Attachment Styles, CFA, and Fit Indices

Did you know people can have different styles of attachment in their relationships? Do you like Network Psychometrics and Structural Equation Modeling/Confirmatory Factor Analysis? Want to see how these things connect to fit indices? Read one empirical example below... Lafontaine et al. (2015) validated an instrument to measure attachment styles in close relationships. The two-factor structure of Anxiety and Avoidance styles aligns closely with attachment theory as developed by Bowlby and Ainsworth. This theory conceptualizes attachment in terms of anxiety about abandonment and avoidance of intimacy. Lafontaine et al. (2015) point that the two-dimensional factor structure of the ECR has been observed consistently across various populations, cultures, and languages. This robust replication supports the validity of the two-factor model. The paper by Lafontaine et al. (2015) emphasizes that anxiety and avoidance are designed to be orthogonal (uncorrelated) dimensions. This independence is theoretically important and has been supported by research, although small correlations are sometimes observed. We analyzed data from the 12-item Experiences in Close Relationships (ECR-12; Lafontaine et al., 2015) scale to compare the fit of a correlated-factors model against a bifactor model. The ECR-12 is purported to measure two attachment factors, anxiety and avoidance, each measured by six items. In general, the ECR published literature has not considered a bifactor model of attachment for the responses to this scale. The data was obtained from the Open Source Psychometrics Project, which contained full responses by 27,883 persons from the United States. The items were responded via a 5-point Likert scale with options strongly disagree (1), disagree (2), neither agree nor disagree (3), agree (4), and strongly agree (5). Cronbach’s alpha reliability was .858 for avoidance and .840 for anxiety. The factor models were estimated using robust maximum likelihood. The two-factor CFA model produced a good fit to the data with CFI = 0.95, RMSEA = 0.07, and SRMR = 0.05. Additionally, AIC = 1825558.68 and BIC = 1825779.909 for this model. The standardized loadings on the avoidance factor ranged from .54 to .80 (M = .70), while the loadings on the anxiety factor ranged from .50 to .79 (M = .6785). The two attachment factors were estimated to be approximately orthogonal, with a correlation of -0.002.

The bifactor model produced an even better fit to the data according to all factor-analytic fit indices, with CFI = 0.97, RMSEA = 0.05, and SRMR = 0.03, AIC = 1819293.09, and BIC = 1819611.659 for this model. However, the standardized loadings did not support this bifactor structure as none item of the avoidance dimension had loadings above .12 on the general factor (M = -0.01), while the anxiety items had a mean loading of .67 on it. Conversely, the anxiety items did not load on the anxiety group factor well with a mean loading of -0.13, while the avoidance items had a large mean loading of .70 on the avoidance group factor.

When Exploratory Graph Analysis in the ECR data, the two-dimensional structure of the avoidance and anxiety items became very clear (see Figure below). The generalized total entropy fit results point to the first-order two-community structure with avoidance and anxiety factors (TEFIfirst?order = -9.74) as fitting better than the bifactor structure with a general factor (TEFIsecond?order = -6.22). The lower TEFI value for the first-order structure, compared to the second-order TEFI value, indicates that a two-community structure presents a lower level of disorganization, fitting the data better.

A bifactor model does not make theoretical sense, although it is shown to fit the data better than a correlated-traits structure with two factors, according to the traditional indices (CFI, RMSEA, SRMR, AIC, and BIC). The new Generalized Total Entropy Fit index, on the other hand, identified the two-factor structure as fitting the data better than the bifactor structure. Interested in knowing more about the GenTEFI Index? Read the paper here: Golino, H., Jiménez, M., Garrido, L. E., & Christensen, A. P. (2024, March 19). Generalized Total Entropy Fit Index: A new fit index to compare bifactor and correlated factor structures in SEM and network psychometrics.