Ab Initio International 2010
Feature Article

Use of the Asymmetric Block Design and Variance Component Analysis in Research on Adult-Child Language Interaction

Thomas E. Malloy, Ph.D. Rhode Island College
Beverly Goldfield, Ed.D. Rhode Island College

This research was supported by RI-INBRE Grant # P20RR016457 from the National Center for Research Resources (NCRR), a component of the National Institutes of Health (NIH). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of NCRR or NIH. We thank Dr. Kathleen McCartney for sharing her data with us and Dr. Elizabeth Jordan for her assistance with the organization of the data set.

Research Goals



3 babiesAlthough dyadic processes are central in some developmental theories, dyadic research has not received sufficient attention in developmental psychology. However, recent methodological advances and the availability of software for dyadic research have energized work in this area. We demonstrate the use of the asymmetric block design and variance component analysis in a study of language behavior in adult-child dyads. Results showed that adult women adapt their speech to a 28-month-old child’s speech, particularly when that child is a biological offspring.
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In some developmental theories, dyadic processes are the major mechanism for change. Vygotsky (1962), for example, viewed adult-child interaction as the basis for the construction of mind, moving thought from the interpersonal to the intrapersonal over time. Social-interaction theories of language development (e.g., Bruner, 1978; Ninio & Snow, 1999; Tomasello, 2003) likewise examine the emergence of linguistic skill within the context of talk between a proficient adult and a novice communicator. Numerous studies have documented adults using shorter, simpler sentences while talking to children about visible objects and ongoing activities (e.g., Snow, 1972; Cross, 1977; Hoff-Ginsburg, 1986).

Social interaction theories of language posit that children cue adults to provide the appropriate level of language experience that both fits the child’s current skills and leads to language advancement, creating a dynamic system between the child and the language environment (Bohannon & Bonvillian, 2009). What remains unclear is the precise nature of both child cues and adult adjustment. The study of these dyadic variables has remained elusive, in part because they are complex, inter-dependent behaviors that pose significant analytic challenges. Fortunately, methodological developments in the past 25 years have energized research on dyadic interaction making this research much more practical. (Kenny LaVoie, 1984; Malloy Albright, 2001; Kenny, Kashy, Cook, 2006). Yet, in spite of these developments, research on child-adult language interaction has been slow to utilize these new methods.
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Research Goals

In this paper we introduce a conceptual and statistical model of child-adult language interaction, and discuss a research design well suited for dyadic research. We also present an empirical example.

A Model of Child-Adult Language Interaction
If child C interacts with her mother M and a verbal behavior from each is recorded (X), the score on X for each member of the dyad can be expressed theoretically.   Equation 1 is a model of child C’s verbal response to her mother.

Xcm  = M + αc + βm + γcm + ecm    (Equation 1)

where M is the average level of children’s verbal behavior on X, αc is the consistency of C’s verbal behavior when interacting with adults (including the mother) and is called an actor effect, βm is the verbal behavior elicited by mother M when interacting with children (including her child) and is called a partner effect, γcm is child C’s unique verbal response on X made to her mother and is called a uniqueness effect, and ecm is random error. Likewise, mother M’s verbal response to her child is represented by equation 2.

Xmc  = M + αm + βc + γmc + emc    (Equation 2)

where M is the average level of verbal behavior on X when adults respond to children, αm is the consistency of M’s verbal behavior when interacting with children (including her child) and is an actor effect, βm is the verbal behavior elicited by child C when interacting with adults (including her mother) and is a partner effect, γmc is mother M’s unique verbal response to her child C on variable X and is a uniqueness effect, and emc is random error. This model of child-adult dyadic language interaction is based on the Social Relations Model (Kenny & LaVoie, 1984) and acknowledges that responses in a dyad are due to the person, the person’s partner, and the person’s unique response to a specific partner. To estimate the terms of equations 1 and 2 specialized research designs are required (Malloy & Albright, 2001); the asymmetric block design is one example.


The Asymmetric Block Design
Dyad members may be distinguishable or indistinguishable on a dimension relevant to the behavior of interest; mothers and children are distinguishable developmentally whereas same sex peers are not. When dyad members are distinguishable, the asymmetric block design (ABD) is well suited for research on the behavior of people at different levels of development.

To illustrate the ABD, imagine that two 28- month-old children interact with two adult women in separate dyadic interactions and that the mean lengths of children’s and adults’ utterances in each dyad are measured. The resulting data structure would be an ABD.

Table 1: Asymmetric Block Design

  C1 C2 M1 M2
C1     x x
C2     x x
M1 x x    
M2 x x    

Note. M is a mother and C is a child. An x is a measure of verbal behavior in a dyadic interaction.

Adults do not interact with adults, nor do children interact with children. Data from the ABD permit estimation of the parameters of equations 1 and 2, as well as the reciprocity in child-adult verbal behavior. Below we describe how the terms of equations 1 and 2 are used to compute variance components that quantify conceptually distinct language phenomena.

Variance Component Analysis: Actor, partner, and uniqueness variance
Analysis of data from the ABD departs from traditional analyses. Phenomena are not estimated by points such as the mean, but rather by variance components. The terms of equations 1 and 2 (i.e., α, β, and γ components) are estimated and the variances of these terms are computed. A study has many asymmetric blocks; within each the terms of equations 1 and 2 are estimated and pooled across blocks. The null hypothesis is that a variance component equals zero, and tested with a one sample t test (degrees of freedom equal to the number of asymmetric blocks minus 1.00). These variance components quantify conceptually distinct forms of verbal behavior in child-adult dyads, and when standardized as proportion of total variance can range from 0 to 1.00.

Table 2: Variance Components in Verbal Behavior in Adult-Child Dyads

Children’s Verbal Responses to Adults

Variance Component Psychological Interpretation
Actor αc² Individual differences among children in the verbal behavior emitted consistently with multiple adults
Partner βm² Individual differences among adults in the verbal behavior elicited consistently from multiple children
Uniqueness γcm² A unique verbal response by a specific child to a specific adult after controlling for the child’s actor effect and the adult’s partner effect


Adults’ Verbal Responses to Children

Variance Component Psychological Interpretation
Actor αm² Individual differences among adults in the verbal behavior emitted consistently with multiple children
Partner βc² Individual differences among children in the verbal behavior elicited consistently from multiple adults
Uniqueness γmc² A unique verbal response by a specific adult to a specific child after controlling for the adult's actor effect and the child's partner effect


Two forms of reciprocity are estimated using the terms of equations 1 and 2; generalized and dyadic. Individual person is the unit of analysis for generalized reciprocity and dyad is the unit for dyadic reciprocity. Generalized reciprocity examines whether the consistency of verbal behavior emitted when interacting with multiple partners is associated with the consistent elicitation of that behavior from them.  For example, do children who use very short sentences when speaking with adults elicit short sentences from the adults with whom they interact? For adults, generalized reciprocity is estimated by the correlation of αm (from equation 1) and βm (from equation 2); for children, this estimate is the correlation of αc (from equation 1) and βc (from equation 2). These are termed actor-partner correlations. 

Dyadic reciprocity occurs at the level of the dyad, and is the association of unique responses that people make to one another (γcm and γmc of equations 1 and 2, respectively).If an adult tends to use long utterances when speaking with her own child, does her child tend to use long utterances when speaking to her? Dyadic reciprocity is estimated after generalized reciprocity has been controlled; each is psychologically distinct and failure to separate them is a conceptual error (Kenny & Nasby, 1980)

Different software can be used to estimate the terms of equations 1 and 2, the variance components, and the reciprocity correlations of interest in dyadic research (Kenny et al., 2006). We prefer to use BLOCKO software that is available for free at http://davidakenny.net/srm/srmp.htm
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The data reported here are a subset of a longitudinal study of adult-child language interaction by McCartney and her colleagues (1991) and have not been published.

Participants were recruited in Massachusetts. Dyadic interactions occurred in 25 minute laboratory play sessions when children were 28 months of age; each mother played with her own child and another child.Children were first born and matched on sex and age (within two weeks). Videotaped interactions were transcribed producing a data base of reciprocal language samples for mothers and children. There were 38 asymmetric blocks; each contained 2 mothers and 2 children. Additional specific details of this project are available in McCartney et al. (1991).

Two variables indicated utterance length: mean length of utterance (MLU) and mean upper bound (MUB; the median of the five most syntactically complex utterances). Utterance length indexes syntactic and semantic complexity, with longer utterances indicating more meaning and structure.  Six variables were related to specific syntactic structures, including noun phrases per utterance  (NP),  inflections per noun phrase  (INFL; e.g., plural or possessive s), verb phrases per utterance (VP), auxiliaries per verb phrase (AUX; e.g., will, could, should), WH questions per utterance (WH-Q), and negatives per utterance (Neg_Utt).In addition, we computed two factors using verbal behaviors that were most frequent. One factor was sentence length that was indicated by MLU and MUB; another factor was sentence complexity that was indicated by noun and verb phrases. Factors were formed by averaging scores on the measured variables with reliabilities of .85 and .83 for children and .63 and .78 for adults, respectively.
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Variance Components: Mothers with Children
Significant actor variance in mothers’ verbal responses to children was observed on three variables: MLU (.417), MUB (.321), and NP (.415), and the median actor variance component across the eight variables was .157. This showed that mothers’ sentence lengths and use of noun phrases were consistent while interacting with their own and another 28 month-old-child. Different children elicited similar verbal responses from their mothers and non-mothers. The median partner variance component across the eight variables was .125; about 13% of the variance in language behavior of mothers to children was elicited by variation among children in their language ability.

Because uniqueness variance is confounded with error in the univariate analysis, we partitioned stable uniqueness variance from error for the sentence length and sentence complexity constructs. The remaining variables were not included in constructs because they occurred with a low frequency. Analysis of the sentence length construct showed that actor, partner, and uniqueness variance accounted for about 16%, 3%, and 19% of the total variance in sentence length. This showed that the length of mothers’ sentences to children was stable across interaction with their own and another child; children did not elicit similar sentence lengths from two adults, and mothers adjusted language length with specific children. For the sentence complexity construct, results showed that actor, partner, and uniqueness variance components accounted for about 16%, 7%, and 37% of the variance in sentence complexity. Mothers used similarly complex sentences with different children, different children elicited more or less complex sentences from different adults, and mothers substantially adjusted sentence complexity with specific children. These results are summarized in Table 3.

Table 3: Variance Components and Means: Mothers with Children


Variable Actor  Partner Uniqueness Mean
MLU .417* .123 .460 5.00
MUB .321* .000 .679 14.96
NP .415* .162 .422 1.54
VP .192 .111 .697 1.04
AUX .011 .092 .897 .33
INFL .043 .208 .749 .05
WH-Q .122 .127 .751 .11
NEG_UT .092 .172 .736 .07



Construct Actor  Partner Uniqueness Mean
Sentence Length .163 .028 .190 9.98
Sentence Complexity .156 .072 .372 1.29

* Variance component is significantly different from zero.


Variance Components: Children with Mothers
Significant and quite substantial actor variance in children’s verbal responses to adults was observed on seven of eight variables: MLU (.840), MUB (.660), and NP (.643), VP (.633), AUX (.437), INFL (.419), and NEG_UTT (.265).   The median actor variance component across the eight variables was .535. These results showed that the language behavior of 28-month-old children was very consistent in their interactions with their own and another mother.  There was no evidence that different women elicited similar verbal responses from their own child and another child. The median partner variance component across the eight variables was .00.

For children’s verbal responses to adults, analysis of the sentence length construct showed that actor, partner, and uniqueness variance accounted for about 56%, 0%, and 13% of the total variance in sentence length. This showed that the length of children’s sentences to adults was highly stable across interaction with their own and another mother, mothers did not elicit similar sentence lengths from two children, and children adjusted somewhat their sentence length with specific adults. For the sentence complexity construct, actor, partner, and uniqueness variance components accounted for about 49%, 0%, and 14% of the variance in sentence complexity. Children were highly consistent in the use of sentence complexity with different adults, different adults did not elicit more or less complex sentences from different children, and children adjusted sentence complexity with specific adults. We return to this finding later in the discussion. These results are presented in Table 4.

Table 4: Variance Components and Means: Children with Mothers


Variable Actor Partner Uniqueness Mean
MLU .840* .000 .160 3.01
MUB .660* .000 .340 6.34
NP .643* .000 .357 1.06
VP .633* .000 .367 .62
AUX .437* .174* .389 .21
INFL .419* .157 .424 .04
WH-Q .022 .000 .978 .09
NEG_UTT .265* .000 .735 .06



Construct Actor Partner Uniqueness Mean
Sentence Length .564 .000 .125 4.68
Sentence Complexity .494 .000 .140 .84

* Variance component is significantly different from zero.

There was very strong evidence for generalized and dyadic reciprocity of language use in child-adult dyads. At the individual level of analysis, generalized reciprocity only occurred in children’s responses to adults with estimates of r = .98 and r = .99 for the sentence length and complexity constructs, respectively. Children who consistently used short or long sentences elicited short or long sentences from the adults with whom they interacted. Children who consistently used more or less complex sentences elicited sentences from adults that matched this level of complexity. These results are consistent with the prediction of Kenny and Malloy’s (1988) partner effect model that actor effects are the cause of partner effects. In this case, individual differences among 28-month-old children that were consistent across interactions with adult women (i.e., actor effects) elicited consistent language responses from two women (i.e. partner effects). Because children were generally unresponsive to sentence length and complexity of mothers’ utterances, adults’ generalized reciprocity correlations were r = .00 for these two constructs.

Dyadic reciprocity correlations (see Table 5) were substantial and statistically significant for the sentence length and complexity constructs with estimates of r = .75 and r = .61, respectively. Because it was mothers who adjusted their verbal behavior with children, these results demonstrate that if a specific child used short or long sentences, or more or less complex sentences, adult women matched these verbalizations in specific dyads.

Table 5

Generalized and Dyadic Reciprocity

Construct Actor with Partner Generalized Reciprocity
Sentence Length Mothers with Children r = .00
Sentence Complexity Mothers with Children r = .00
Sentence Length Children with Mothers r = .98*
Sentence Complexity Children with Mothers r = .99*


Dyadic Reciprocity

Construct Actor with Partner Dyadic Reciprocity
Sentence Length Specific Mothers with Specific Children r = .75*
Sentence Complexity Specific Mothers with Specific Children r = .61*

Note. * p < .05
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Although dyadic processes are core mechanisms of influential theories in developmental psychology (Vygotsky, 1962; Bowlby, 1969; Bronfenbrenner, 1995) and in theories of language development (Bruner, 1978; Ninio & Snow, 1996; Tomasello, 2003), empirical work on dyads has been slow to progress. Dyadic research has posed significant challenges for those who have undertaken it; in fact, some developmental psychologists have actively avoided dyadic research (see Applebaum & McCall, 1983). Although there were early solutions offered to developmental psychologists interested in dyadic processes (Kramer & Jacklin, 1979), there has been a dramatic increase in the development of sophisticated new methods (Card et al., 2008).

Perhaps the most fundamental issue to be confronted is the non-independence of data within dyads that occurs because one’s response affects the response of the other. In addition, dyadic research is complex because of the theoretical necessity of considering the actor, partner, and uniqueness effects delineated in Table 2. Yet even when these theoretical effects are recognized, one must design research so that they may be estimated. We discuss these challenges.

In classic psychological research an individual is presented with a stimulus and a response is recorded. Data from different individuals provide independent information on which statistical analyses are based; if 100 (N) independent pieces of information (i.e., data) are gathered from 100 participants there are 99 total degrees of freedom (N – 1); there are 99 independent pieces of information. In dyadic research the situation is more complex. Because interacting people affect each other’s responses, it is unlikely that measurements of their behaviors are independent. Rather, one’s score may be dependent, to some degree, on the score of the other. In our distinguishable dyads we estimated non-independence within dyads using the Pearson product-moment correlation. When dyad members are indistinguishable (e.g., two same sex peers) the intraclass correlation coefficient can be used (Kenny et al., 2006). Non-independence of data within dyads is important because one may think there is more independent data upon which to base inferences than is actually the case.

Consider adult and child scores on the MLU variable. If the length of utterances by one member affects the length of utterances of the other member, then these responses are non-independent.  When women interacted with their own children the correlation of their MLU scores was r = .56, p < .05, but when women interacted with the other child the correlation of their MLU scores was r = .02, p > .05. MLU scores were substantially dependent in mother-child dyads, but not in biologically unrelated dyads.

That the non-independence was substantially larger in mother-offspring dyads suggests that mothers were responding uniquely to their own children.  Given this non-independence in biological dyads, failure to undertake the analysis used here could lead to substantial bias and inferential error. Non-independence produces bias by presuming more independent information (i.e., degrees of freedom) than actually exists and making inferences based on that presumption. Variance component analysis treats non-independence as a phenomenon worthy of study and not a statistical nuisance.

Conceptual Precision
Equations 1 and 2 are a precise specification of the effects that determine language behavior in a dyad. Our findings suggest that there is substantial cross-situational consistency of language behavior among 28 month-old-children while interacting with their mothers and another adult woman. In addition, children elicited similar language responses from two women, and there was evidence of unique responses by specific women to specific children.  That the correlation for MLU’s was greater in biologically linked than in non-biologically linked dyads suggested that mothers were uniquely responsive linguistically to their own children. Mothers’ language behavior was much less consistent in interaction with two children, and there was no evidence they elicited similar responses from different children. Adult women were uniquely responsive to specific children; their own.

These findings show the theoretical importance of the effects specified in equations 1 and 2; they were only estimable because the data were from an ABD with reciprocal measurements. Often in dyadic research there is only one partner; for example, a mother interacts with her child and language behavior for each is measured.  While there are some dyadic analyses that can be conducted with this classical dyadic design (Kenny et al., 2006) there are limitations. Such a design provides insufficient measured information to estimate all of the terms of equations 1 and 2. Consequently, conceptually distinct phenomena indexed by actor, partner, and uniqueness variance components are confounded. As a result, findings based on un-decomposed scores (i.e., Xmc and Xcm ) of Equations 1 and 2 are difficult to interpret because one cannot know precisely which effects are determining verbal responses. If Xmc and Xcm are correlated, one cannot know if the observed correlation is due to generalized processes (e.g., the correlation of αc and βc for the sentence length construct which was r = .98) or dyad specific processes (i.e., the correlation of γc γm for sentence length which was r = .75).
To achieve conceptual precision it is advantageous to use a design where participants interact with more than one person. Use of the ABD permits a departure from traditional statistical analysis that involves the estimation of means; ANOVA is the classical case. Within social psychology (e.g., Kenny, West, Malloy, & Albright, 2006) and developmental psychology (e.g., Malloy and Cillessen, 2008) there has been increased use of variance component analysis to study phenomena quantified by variances rather than means. A comprehensive treatment of different dyadic research designs and statistical models for analyses of data from them in developmental science is presented in Card et al., (2008).

Broader Theoretical Implications
The complexity – consistency hypothesis states that the actor, partner, and uniqueness effects in dyads vary systematically with cortex size; that is, as one ascends the phylogenetic scale (Malloy et al., 2005). Animals with very little cortex, such as mice, are predicted to show considerable cross-situational consistency in behavior (i.e. actor effects) as well as the consistent elicitation of behavior from conspecifices (i.e., partner effects) because behavior emitted and elicited is controlled rigidly by primitive brain centers. As cortex increases, there is more behavioral flexibility and there should be an increase in uniqueness effects. While data to test this hypothesis are difficult to accumulate, there is some empirical support for this proposition (e.g., Malloy, Barcelos, Arruda, DeRosa, & Fonseca, 2005; Malloy & Cillessen, 2008).

This logic may be extended to developmental processes. An adult with a highly integrated cortex should show greater behavioral flexibility than a child with a relatively less integrated cortex.The present results are consistent with this prediction. Twenty- eight- month-old children’s actor effects were very strong and their partner effects were present, yet modest. These same effects were substantially weaker among adult women who displayed both generalized and dyadic linguistic adjustment to children in general and to specific children. Mothers adapted, children did not. Mothers appeared to fine-tune the length and complexity of their utterances in response to these same cues in the utterances of their less competent conversational partners. While perhaps unsurprising, this finding could not have been isolated in natural social interaction without the unique design used and the variance component analysis. We suggest that others consider instituting these methods to address other dyadic developmental phenomena.
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