In defense of unresolved attachment: re-modelling intergenerational transmission of attachment

ABSTRACT Intergenerational transmission of attachment is one of the core hypotheses of attachment theory. How parents or other caregivers look back on their childhood attachment experiences is suggested to shape their infants’ attachments. In the current paper, we show that a new twist to correspondence analysis (Canonical Correlation Analysis [CCA]) of cross-tabulated attachment classifications with oblique rotation Correspondence Analysis (CA) may uncover the latent structure of intergenerational transmission showing the unique role of parental Unresolved representations in predicting infant Disorganized attachments. Our model of intergenerational transmission of attachment supports predicted associations between parental and infant attachments. Despite growing skepticism about the validity of parental Unresolved trauma and infant Disorganized attachment, we come to an evidence-based statistical defense of these generative clinical components of attachment theory awaiting a substantive experimentum crucis.


Introduction
The correspondence between parental attachment representations and infant attachment classifications, labeled "intergenerational transmission of attachment," is one of the core hypotheses of attachment theory. How parents or other caregivers look back on their childhood attachment experiences as assessed with the Adult Attachment Interview (Hesse, 2016;Main et al., 1985) is suggested to shape their infants' attachments as observed in the Strange Situation Procedure (Ainsworth et al., 1978). The validity of the Adult Attachment Interview hinges on its predicted associations with infant attachment CONTACT Marinus H. van IJzendoorn marinusvanijzendoorn@gmail.com Author Note: John Bowlby wisely advised Mary Ainsworth to use the capital letters ABC for the infant-parent attachment classifications to save space and make for quick communication of the organized Strange Situation responses: Secure, Resistant and Avoidant. ABC notations however make papers less readable which is why we decided to use the full classification labels when referrring to Adult Attachment Interview responses: Autonomous, Dismissing, Preoccupied, and Unresolved, and similarly for infant-parent attachment classifications: Secure, Avoidant, Resistant, and Disorganized. In the current paper, the Strange Situation labels always refer to the parent whose AAI pattern of attachment is being considered in the intergenerational comparison. This way we hope to (i) increase readability and at the same time (2) emphasize that attachment in infancy is a relationship-specific construct, while attachment in adult is normally a construct applying to a singular AAI pattern of response that may or may not accompany Unresolved loss/trauma. classifications . Intergenerational transmission of attachment has been studied on several levels, from a simple association between secure-autonomous attachment representations of the parents and secure infant attachment classifications to more complex models differentiating between several types of insecure parental representations and infant attachment patterns. Here we present a re-analysis of the most differentiated model in the literature up to date (Verhage et al., 2016) and show that a new twist to correspondence analysis (CA) of crosstabulated data may uncover the latent structure of intergenerational transmission examining the contested role of parental unresolved representations in predicting infant disorganized attachments.
In a first meta-analysis on intergenerational transmission of attachment, the correspondence between parental and child attachment was shown to be impressive. In a 4 × 4 crosstabulation of the four parental attachment representations (Dismissing, Autonomous, Preoccupied, and Unresolved) with the infant attachment classifications (Avoidant, Secure, Resistant, and Disorganized) the correspondence for N = 548 parent-child dyads was found to be in accordance with the prediction in 63% of the cases, with a chance-corrected kappa of .42 (Van IJzendoorn, 1995). The adjusted standardized residuals showed that the Preoccupied category was the least predictive classification, also in relation to infant Disorganized attachment. Two decades later, Verhage et al. (2016) were able to retrieve five times more data on the four-way transmission of attachment (N = 2,774 parent-infant dyads) and reported a lower but still significant correspondence of 51%, amounting to a kappa of .26.
One of the findings was that parental Unresolved representation was more likely than chance to predict infant Disorganized attachment and less likely than chance to go together with a Secure or Avoidant infant attachment. Again, however, Unresolved attachment representation was not less (or more) likely to be associated with Resistant attachment of the infant to the parent, and the Preoccupied representation did not predict Disorganized attachment. Thus, in terms of prediction from parental attachment representations to infant attachment patterns, Unresolved and Preoccupied classifications do not seem to be the same, and Resistant and Disorganized attachment also seem to be separate classifications.
Several studies, however, have thrown doubt on the independent status of Unresolved classifications or dimensions as separate from the Preoccupied classifications or dimensions respectively. From the analyses of the NICHD SECCYD dataset, Booth LaForce et al. (2014) concluded that the Adult Attachment Interview captures two dimensions, one for Dismissing and the other for Preoccupied representations without room for a separate Unresolved dimension (see also Haltigan et al., 2014 for a rebuttal, see Van IJzendoorn & Bakermans-Kranenburg, 2014). Recently, Raby et al. (2020) concluded that both a twodimensional (Dismissing and Preoccupied) as well as a three-dimensional model (with Unresolved as the third dimension) fitted the data in a combined dataset of N = 3,218 respondents, but the latter model came at the expense of strongly correlated Preoccupied and Unresolved dimensions (Raby et al., 2020). They emphasized the importance of additional tests of the predictive validity to see whether the Unresolved part of the AAI was really needed or could be dissolved in the Preoccupied dimension.
As suggested above, one approach to the predictive validity question is examining the intergenerational transmission of attachment from parent to infant. Numerous studies have reported cross-tabulations of parental attachment representations associated with infant attachment classifications, and these data have been synthesized in two metaanalyses (Van IJzendoorn, 1995;Verhage et al., 2016). In these meta-analyses, the resulting 4 × 4 cross-tabulations were analysed with adjusted standardized residuals showing larger than chance correspondences between parental and infant attachments. A more sophisticated approach is Correspondence Analysis (CA; Greenacre, 2006). A solution of CA is commonly interpreted using a biplot to represent graphically the relations between the two categorical variables, but CA can also be viewed as Canonical Correlation Analysis (CCA) of categorical data (e.g. Greenacre, 2006;Hwang et al., 2009). In the latter approach, we can examine the latent structure using a canonical loading and inter/intra correlations between canonical variates, which is analogous to the exploratory factor analysis or principal component analysis (EFA/PCA) interpretation procedure. Therefore, a next step in the application of CA to cross-tabulated data is a CCA-based CA approach with oblique rotation, which was adopted in the current study.
In his paper on the statistical underpinnings of the new CCA-based CA method with oblique rotation, Makino (2022) used the cross-tabulation of parental and infant attachment classifications in N = 548 participants with their offspring from the first meta-analysis in this field of inquiry (Van IJzendoorn, 1995). The first canonical variate for the parents was based on a strong positive association with Dismissing and a negative association with Autonomous, whereas the second canonical variate showed a strong positive association with Unresolved and a negative link with Autonomous. For the infant attachment classifications, a similar dimensional structure was found, consisting of an Avoidant-Secure and a Disorganized-Secure factor. The correlations between the canonical dimensions showed substantial associations between the parental Dismissing-Autonomous and the infant Avoidant-Secure dimensions, and between the Unresolved-Autonomous and Disorganized-Secure dimensions (Makino, 2022). Preoccupied representations and Resistant infant classifications did not fit in this obliquely rotated CCA-based CA solution.
In the current study, we wondered whether a similar structure could be uncovered in the much larger 4 × 4 cross-tabulation in the Verhage et al. (2016) meta-analysis. Our hypothesis was that similar to the previous modeling with CCA-based CA by Makino (2022) a more parsimonious latent model of intergenerational transmission of attachment would be compatible with the cross-tabulated data. The use of correspondence analysis in combination with canonical correlation with oblique rotation was hypothesized to lead to a model that includes latent dimensions and uncovers the most important components of intergenerational transmission of attachment. We do not aim at a defense of the categorical versus dimensional structure of attachment assessments, let alone of attachment reality. In contrast, our main hypothesis was that Unresolved attachment representations are part and parcel of the validity of the Adult Attachment Interview in predicting the four-way infant attachment patterns apart from Preoccupied representations.

Methods
We applied CCA-based CA to the crosstabulation of AAI and SSP classifications as presented in the paper by Verhage et al. (2016). In this analysis, we used twodimensional solutions in the same manner as Makino (2022). The row and column solutions in CA have rotational indeterminacy, and thus they were rotated in order to obtain the interpretable canonical loading matrices. In the CCA-based CA rotation, there are two approaches to rotate the solutions. One is referred to as the concurrent rotation, and the row and column canonical loading matrices are concurrently rotated by the same rotation matrix. The other is termed as the separate rotation, in which the row and column loadings are separately rotated by the different rotation matrices. We adopted the separate rotation approach because the separately rotated solutions can achieve a simpler structure than those given by the concurrent rotation (Makino, 2022;Satomura & Adachi, 2013). The parent and infant canonical loading matrices were separately rotated by the quartimin rotation method (Carroll, 1953), whose computer program has been provided in the GPArotation package in R (Bernaards & Jennrich, 2005).
The canonical loadings are interpreted by considering their magnitude, which indicates how strongly each of categories loads on a canonical variate. The commonly used rule of thumbs is to ignore loadings which absolute values are lower than some threshold value, e.g. 0.3. Cudeck and O'dell (1994) criticized this practice and recommended that researchers consider standard errors or confidence intervals of the rotated loadings. Therefore, we used the bootstrap method in order to estimate confidence intervals of the rotated loadings and inter/intra canonical correlations. Zhang et al. (2010) applied the bootstrap method to estimate confidence intervals of rotated loadings. We adopted their technique and the bootstrap confidence intervals were constructed with 2,000 bootstrap samples in the current analysis. There are several methods for assigning bootstrap confidence interval. Here, we used the SE-based bootstrap confidence interval (Efron & Tibshirani, 1993;Zhang et al., 2010).  Note. Correlations in bold are those with a 95% confidence interval excluding zero.

Results
In Table 1, the loadings of the classifications on the latent dimensions for parental attachment representations and for the infant attachment classifications are presented. The first dimension of the parental model was characterized by a large positive loading of Dismissing and a large negative loading of Autonomous and this dimension was labeled "Dismissing-Autonomous." Preoccupied did load positively on this dimension too but less strongly compared to Dismissing. Unresolved did not show a loading on this first dimension but it loaded strongly on the second dimension. Both Autonomous and Dismissing loaded negatively on this second dimension. Preoccupied did not load on this dimension. For ease of comparison between dimensions, we labeled this second dimension "Unresolved-Autonomous." For the first dimension of the infant attachment classifications, we found a clear contrast between the positive loading of Avoidant and a negative loading of Secure which led to the label "Avoidant-Secure." Resistant showed a positive but lower loading on this first dimension. The second infant dimension was dominated by the opposite loadings of Disorganized and Secure, allowing for the label "Disorganized-Secure." Resistant loaded positively on this second dimension, similar to its association with the first dimension but again with a weaker loading compared to Disorganized or Avoidant. See Table 2 for the correlations between mother and infant canonical variables. See Figure 1 for a graphical display of the dimensions and loadings, omitting loadings and inter/intra correlations with a 95% confidence interval including zero.
In a final step, the associations between the parental and infant dimensions were computed. The association between Dismissing-Autonomous and Avoidant-Secure amounted to .26. A similar link (.24) was found between Unresolved-Autonomous and Disorganized-Secure. See Figure 1 for the model including these associations.
Alternative solutions were probed as well. The 1-dimensional solution showed substantial positive loadings of Autonomous (0.72) and Secure (0.69) and significant negative loadings of smaller sizes for the other classifications. For the adult classifications, loadings were as follows: Dismissing −0.49; Preoccupied −0.37, and Unresolved −0.33. For the infant classifications, loadings were as follows: Avoidant −0.45; Resistant −0.35; Disorganized −0.45. The 1-dimensional solution was supported by the so-called "average rule," but it only explained 59% of the total variances of the contingency table which may be insufficient to capture a majority of the associations among the response categories. It was therefore less preferred than the 2-dimensional solution explaining about 87% total variances of the contingency table, likely to capture a majority of the associations among the response categories.
The 3-dimensional solution also fitted the data. On the first adult dimension , Dismissing (−0.86) loaded highest; on the second dimension, Unresolved (0.88) loaded highest, and Preoccupied (−0.95) loaded highest on the third dimension. Loadings of Autonomous on the three dimensions were smaller, amounting to 0.51, −0.46, and 0.26 for dimensions 1, 2, and 3, respectively. On the first infant dimension, Disorganized (−0.85) loaded highest; on the second dimension, Avoidant (−0.92) loaded highest, and Resistant (−0.94) loaded highest on the third dimension. Loadings of Secure on the three dimensions were smaller: 0.52, 0.38, and 0.30 for dimension 1, 2, and 3 respectively. The 3-dimensional solution represented the contrasts of each of the insecure/nonautonomous classifications against the secure/autonomous. The main purpose of CCAbased CA was to obtain a meaningful structure in reduced space, and the 3-dimensional solution was considered uninformative because no dimensional reduction was performed.

Discussion
We uncovered an alternative model of intergenerational transmission of attachment with latent dimensions underlying the categorical parental and infant attachment classifications. The model showed specific linkages between two dimensions on both sides of the dyadic transmission, from Dismissing-Autonomous to Avoidant-Secure and from Unresolved-Autonomous to Disorganized-Secure, with substantial effect sizes that nevertheless leave quite a lot of room for measurement errors and other predictors of infant attachment. It should be noted that the correlations between the parental and infant dimensions for the available data almost 30 years ago were about twice the size (.47 and .41 for the first and the second dimension, respectively, see Makino, 2022). Measurement errors in assessments of parental as well as infant attachment classifications may play an important role in attenuating associations. But our model also resonates calls for a more intensive search of understudied predictors, in particular contextual ones that explain part of the variance of infant attachment classifications (Verhage et al., 2019). Family functioning and child differential susceptibility to parenting seem excellent candidates to complement main effects of parental attachment representations in predicting child attachment and bridging the transmission gap (Belsky & van IJzendoorn, 2017;Verhage et al., 2016).
The model shows that Unresolved and Disorganized do not dissolve in dimensions dominated by Preoccupied and Resistant, which is in contrast with positions based on the attachment style literature in social psychology (e.g. Mikulincer & Shaver, 2016), arguing that Unresolved and Disorganized do not survive modeling as separate styles or classifications but merge with the anxiety dimension that represents Preoccupied and Resistant. Instead, in our model Preoccupied seems to have more affinity to Dismissing-Autonomous than to Unresolved-Autonomous, whereas on the infant side for Resistant the significance bar seems to be set too high to play a statistically warranted role at all in our 2-dimensional model of intergenerational transmission of attachment. Thus, in contrast to speculations about the Unresolved and Disorganized categories being superfluous or at least less important (Haltigan et al., 2014but see Van IJzendoorn & Bakermans-Kranenburg, 2014, the current analysis showed that Preoccupied and Resistant do not coincide with dimensions determined by Unresolved and Disorganized. If anything, Preoccupied and Resistant occupy problematic positions in the model that call for more research on their construct, discriminant and predictive validity and interrater reliability (Ariav-Paraira et al., 2022). It should be noted that in the 3-dimensional solution, Unresolved and Disorganized did not load on the same dimension as the Preoccupied and Resistant classifications which is another illustration of our main hypothesis that Unresolved and Disorganized do not dissolve in the Preoccupied and Resistant classifications, respectively. The Unresolved and Disorganized classifications seem to occupy their own positions in a two-dimensional space.
The position of Unresolved is a crucial issue from the perspective of clinical applications of attachment theory that often rely on the Unresolved and Disorganized categories to better understand the problems of clinically atypical children or adults struggling with loss, maltreatment, or other traumatic experiences. In their meta-analysis on adult attachment and anxiety issues Dagan et al. (2020) derived from their exploratory analyses, the somewhat premature conclusion that Preoccupied and Unresolved would not point at "psychologically distinct phenomena" and suggested that Unresolved did not predict anxiety issues over and above Preoccupied. However, if Unresolved is cut loose of the network of attachment concepts without sufficient evidence, attachment theory runs the risk of losing its clinical promise and potential (Hesse, 2016). Of course, in clinical training and practice, various misunderstandings around Unresolved and Disorganized exist (e.g. see Forslund et al., 2022;Granqvist et al., 2017), but this means that more work should be invested in clinical research and clarification of these categories for professionals. Surely, it is important to acknowledge that several attachment scholars have articulated reasons for continuing to use the four traditional AAI and Strange Situation classifications, in particular when studying the intergenerational transmission of attachment and its unexplained gap (e.g. Sroufe, 2003;Steele & Steele, 2021;Verhage et al., 2016). However, here we argue that dimensional solutions of adult attachment representations and infant attachment patterns resulting in the dissolution of Unresolved and Disorganized classifications or dimensions (Fraley & Spieker, 2003;Groh et al., 2019;Haltigan et al., 2014;Shakiba & Raby, 2021) are based on equivocal evidence (Raby et al., 2020) and needs to be tested with a variety of statistical modeling approaches such as the CCA CA model applied here, and most importantly, with (clinical and intervention) studies on the incremental predictive validity of models with and without Unresolved and Disorganized.
Most importantly for enhancing validity and feasibility, work on facilitating better interrater reliability of coding systems for Unresolved and Disorganized is urgent, in particular to decrease the attenuating effects of measurement errors on predictive models such as developed for intergenerational transmission of attachment but also for other facets of child development. For example, it is somewhat problematic that Disorganized does not predict internalizing behavior problems, whereas Avoidant did show a significant association with later internalizing problems (Groh et al., 2017). Considering great strides in computerized voice analyses in recent years (see Biggiogera et al., 2021, for an application to communicative behavior in couples' conflict interactions) automatic coding of verbal behavior in the AAI might be possible in the near future, and automatic analysis of videotaped non-verbal behavior in the SSP might also profit from the fast progress made by facial and interactional recognition programs based on machine learning. In a rodent study on parenting, Jelle Knop developed a promising pipeline to continuously record home-cage videos of communally nesting dams with their litters using Raspberry Pi devices with video recordings processed using DeepLabCut (Knop et al., 2021). Automatization might promote the use of AAI and SSP in powerful large-scale clinical and intervention studies and create a firmer basis for clinical applications in the future.
We should mention some limitations of the current work. First, the attachment classification data used in the current modeling were derived from various studies, and therefore they have a multilevel structure. However, to our knowledge, a multilevel approach to CCA-based CA has not yet been developed. Second, moderator analyses for variables such as socioeconomic status or age were not conducted. Our aim was to test a latent model of the observed cross-tabulations of parent and infant attachment classifications in the most powerful way on the largest dataset available. Future work might examine whether the model fits equally well in various sub-sets of the crosstabulation. Third, the four AAI and the four Strange Situation classifications are sometimes considered mutually exclusive creating negative correlations among the attachment classifications that may or may not be present among the underlying constructs. In contrast, for the various AAI and Strange Situation scale ratings would be assigned independently of one another. However, the same coder usually assigns all ratings in the AAI or in the SSP coding system, and no independent coders are used for all the scales. This is mirrored in the classifications which also may show fuzzy boundaries. Fourth, the model is based on correlational studies that cannot establish causality. Further experimental work using randomized controlled trials or Mendelian Randomization (Hamaker et al., 2020) is needed to establish the causal nature of the link between parental and child attachment independent of genetic determinants or other confounders.
To conclude, in our model of intergenerational transmission of attachment, the predicted associations between parental and child attachments seem to be more visible and robust than the cross-over predictions. In fact, a significant association between Unresolved and Avoidant is absent, whereas the association between Dismissing and Disorganized is relatively small. In this sense, the model provides support for one of the core hypotheses of attachment theory, i.e. intergenerational transmission of attachment. Furthermore, this study is not meant to be a defense of the categorical versus dimensional structure of attachment assessments, let alone of attachment reality. Its only ambition is to save Unresolved and Disorganized (dimensional or categorical) components of the AAI and Strange Situation respectively from premature dismissal from further scrutiny without sufficient empirical evidence. Importantly, our model illustrates that despite the rather harsh climate some of the most exotic but also most valuable clinical components of attachment theory, Unresolved and Disorganized, may be here to stay for a little while longer to bring their scientific and clinical potential to fruition.
In memory of Mary Main whose bold conjectures about Unresolved and Disorganized inspired our statistical defense.

Disclosure statement
The authors report that to their knowledge, there are no competing interests to declare.

Funding
The work of MHVIJ is supported by the Netherlands Organization for Scientific Research, Spinoza Award 2004.