Poster #47 - Resolving Lord’s Paradox in Cross-Lagged Panel Models and Latent Growth Models

• In Event: Poster Session 05

Abstract

The two basic methods for analyzing change often produce inconsistent results, known as Lord’s paradox, e.g., in corrective actions by parents. ANCOVA-type analyses have been preferred for causally relevant estimates traditionally, but they are biased by stable pre-existing differences on outcome scores, according to recent critiques (e.g., Berry & Willoughby, 2017). The alternative, difference-score analysis, has less statistical power and cannot test Pretest X Treatment interactions. Testing both change analyses could help satisfy the call for robustness in developmental research (Duncan et al., 2014). This study investigates the applicability of Lord’s paradox to three-occasion analyses, contrasting cross-lagged panel models (CLPM) and latent growth models (LGM). Group-mean centering of Time-1 and Time-2 data around T1 group means has produced robust results in 2-occasion data and overcomes biases associated with CLPM, although this cannot guarantee unbiased results (Lin & Larzelere, 2020). Although the ultimate goal is to improve causally relevant analyses of corrective actions by parents, this study tested the outcomes of a corrective action with known causal evidence from randomized trials, namely depression therapy for the mothers in the Fragile Families dataset.
Method. Mothers’ (N = 4456) depression severity was an 11-point score for Time 1, 2, and 3 (when children were 3, 5, and 9). They reported receiving therapy for depression (or not) at T1 and T2. Time-1, T2, and T3 depression scores were centered around their T1 group means for 4 groups: those in therapy at Time 1 & 2, in controls at Time 1 and 2, in therapy only at Time 1, and in therapy only at Time 2.
Result. Figure 1 shows the mean trajectories in depression symptoms for the four groups, before and after centering each group around their T1 group means. Figure 2 shows the contradictory results for corrective actions using the original data. Like 2-occasion ANCOVA, CLPMs make therapies look harmful, predicting more depression severity subsequently. In contrast, LGM’s analyses of difference scores shows that therapy reduces subsequent depression significantly. After centering all depression scores on T1 group means, CLPM and LGM agree that therapy reduces subsequent depression severity, significantly so for all but one coefficient.
Discussion. These results add to evidence of unrecognized biases in CLPM (Berry & Willoughby, 2017). The results of developmental analyses should be consistent with known causal evidence to have confidence in their results when such evidence is lacking. Like two-wave dual-centered ANCOVA, the coefficients from T1 therapy to T1-to-T2 change are nearly equivalent across CLPM and LGM and the original LGM after centering. Centering all data around their T1 group means keeps all the difference scores the same, but the CLPM coefficient from T2 therapy to T3 depression agrees with the other analyses in sign, but not significance, partly because the groups differ on T2 group means. Nonetheless, it is informative to distinguish groups that come in and out of therapy from those consistently in therapy or not, rather than the usual one-size fits all analyses of corrective actions, whether by parents or professionals.

Authors

• Robert E Larzelere, Oklahoma State University - Stillwater
  Presenting Author

• Hua Lin, Oklahoma State University - Stillwater