Understanding Long-Term Trajectories in Web-Based Happiness Interventions: Secondary Analysis From Two Web-Based Randomized Trials

Background A critical issue in understanding the benefits of Web-based interventions is the lack of information on the sustainability of those benefits. Sustainability in studies is often determined using group-level analyses that might obscure our understanding of who actually sustains change. Person-centric methods might provide a deeper knowledge of whether benefits are sustained and who tends to sustain those benefits. Objective The aim of this study was to conduct a person-centric analysis of longitudinal outcomes, examining well-being in participants over the first 3 months following a Web-based happiness intervention. We predicted we would find distinct trajectories in people’s pattern of response over time. We also sought to identify what aspects of the intervention and the individual predicted an individual’s well-being trajectory. Methods Data were gathered from 2 large studies of Web-based happiness interventions: one in which participants were randomly assigned to 1 of 14 possible 1-week activities (N=912) and another wherein participants were randomly assigned to complete 0, 2, 4, or 6 weeks of activities (N=1318). We performed a variation of K-means cluster analysis on trajectories of life satisfaction (LS) and affect balance (AB). After clusters were identified, we used exploratory analyses of variance and logistic regression models to analyze groups and compare predictors of group membership. Results Cluster analysis produced similar cluster solutions for each sample. In both cases, participant trajectories in LS and AB fell into 1 of 4 distinct groups. These groups were as follows: those with high and static levels of happiness (n=118, or 42.8%, in Sample 1; n=306, or 52.8%, in Sample 2), those who experienced a lasting improvement (n=74, or 26.8% in Sample 1; n=104, or 18.0%, in Sample 2), those who experienced a temporary improvement but returned to baseline (n=37, or 13.4%, in Sample 1; n=82, or 14.2%, in Sample 2), and those with other trajectories (n=47, or 17.0%, in Sample 1; n=87, or 15.0% in Sample 2). The prevalence of depression symptoms predicted membership in 1 of the latter 3 groups. Higher usage and greater adherence predicted sustained rather than temporary benefits. Conclusions We revealed a few common patterns of change among those completing Web-based happiness interventions. A noteworthy finding was that many individuals began quite happy and maintained those levels. We failed to identify evidence that the benefit of any particular activity or group of activities was more sustainable than any others. We did find, however, that the distressed portion of participants was more likely to achieve a lasting benefit if they continued to practice, and adhere to, their assigned Web-based happiness intervention.


Basic Description of Cluster Membership
We observe here that when the clustering is permitted to extend beyond a K factor of 5, some of the resulting clusters demonstrate a group membership that is low enough to lead us to seriously question the validity of those clusters as actual trends in the data, rather than a capitalization on chance variation (this is especially true in Sample 1).
Omnibus comparison of cluster solution fit, varying the K factor The following two plots were incremental to the derivation of a four-factor solution in that they provided initial evidence of model fit in the four-factor solution when compared to solutions with a different number of factors. Our first analytic step in establishing the four-factor solution was an interpretation of these plots according to Cattell's (1966) Scree approach.
In each clustering, participants were assigned to the prototype that they most resembled according to the K-means clustering approach and the calculus-based distance function described in the primary publication. Model fit is summarized in these graphs as a total of the Euclidean variance between each participant and the prototype that they were assigned to in each clustering. Clusterings here are varied by the K factor, otherwise known as the number of possible atheoretical clusters permitted for each solution (e.g., a K of 3 tranlsates to a three-cluster solution, and so on). In the following two graphs, model fit is summarized across the LS curves and the AB curves within the same observation ranges as reported in the citing publication.
The difference in the range of the y-axis in the following two graphs is largely an artifact of a difference in the sample sizes and observation range between the two samples.
Another approach that we employed in the comparative analysis of cluster solutions relies on comparing how individual clusters varied between cluster solutions. Specifically, we focused on how group membership differed between the four-cluster solution and the three-and five-cluster solutions. In this section, we describe our comparison of the four-factor solution to the three-factor solution. The other comparison of differential cluster membership, that between the four-and five-cluster solutions, is presented in the subsequent section.
Our primary foci in the analysis of group-membership differences between the three-and four-factor solutions are the following two contingency tables: Sample Given the fact that some of the cells in the above two tables hold zero values, a Chi-Square interpretation of these tables is likely to be heavily biased, so the following results should be interpreted with caution. In both samples, we observed a significant relationship between the two cluster solutions; χ 2 (6, N = 276) = 360.84, p < .0001, Cramer's V = 0.8085, and χ 2 (6, N = 579) = 831.84, p < .0001, Cramer's V = 0.8476. Specifically, in Sample 1 we observed the greatest deviations from chance between the Residual and B clusters (+254%), between the Lasting Benefit and C clusters (+239%) and between the Hedonic Adaptation and A clusters (+120%). In Sample 2, this pattern differed in that members of the Lasting Benefit and Hedonic Adaptation clusters were more likely to be grouped together in the threefactor solution; the greatest observed deviations from chance in this sample occurred between the Residual and U clusters (+523%), the Lasting Benefit and T clusters (+212%), and the Hedonic Adaptation and T clusters (+193% Taken together, these results indicate a strong relationship, in terms of cluster membership, between the two clustering solutions. When moving from a K factor of 3 to a K factor of 4 in both samples, we primarily see two effects: an emerging distinction between the Lasting Benefit and Hedonic Adaptation clusters and an isolation of the Non-Distressed cluster.

Comparison of the Four-Factor Model to the Five-Factor Model
Our primary foci in the analysis of group-membership differences between the four-and five-factor solutions are the following two contingency tables: Comparing these two cluster solutions via a chi-square analysis, and again noting the biases introduced by the empty cells in our above tables, we observed a significant dependence between the four-and five-cluster solutions; χ 2 (12, N = 276) = 548.09, p < .0001, Cramer's V = 0.8136 in Sample 1, and χ 2 (12, N = 579) = 1117.02, p < .0001, Cramer's V = 0.8019 in Sample 2. In Sample 1, the greatest deviations from chance occurred when relating the Hedonic Adaptation and F clusters (+626%), the Residual and G clusters (+487%), and the Lasting Benefit and H clusters (+265%). A similar pattern emerged in Sample 2, whereby the greatest deviations from chance were observed between the Residual and Y clusters (+566%), the Hedonic Adaptation and Z clusters (+530%), and the Lasting Benefit and W clusters (+445%). In predicting membership in the five-cluster solution based on membership in our chosen solution, the four-cluster solution, we observed a significant Lambda value in both samples; λ = 0.420, 95% CI: [0.298, 0.542], and λ = 0.398, 95% CI: [0.316, 0.480], respectively.
When moving from a cluster solution with a K factor of 4 to one with a K factor of 5, we find in both samples, that a large portion of the members in the Non-Distressed and Lasting Benefit clusters cluster together, forming the fifth cluster without causing too large of a disturbance to the other clusters. We interpret this consistent pattern of effects between samples as additional evidence of the efficacy of our clustering approach in identifying naturally-occurring trends. One possible interpretation of the new cluster that seemed to emerge from the application of a five-cluster solution (i.e., clusters E and X), in the context of the findings presented in the primary publication, is that the longitudinal effects that we reported in regards to the primarily-distressed participants might also generalize to non-distressed participants. We also observe, however, that very little information is gained by including a fifth cluster in our solution because and chose to report the four-cluster solution rather than the five-cluster solution in the interest of presenting the most coherent set of findings possible.
Ultimately, our decision to analyze a four-cluster solution was contingent on the size of our sample. Evidence emerged that the four-cluster solution demonstrated considerably better model fit than the three-cluster solution, especially in regard to the change in model fit between the four-and five-cluster solutions. Additionally, we learned that the inclusion of a four cluster produced a pattern of trends that was largely consistent between samples, especially in comparison to solutions with a lower K factor. The inclusion of a fifth cluster had a similar effect across clusters; however, our sample sizes were not large enough for a reasonable interpretation of a five-cluster solution. We chose to proceed with a fourcluster solution in the interest of maintaining statistical conservatism considering the findings presented in this report. We admit that there is a great deal of further room for exploration using a higher-order model, should future researchers choose to employ a similar analytic approach to a larger sample of OPPI-enrolled online happiness seekers.