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Cognitive Therapy and Research

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01.08.2007 | ORIGINAL ARTICLE

Comparing the Validity of Alternative Cognitive Case Formulations: A Latent Variable, Multivariate Time Series Approach

verfasst von: Gregory H. Mumma, Scott R. Mooney

Erschienen in: Cognitive Therapy and Research | Ausgabe 4/2007

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Abstract

This article describes a latent variables approach to empirically comparing the validity of independently generated, idiographic, cognitive case formulations (CCFs) of a single case. Each of two CCFs differed in the content of idiosyncratic cognitive schema (ICS) and their hypothesized relationships to distress. The CCFs were compared using multivariate time series ratings collected daily. First, the convergent and discriminant validity and dynamic structure of the ICSs hypothesized by each of the two clinicians were evaluated using confirmatory dynamic factor analysis. Second, the two CCFs were compared as to how well the ICSs predicted daily variability in latent distress variables. Compared to the novice clinician, the ICSs in the CCF of the clinician with expertise in CCF explained an average of twice the proportion of variance in the distress variables. This methodology permits the direct empirical comparison of the validity of alternative CCFs without appealing to external judges or criterion groups.

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More formally, the statistical models for the alternative case formulations must be nested for that approach to be used.

Watson et al (1995) condensed their three General Distress MASQ sub-scales into a single Negative Affectivity scale given the results of their R-technique factor analyses. However, so as to obtain a specific and fine-grained multidimensional assessment of symptoms and distress, GD: Depressed and GD: Mixed were retained as separate intraindividual scales. Permission to use selected items from the copyrighted MASQ obtained from L.E. Clark (9/29/1999).

In the WNFS model, today’s score for a particular item is predicted by both today’s factor score and yesterday’s factor score. The extent to which an item’s score is predicted by yesterday’s versus today’s factor score can vary between items within a factor (Mumma, 2004). In the DAFS model, today’s item score is predicted only by today’s factor score, but yesterday’s factor score can predict today’s factor score via an autoregressive parameter (Nesselroade et al., 2002; Ferrer & Nesselroade, 2003). The DAFS model is a more constrained (more parsimonious) model in that the proportion of item variance explained by yesterday’s factor score is constant for all items in that factor (for a CDFA). Within-structure lagged regressions (WSLRs) permit yesterday’s score on factor i to predict today’s score on factor j. WSLRs are cross lagged regression coefficients that clarify between-scale dynamic structure within the set of either the ICSs or the distress latent variables.

Specifically, items were assigned to parcels in a quasi-random, domain-representation procedure as follows. The concurrent (lag 0) correlations of the items comprising each ICS were subjected to an exploratory iterative principal factor analysis with an oblique three factor solution. If there was insufficient evidence for a 3 factor solution, a 2 or, if necessary, 1 factor solution was used. Items from each factor (domain) were quasi-randomly assigned to each of the three item parcels, blocking on type of cognition and variance explained. Thus, whenever possible, each item parcel included items that were core beliefs, intermediate beliefs (assumptions, rules, and attitudes) and automatic thoughts as well as items with comparatively high versus low proportion of variance explained in the unidimensional CDFA (see Appendix). Note: Given that Clinician 1’s ICS1 and ICS2.2 had only five usable items, two item parcels were formed for each ICS with loadings constrained equal in the CDFAs.

Certain ICS subcomponents were combined, either because the CDFA indicated they were not empirically distinguishable (e.g., ICS 2.1 and 2.3) or because the clinician made identical predictions for each component (e.g., ICS3 and its brief four item elaboration).

Both the non-dynamic (lag 0) and DAFS models had poorly distributed residuals whereas the residuals for the WNFS model were approximately unimodal symmetric. The WNFS model fit significantly better than the non-dynamic model, χ² _diff (df = 10) = 27.96, P < .0018 and marginally significantly better than the DAFS model, χ² _diff (df = 5) = 10.76, P < .056. Finally, a WNFS dynamic model which relaxed the equal loadings and error variance, equal disturbance covariances, and equality of certain WSLRs and concurrent cross regression constraints did not fit the data significantly better than the WNFS model with these constraints (χ² _diff (df = 12) = 12.87, P = n.s.).

Unidimensional CDFA tests for convergent validity of the items developed to measure each ICS resulted in dropping six items with poor convergent validity (see Appendix). Bidimensional CDFA tests using the remaining 13 items indicated that the correlation between the two ICS factors was 1.0, indicating inadequate discriminant validity between the two ICS. An alternative procedure, involving retaining items if their correlation with the corrected total score was .15 or greater, resulted in retaining 17 items from which 3 item parcels were created for each of the two ICS. Note that the item total correlation of .15 was chosen so as to be close to the .16 squared loading in a factor analysis whereas the slightly lower correlation permitted inclusion of several more items from which the item parcels were made. However, CDFA of these item parcels again revealed inadequate discriminant validity between Clinician 2’s ICS1 and ICS2.

Four additional items were dropped due to poor convergent validity with the combined ICS: see Appendix. For the three item parcels, the dynamic WNFS model fit significantly better than a non-dynamic model, χ² _diff (df = 3) = 8.84, P < .032 and marginally significantly better than a DAFS model, χ² _diff (df = 2) = 5.88, P < .053. It was retained over the latter because the distribution of asymptotically standardized residuals involved fewer relatively extreme residuals and RMSEA for the DAFS model = .047. The WNFS model demonstrated a “perfect fit” with RMSEA = .000.

For the three distress measures, a DAFS model with the same constraints did not fit significantly better than the non-dynamic model with these constraints (χ² _diff (df = 3) = 5.28, n.s.). In the DAFS model, all three autoregressive parameters between the lag 1 and lag 0 factors were non-significant. A WNFS model did not improve fit over either the DAFS or non-dynamic model. Finally, a non-dynamic model without the above-described constraints did not fit the data significantly better than the non-dynamic model with these constraints (χ² _diff (df = 14) = 17.3, n.s.). With the parameter estimation constraints, this model necessitated estimating just seven parameters.

This model fit significantly better than a model which was non-dynamic for both the ICSs and the distress variables: χ² _diff (df = 10) = 28.28, P < .0016. A model that included the dynamic (WNFS) ICS factors but which relaxed the equal loadings and error variance, equal disturbance covariances, and equality of certain WSLR and CCR constraints required the estimation of 28 additional parameters and yielded an improper solution.

The somewhat high standardized partial path coefficients from ICS1 to GD: Depressed and GD: Mixed are not an artifact of content overlap between the ICS and distress items. The items used for GD: Depressed and Mixed did not include any cognitively oriented items that were in the MASQ.

A model which combined the non-dynamic model for the three distress measures and the WNFS dynamic model for Clinician 2’s combined ICS did not fit the data significantly better: χ² _diff (df = 3) = 6.37, n.s. than the completely non-dynamic model. Also, the lag 1 loadings of the two ICS item parcels that were significant in the model for Clinician 2’s combined ICS (Fig. 2) were no longer significant when the concurrent regressions of the ICS to the three distress measures were included. Thus, a non-dynamic model was retained.

This is the correlation between the latent variables or factors for these ICSs obtained from a CDFA using a dynamic WNFS model for Clinician 1’s four ICSs and Clinician 2’s combined ICS.

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Titel: Comparing the Validity of Alternative Cognitive Case Formulations: A Latent Variable, Multivariate Time Series Approach
verfasst von: Gregory H. Mumma
Scott R. Mooney
Publikationsdatum: 01.08.2007
Verlag: Kluwer Academic Publishers-Plenum Publishers
Erschienen in: Cognitive Therapy and Research / Ausgabe 4/2007
Print ISSN: 0147-5916
Elektronische ISSN: 1573-2819
DOI: https://doi.org/10.1007/s10608-006-9062-5

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