enables quantitative modeling of family structures, which complements prior family research that only used clinical observations to capture the holistic family system (Minuchin, 1974; Nichols & Everett, 1986). Moreover, MLPA provides new opportunities to study the dynamics of family structures on a daily basis beyond traditional family systems theories (which view family structure as an established interaction pattern) (Nichols & Everett, 1986). In MLPA with daily diary data, the Level-1 model can identify family structures across all days by estimating patterns across indicators from multiple subsystems, and the Level-2 model can describe family dynamics by identifying types of families based on the proportions of days that families spend in different structures. This innovative approach makes empirical and theoretical contributions to family research.

The Present Study

In this study, we used MLPA to identify structures and describe dynamics of MFA relationships using adolescent-report daily dairy data. The two research questions are as follows: (1) at the day-level, what MFA relationship structures can be identified across all families and all days (in our sample) from the adolescent’s perspective? (2) at the family-level, what are the different dynamics experienced by those families from the adolescent’s perspective? Accordingly, (Hypothesis 1) we expected to identify 8 structures as shown in Figure 1 (i.e., Cohesive, Mother-Centered, Father-Centered, Adolescent-Centered, MA-Coalition, FA-Coalition, MF-Coalition, and Disengaged) at the daily level. And, (Hypothesis 2) we expected to identify at least stable cohesive and stable disengaged dynamics, where the MFA relationships stay in a Cohesive structure and a Disengaged structure most days (respectively), at the family level; other dynamics were permitted, and were examined in an exploratory manner.

Method

Participants and Procedure

Participating adolescents and caregivers completed up to 21 days in a daily-diary, family-focused study. After being notified through school emails and family referrals, interested parents received detailed study information, were checked for eligibility, and provided consent and contact information. The original sample involved 150 eligible families who met the following criteria: (1) adolescent in 9^th or 10^th grade, (2) two-caregiver family status, (3) adolescent lived in the household continuously, (4) participants demonstrated English fluency, (5) access to the internet and a device to complete surveys, and (6) caregiver and adolescent consented/assented to participate. Daily surveys were sent separately to caregivers and adolescents at 7 p.m., followed by reminders.

A subsample of 144 families with “mother-father” caregivers was used here because the focus is on MFA relationships. “Mother-father” in this study refers to caregivers in one of mother-father, mother-stepfather, stepmother-father, mother-mother’s fiancé, and mother-mother’s partner combinations; families with other caregivers (e.g., sister, grandmother) were excluded. The analytic sample contained 83.3% (n=120) biological mother-father families, 12.5% (n=18) biological mother-stepfather families, 2.8% (n=4) biological father-stepmother families, and 1.4% (n=2) families of biological mother and their partner/fiancé. Adolescents provided daily reports ranging from 11 to 21 days, with an overall completion rate of 90.6% (M = 19.03 days, SD = 2.44) of daily surveys. Adolescent participants were 14 to 16 years old (M = 14.76 years, SD = 0.73; reported by caregiver); 61.1% were female (n=88). Adolescents were identified (by caregiver-report) as White (84.7%), African American/Black (2.8%), Native American/American Indian (0.7%), Asian American (4.2%), Hispanic/Latino (0.7%), and Mixed or Other (6.9%). Participating caregivers were 30 to 61 years old (M = 43.40 years, SD = 6.92) and identified their ethnicities as White (90.3%), African American/Black (2.8%), Asian American (2.8%), Hispanic/Latino (1.4%), and Mixed or Other (2.7%). Most caregivers (97.2%) had graduated from high school or earned a GED certificate. The yearly household income ranged from “less than $10,000” to “$125,000 or more” (Median = “$70,000 to $79,999”).

Measures

Adolescents completed measures of dyadic closeness, by rating the degree to which they agreed with items presented on a 0-10-point slider with 0.1 decimal increments (0=Not at all, 10=A lot). Each were scored such that higher values reflected greater closeness in relationships. Exact relationship codes (e.g., mother, stepmother) were piped into question text for accuracy.

Daily Mother-Father Closeness.

Two items assessed daily MF closeness: (1) “my [mother] and [father] were loving and affectionate with each other today” and (2) “my [mother] and [father] got along with each other well today”? Items were highly correlated r = 0.76 (p < .001). The average MF closeness, across all families, days, and items was 8.18 (SD = 2.39).

Daily Mother-Adolescent Closeness.

Two items assessed MA closeness: (1) “how warm and affectionate was your [mother] with you?” and (2) “how close and connected did you feel to your [mother]?” Items were highly correlated r = 0.88 (p < .001). The average MA closeness, across all families, days, and items, was 8.41 (SD = 2.21).

Daily Father-Adolescent Closeness.

FA closeness was measured with the same items as MA closeness. Items were highly correlated r = 0.90 (p < .001). The average FA closeness across all families, days, and items was 7.54 (SD = 2.93).

Data Preparation

An assumption of LPA is multivariate normality of the items conditional on profiles; although items with non-normal distributions in a sample overall could theoretically still meet this assumption, transforming items that are highly skewed can increase the plausibility of this assumption. In our data, all three indicators for the LPAs (i.e., MF, MA, and FA closeness) were highly, negatively skewed (skewness = −1.45, −1.73, and −1.16, respectively); cube root transformations of 10 minus the raw average score for each of the indicators (DeCoster, 2001; Wilson & Hilferty, 1931) were used to increase the plausibility of this assumption. The three transformed items (skewness = 0.12, 0.21, and −0.07, respectively) were used as indicators in the MLPA. Higher values of transformed indicators represented lower levels of closeness in that dyad on a given day. Missing data on indicators were accounted for under the missing at random assumption using full information maximum likelihood estimation (Widaman, 2006).

Analytic Plan

Data analysis proceeded in two steps. The first step used LPA to identify profiles of unique MFA relationship structures with (transformed) indicators of closeness in MF, MA, and FA dyads at the day level (by pooling data from all families and all days). Standard errors were adjusted to account for days nested within families. LPAs were interpreted using two sets of parameters: (1) latent profile membership probabilities (i.e., profile prevalences), which describe the distribution of the profiles in the sample; and (2) item means (and variances), which describe the means (and variances) of the items within each profile. Profiles were named and interpreted based on the patterns of item means.

Building from the optimal Level-1 (i.e., day-level) solution selected in step one, the second step estimated Level-2 random effects using a non-parametric approach (e.g., Henry & Muthén, 2010). This approach identifies mutually exclusive and exhaustive latent classes at Level-2 based on prevalences of Level-1 profiles within a Level-2 unit. That is, this approach was used to identify latent classes of family dynamics (i.e., at the family-level) with similar patterns of prevalences across days of the identified MFA relationship structures (i.e., at the day-level). To improve model stability, item means for day-level profiles were constrained to be equal to the estimates from step one. Although there are alternative approaches to MLPA (e.g., a parametric approach), the non-parametric approach had distinct advantages here: (1) its estimation of latent class/profile variables at both Level-1 and Level-2 mapped directly onto our theoretical conceptualizations of family dynamics (Level-2) and MFA relationship structures (Level-1); and (2) it avoids strong distributional assumptions for the random effects and is less computationally burdensome (Vermunt & Van Dijk, 2001). Proportions of specific day-level profiles within each family-level class were used to interpret and name the family-level classes that represent unique family dynamics.

To select the optimal model in both steps one and two, a series of models were compared based on (1) model identification, (2) model fit indices, (3) profile stability, and (4) theoretical interpretability (Nylund-Gibson & Choi, 2018; Yu & Park, 2014). A model was deemed “identified” if the best loglikelihood value was replicated at least twice with multiple sets of random starting values. Fit indices included the Akaike information criterion (AIC; Akaike, 1974), Bayesian information criterion (BIC; Schwarz, 1978), sample-size adjusted BIC (a-BIC; Sclove, 1987), entropy (Celeux & Soromenho, 1996), and a bootstrapped likelihood ratio test (BLRT, McLachlan & Peel, 2000). More optimal models are indicated by lower AIC, BIC, and a-BIC, higher entropy, and a non-significant BLRT. Note that the BLRT was only applicable for the day-level (i.e., Level-1 model) and indicates whether a model fits significantly better than the model with one fewer profiles. Profile and class stability were determined by manual inspection of solutions and indicated by minimal changes in item means/response probabilities and profile/class prevalences as successively larger models were considered. Stability after extraction was particularly important for profiles and classes that were small (e.g., 0-10% prevalence). The final, interpreted MLPA should have theoretically distinct and meaningful profiles at both levels, based on item means (and variances) and profile prevalences in the Level-1 model and on proportions of day-level profile prevalences within each family-level class in the Level-2 model. The selected model should also result in high profile/class-specific average posterior probabilities after modal assignment (> 0.70; Nagin, 2005), which provides some indication as to how well the model classifies cases. All models were estimated using Mplus version 8.3 (Muthén & Muthén, 1998-2017); model identification was checked for all models with at least 500 initial stage starts and 100 final stage starts.

Results

Level 1 Profiles: Day-Level MFA Relationship Structures

Models with 1-10 profiles at Level-1 were well-identified and considered for model selection. Model fit and selection information are shown in Table 1. The AIC, BIC, and a-BIC kept decreasing, but with relative improvements declining at about 5 or 6 profiles; entropy suggested models with 5 or more profiles provided somewhat better classification utility than smaller models; the BLRT suggested the 2-profile model as optimal. Given this inconsistency, we relied heavily on profile stability and theoretical interpretability for model selection. Comparing the 5- to 6- profile model, the newly emerged profile was theoretically distinct from all profiles in the 5-profile model, and it helped to refine and stabilize the interpretations and sizes of the other profiles. Comparing the 6- to 7-profile model, the newly emerged profile was repetitive theoretically, suggesting the 6-profile model was more parsimonious and the 7-profile model was likely over-extracted. Regarding the quality of the 6 identified profiles, the 6-profile model had average posterior probabilities ranging between 0.95 and 0.99. Considering all of the above, the 6-profile model was selected as optimal for interpretation and further analysis.

Table 1.

Model Fit Information and Selection Criteria for Latent Profile Models at Two Levels

No. of Profiles	Log-Likelihood	No. of parameters estimated	AIC	BIC	a-BIC	Entropy	BLRT
Level 1 Model Fit and Selection
1	−9060.43	6	18132.86	18168.35	18149.28	--	--
2	−6540.47	10	13100.95	13160.08	13128.31	0.94	0.03
3	−5844.76	14	11717.53	11800.32	11755.84	0.91	0.22
4	−5399.80	18	10835.61	10942.06	10884.86	0.91	0.46
5	−4901.86	22	9847.72	9977.83	9907.93	0.95	0.25
6	−4612.50	26	9277.00	9430.76	9348.15	0.96	0.28
7	−4388.27	30	8836.55	9013.96	8918.64	0.96	0.47
8	−4198.59	34	8465.17	8666.25	8558.22	0.94	0.46
9	−3989.33	38	8054.66	8279.39	8158.65	0.96	0.70
10	−3795.78	42	7675.56	7923.96	7790.50	0.96	0.25
Level 2 Model Fit and Selection
1	−4612.51	8	9241.01	9288.32	9262.90	0.96	--
2	−3611.62	14	7251.23	7334.03	7289.54	0.97	--
3	−3159.17	20	6358.35	6476.63	6413.08	0.97	--
4	−2998.44	26	6048.88	6202.65	6120.03	0.98	--
5	−2881.76	32	5827.51	6016.76	5915.08	0.98	--
6	−2807.94	38	5691.88	5916.61	5795.87	0.97	--
7	−2753.25	44	5594.50	5854.71	5714.90	0.97	--

Notes. AIC = Akaike information criterion; BIC = Bayesian information criterion; a-BIC = sample size adjusted BIC; BLRT = bootstrapped likelihood ratio test. Dashes indicate criterion was not applicable; bold font indicates selected model.

Parameter estimates for the 6-profile model at Level-1 (day-level) are shown in Table 2. The upper entries present profile-specific item means, corresponding significance tests, and effect sizes of differences from overall sample means (Cohen’s d) for the transformed MF/MA/FA closeness indicators within each profile; the lower entries present back-transformed indicators in the raw metric to facilitate interpretation. Approximate Cohen’s d for each indicator in each profile was calculated by taking its profile-specific item mean minus the corresponding overall sample mean, then dividing by the corresponding overall sample standard deviation to determine if profile-specific item means were substantially different from overall means (small: <0.2, medium: 0.2-0.5, large: >0.5; Cohen, 2013). In the transformed metric, higher values indicate lower levels of closeness whereas in the raw metric lower values indicate lower levels of closeness. To make the profile interpretations more intuitive given this difference between the transformed and raw metrics, we used raw metrics to describe each profile’s characteristics (while referring to significance tests and effect sizes that were based on the transformed metrics).

Table 2.

Parameter Estimates for the Six-Profile Model at Level 1

Latent Profile Size (Membership Probability)		P1 Cohesive	P2 Mother- Centered	P3 Adolescent- Centered	P4 MA- Coalition	P5 Disengaged	P6 Average
		n=918 34%	n=238 9%	n=115 4%	n=80 3%	n=624 23%	n=760 28%
Transformed Indicators
	Overall Sample Means (SDs)	Profile-Specific Mean of Each Item [Cohen’s d in comparison to overall sample mean]
MF Closeness	0.80 (0.73)	0.03b [−1.06]	0.05b [−1.03]	1.28a [ 0.66]	1.89a [ 1.49]	1.66a [1.17]	1.08a [0.39]
MA Closeness	0.74 (0.70)	0.09b [−0.93]	0.68 [−0.08]	0.24b [−0.72]	0.06b [−0.98]	1.59a [1.21]	1.01a [0.38]
FA Closeness	0.94 (0.77)	0.05b [−1.16]	1.32a [ 0.49]	0.05b [−1.16]	1.92a [ 1.27]	1.80a [1.12]	1.22a [0.37]
Raw Indicators
	Overall Sample Medians/Means (SDs)	Profile-Specific Mean of Each Item
MF Closeness	9.25 / 8.18 (2.39)	10.00	10.00	7.90	3.25	5.47	8.73
MA Closeness	9.45 / 8.41 (2.21)	10.00	9.68	9.99	10.00	6.01	8.97
FA Closeness	8.60 / 7.54 (2.93)	10.00	7.72	10.00	2.94	4.18	8.17

Notes. P1 ~ P6 = Profile 1 ~ Profile 6 (at Level 1).

Profile prevalences may not sum to 100% because of rounding.

Given that the raw data were highly skewed, medians and means for the whole sample are listed for reference in the raw data.

Higher values in transformed MF/MA/FA closeness indicated lower levels of closeness in that dyad; higher values in raw MF/MA/FA closeness indicated higher levels of closeness in that dyad.

^aValue is statistically significantly higher than the overall item mean at p < .05, which means closeness is lower than the sample mean in the dyad due to item transformation for analysis.

^bValue is statistically significantly lower than the overall item mean at p < .05, which means closeness is higher than the sample mean in the dyad due to item transformation for analysis.

Cohen’s d for each indicator in each profile was calculated by taking its profile-specific item mean minus the corresponding overall sample mean, then dividing by the corresponding overall sample standard deviation (effect size: 0.2<small<0.5, 0.5<medium<0.8, large>0.8).

Profile 1 (33% of all days) was characterized by significantly higher than sample mean levels of MF, MA, and FA closeness (with large effect sizes); this profile was labeled Cohesive (MFA relationship structure). Profile 2 (9%) was characterized by significantly higher than sample mean level of MF (in large effect size), average MA, and significantly lower than sample mean level of FA (in medium effect size) closeness; this profile was labeled Mother-Centered. Profile 3 (4%) was characterized by significantly lower than sample mean level of MF closeness and significantly higher than sample mean levels of MA and FA closeness (in medium to large effect sizes); this profile was labeled Adolescent-Centered. Profile 4 (3%) was characterized by significantly lower than sample mean levels of MF and FA closeness and significantly higher than sample mean level of MA closeness (with large effect sizes); this profile was labeled MA-Coalition. Profile 5 (23%) was characterized by significantly lower than sample mean levels of MF, MA, and FA closeness (with large effect sizes); this profile was labeled Disengaged. Profile 6 (28%) was also characterized by significantly lower than sample mean levels of closeness in all three dyads (in small effect sizes), but in terms of practical significance were essentially average, which is supported by (1) small effect sizes in transformed metrics and (2) close to overall sample means in raw metrics; this profile was labeled Average.

Level 2 Classes: Family-Level MFA Relationship Dynamics

Models with 1-7 classes at Level-2 and 6 Level-1 profiles were well-identified and considered for model selection. Model fit and selection information are shown in Table 1. Similar to Level-1, for the Level-2 model the AIC, BIC, and a-BIC kept decreasing, but with relative improvements declining at about 5 classes; entropy suggested models with 4 or 5 classes provided somewhat better classification utility than other models. Given this inconsistency, we again relied heavily on class stability and theoretical interpretability for model selection. Comparing the 4- to 5-class model, a new theoretically distinct class emerged that refined the interpretations of classes in the 5-class model. Comparing the 5- to 6-class model, the newly emerged class was repetitive theoretically, suggesting the 5-class model was more parsimonious and the 6-class model was likely over-extracted. Regarding the quality of the 5 identified classes, the 5-class model had average posterior probabilities ranging between 0.84 and 1.00. Considering all of the above, the 5-class model was selected as optimal for interpretation.

Parameter estimates for the 5-class model at Level-2 (family level) with 6 profiles at Level-1 (day level) are shown in Table 3. Class 1 was comprised of families that exhibited a Cohesive structure most days (85% of their days); this class was labeled Stable Cohesive and represented 35% of all families and 35% of all days. Class 2 was comprised of families that exhibited a Disengaged structure most days (91% of their days); this class was labeled Stable Disengaged and represented 20% of all families and 19% of all days. Class 3 was comprised of families that exhibited a MA-Coalition structure most days (73% of their days); this class was labeled Stable MA-Coalition and represented 3% of all families and 4% of all days. Class 4 was comprised of families that exhibited an Average structure most days (83% of their days); this class was labeled Stable Average and represented 24% of families and 25% of all days. Class 5 was comprised of families that exhibited multiple different structures across their days: 19% of their days were Cohesive, 34% Mother-Centered, 7% Adolescent-Centered, 3% MA-Coalition, 9% Disengaged, and 28% Average. This class was labeled Variable and represented 17% of families and 18% of all days.

Table 3.

Parameter Estimates for the Level-2 5-Class Level-1 6-Profile Model

Level-2 Class Membership Prevalence (Nfamily)	C1 Stable Cohesive 35% (N=50)	C2 Stable Disengaged 20% (N=29)	C3 Stable MA-Coalition 3% (N=5)	C4 Stable Average 24% (N=35)	C5 Variable 17% (N=25)
	Level-1 Profile Prevalence (nday) Conditional on Level-2 Class
P1: Cohesive	0.85 (nday=808)	0.04 (nday=2)	0.00 (nday=0)	0.01 (nday=10)	0.19 (nday=93)
P2: Mother-Centered	0.04 (nday=41)	0.02 (nday=10)	0.04 (nday=4)	0.05 (nday=32)	0.34 (nday=161)
P3: Adolescent-Centered	0.06 (nday=55)	0.01 (nday=2)	0.08 (nday=8)	0.03 (nday=17)	0.07 (nday=34)
P4: MA-Coalition	0.00 (nday=0)	0.01 (nday=5)	0.73 (nday =71)	0.00 (nday=0)	0.03 (nday=13)
P5: Disengaged	0.02 (nday=17)	0.91 (nday=483)	0.14 (nday=13)	0.08 (nday=53)	0.09 (nday=43)
P6: Average	0.03 (nday=34)	0.01 (nday=30)	0.01 (nday=1)	0.83 (nday=559)	0.28 (nday=136)

Notes. Profile prevalences may not sum to 100% down a column because of rounding.

C1 ~ C5 = Class 1 ~ Class 5 (at Level-2).

P1 ~ P6 = Profile 1 ~ Profile 6 (at Level-1).

Bold font indicates a percentage of days higher than 50% within a given Level-2 class.

Item-response means (and variances) for each Level-1 profile are identical to the values in the Level-1 6-profile model presented in Table 2. To save space, the redundant information is not presented here.

Discussion

This study examined a core feature of structural family systems theory: to understand the patterns of MFA relationships in families, using adolescent-report data. Of particular novelty, family structures were not only characterized across family subgroups, but also in terms of how they fluctuate on a daily basis within families, using MLPA. Thus, we evaluated whether it was possible to identify the 8 proposed unique family structures using adolescent-report data, and whether these family structures were stable or dynamic over a 21-day period. To our knowledge, this is the first study using empirical data to test hypotheses about both structures and dynamics among multiple family relationships in family systems from a person-centered perspective.

MFA Relationship Structures in Family Systems

Our findings lend support to propositions that MFA relationships organize in families in meaningful patterns that conform to theorized structures. Specifically, our findings supported 5 of the 8 hypothesized structures: cohesive, disengaged, mother-centered, adolescent-centered and MA coalitions. Of these, cohesive, disengaged, and coalition structures replicate prior studies documenting similar family relationship structures, suggesting these structures may be particularly robust (e.g., Bell et al., 2001; Kerig, 1995; Sturge-Apple et al., 2014). We also identified two family structures that are characterized by two strong relationships – M-centered and A-centered families – and are less well understood, calling for work investigating the implications of these structures for individual development.

Three hypothesized family structures did not emerge in our analyses: Father-Centered, FA-Coalition, and MF-Coalition. It is possible that our study was unable to detect these families, because of our low-risk sample, where alliances tend to be less prevalent (Bell et al., 2001). Moreover, mothers often are more involved in childrearing and have closer relationships with their adolescents than fathers (McBride & Mills, 1993; Yan, 2017), and adolescents tend to feel closer to mothers than fathers (Grych et al., 2004). Thus, it is possible that future studies using larger samples of families across a broader spectrum of family risk may find Father-Centered and FA-Coalition structures. Nonetheless, the promising nature of our preliminary findings encourage future studies to pursue a range of family structures to enrich the understanding, accuracy, and generalizability of findings on MFA relationships.

The Daily Dynamics of Family Structures

A second contribution of this paper is the finding that there are meaningful ways in which family structures fluctuate on a daily basis. Variability—or the lack thereof—may be an important dimension of family risk that is overlooked in traditional family assessment methods (Fosco et al., 2019). This dynamic perspective on family functioning enables tests of theoretical assumptions and the ability to address deeper family systems questions, such as: Are cohesive and disengaged families stable by nature? How stable are they? Which structures are stable and which ones are not? Answering such questions about stability and variability may provide important insights into adolescent development (Fosco & Lydon-Staley, 2020).

In this study, the majority of families exhibited stable structures across the 21 days. In addition to the expected Stable Cohesive and Stable Disengaged families, two additional stable dynamics—Stable MA-Coalition and Stable Average—were also found. These findings lend empirical support to long-standing clinical observations: that families may establish interactional patterns of relating to one another that become crystalized into normal, everyday functioning (Minuchin, 1974). As such, these findings support family assessment techniques that seek to elicit family interactions to gain insight into whether there are problematic patterns of disengagement, or coalitions that may undermine family health.

As hypothesized, some families fluctuated in their relationship structures from day to day. In particular, unbalanced structures (e.g., Adolescent-Centered and Mother-Centered)—where connections centered around one person—tend to be unstable and fluctuate more frequently from day to day. In addition, a Variable dynamic was identified in our study. With 17% of families and 18% of days in this sample belonging to this class, this finding provides empirical evidence suggesting that changes in family relationships are not uncommon. In particular, Variable dynamic families exhibited moderate to close relationships among the three family members on 81% of their days (19% Cohesive, 34% Mother-Centered, and 28% Average), despite the fluctuating nature of these families. By examining fluctuations in structure, our findings raise important questions about the nature of family variability. It may be the case that variability reflects adaptability to a dynamic extra-familial context, which may support family health (Olson, 2000). A deeper understanding of the implications of various patterns of fluctuation is needed; future studies that directly investigate how family structure variability impact adolescent development will enrich our understanding.

Harnessing Innovative Methods to Enrich Family Science

Historically, research methodology has lagged behind the complex processes theorized about family systems. Our study provides a demonstration of how innovative methods, such as MLPA, are capable of characterizing complex and abstract theories of family process. MLPA is able to capture features across multiple subsystems simultaneously and tap into nonlinear relations among different profiles. This study included continuous indicators of MF, MA, and FA closeness, and MLPA is capable of identifying profiles with any combinations of higher, lower, or average levels for each dyad. Future work may leverage MLPA to extend our models to include multiple family members’ perspectives on the same construct (e.g., parent’s and child’s perspectives on parent-child closeness) and other family system elements, such as other subsystems (e.g., sibling dyad) and other aspects of the same subsystems (e.g., dyadic conflict in addition to closeness). MLPA is a flexible approach that offers a holistic approach to family systems science.

Additionally, as we demonstrated in this study, MLPA can leverage intensive longitudinal data (e.g., daily diaries), nested within families, to differentiate family structures (Level-1) and their dynamic combinations over time (Level-2), by identifying subgroups in organization and patterned change across days. This concept, highlighted in the current study, allows for a more accurate, nuanced characterization of family functioning and provides new insights for understanding families as living, dynamic systems.

Limitations and Conclusion

This study is not without limitations. First, our sample was relatively small, limited in racial/ethnic diversity, and mostly well-educated, middle-class families. As a result, our family profiles were defined through relative comparisons to the sample averages, suggesting our identified family structures should be interpreted with caution and in a relative rather than absolute terms (i.e., more or less close, rather than close or distant). As an example, average closeness in this study was higher than would be expected in a clinical sample. Thus, families labeled “average structures” may be higher than an average level found in a clinical sample. Future studies should seek to generate a more inclusive and diverse sample, with special consideration to family risk (e.g., community and clinical samples) as well as socioeconomic, racial/ethnic, sexual, and gender diversity. Additionally, larger samples are needed to replicate profiles from this study that had smaller group sizes (e.g., MA coalition). Second, some dyadic closeness items assessed behavior (e.g., expression warmth and affection) instead of focusing on the quality of relationship bonds; replication with direct relational indicators of closeness would help validate our findings. Third, the labels for identified family structures and dynamics were based only on assessments of the levels of closeness in three dyads, leaving other aspects of family relationships unknown (e.g., hostility). Future studies that include other family process indicators, such as dyadic conflict, would provide a more comprehensive understanding on the family functioning. Fourth, our study relied solely on adolescent report data, limiting generalizability of our findings to the adolescent perspectives of the family. Multi-informant data will be critical in more fully characterizing family structures in future studies.

Some challenges and suggestions for using MLPA are worth mentioning. Similar to traditional LPA, MLPA is sensitive to multivariate normality assumptions. Indicator selection and plausibility of assumptions need to be considered carefully with any LPA. Moreover, given the comparatively heavy computational burden and complexity of identifying latent classes at both levels, users of MLPA may experience model identification and estimation limitations as the number of Level-2 classes increases. As with many categorical variable models, sparseness can be an issue, particularly as models increase in complexity; parameter restrictions on the Level-1 model may sometimes be required. Finally, when using continuous indicators, increased ranges for the responses can be helpful. Thus, we would recommend using, for example, a slider rather than a Likert scale to increase variability, particularly across days in a daily diary design.

Despite these limitations, this is one of the first family studies that explores diverse forms of MFA relationship structures in normal daily life, considering the dynamic aspects of family relationship structures, and illustrates how MLPA and daily diary data can be used to empirically test specific hypotheses posited by complex, abstract family systems theory. Findings also have several implications for family-based assessment, therapy, and intervention. First, our findings converge with a growing literature calling for more intensive (e.g., daily diary) assessment methods to gain a more comprehensive picture of family functioning (e.g., Fosco et al. 2019). Indeed, our findings suggest that the within-family variability is an important component to understand the overall family functioning. Second, beyond assessments, family therapists may benefit from incorporating dynamic characteristics of the family into their conceptualization of the family. In some families, it may be more salient to address the degree of fluctuation in closeness than the level of closeness. Our findings suggest that day-to-day variability was a defining characteristic in a meaningful subset of families. Third, family-based interventions will be more effective in changing the holistic family interaction pattern if they intervene with multiple dyadic relationships simultaneously, rather than focusing on a subset of the family (e.g., working only with parents).