Corrigendum: Curiosity Does Help to Protect Against Anxiety and Depression Symptoms but Not Conversely

We thank Sorjonen, Nilsonne, et al. (2022) for raising valid points that extend current longitudinal structural equation model (SEM) tutorials. To clarify, we based our original analyses (Zainal & Newman, 2022) on the logic and analytic data codes published in recent books (e.g., Grimm et al., 2017), journal articles (Kievit et al., 2018; Klopack & Wickrama, 2020; McArdle, 2009; Usami et al., 2019), and websites (e.g., Brinberg, 2019). However, we now understand that akin to classic regression models, adjusting for outcome at the initial time-point, mainly when predicting change outcomes, can lead to substantial biases due to regression to the mean (Sorjonen, Melin, et al., 2022; Sorjonen, Nilsonne, Ingre, et al., 2021; Sorjonen, Nilsonne, & Melin, 2021). Therefore, we reran our random intercept-cross-lagged panel model (RI-CLPM) (Hamaker et al., 2015) and bivariate dual latent change score (BDLCS) model without including the outcomes at the initial time-point as covariates to determine the between- and within-person association between trait-like need for cognition (NFC) and anxiety and depression symptoms (ADS).

Tables 1 and 2 show the results from the RI-CLPM and BDLCS models, respectively. We observed a good model fit for the RI-CLPM (χ²(df = 199) = 1656.254, p < .001, Confirmatory Factor Index (CFI) = .965, root mean square error of approximation (RMSEA) = .025, square root mean residual (SRMR) = .042). In the RI-CLPM, within-persons prior higher ADS level significantly predicted lower future level of NFC (β = −0.026, 95% confidence interval [CI] [−0.040, −0.011], d = −0.476), and vice versa (β = −0.062, 95% CI [−0.081, −0.043], d = −0.885). Moreover, at the between-person level, higher NFC significantly correlated with lower ADS across all waves of assessment (correlation between random intercepts; β = −0.070, 95% CI [−0.081, −0.059], d = −1.738). This pattern of findings closely resembled our original RI-CLPM-derived results that included ADS and NFC at baseline (Zainal & Newman, 2022).

Table 1.

Random-intercepts cross-lagged panel model of ADS and NFC across 10 time-points

		Estimate	95% CI	Cohen’s d
Within-person cross-lagged effects
(ADS)[T-1] → (NFC)[T]		−0.026	[−0.040, −0.011]	−0.476
(NFC)[T-1] → (ADS)[T]		−0.062	[−0.081, −0.043]	−0.885
Within-person autoregressive effects
(ADS)[T-1] → (ADS)[T]		0	–	–
(NFC)[T-1] → (NFC)[T]		0	–	–
Between-person covariances
(NFC)[T-1] ↔ (ADS)[T-1]		−0.010	[−0.021, 0.000]	−0.266
(NFC)[T] ↔ (ADS)[T]		−0.008	[−0.012, −0.004]	−0.546
RI(NFC)[T] ↔ RI(ADS)[T]		−0.070	[−0.081, −0.059]	−1.738
Between-person Intercepts
Mean of (ADS)[T1]		2.390	[2.372, 2.408]	35.873
Mean of (ADS)[T2]		2.374	[2.356, 2.392]	34.809
Mean of (ADS)[T3]		2.366	[2.348, 2.385]	34.459
Mean of (ADS)[T4]		2.342	[2.322, 2.361]	32.801
Mean of (ADS)[T5]		2.331	[2.311, 2.350]	31.951
Mean of (ADS)[T6]		2.339	[2.320, 2.358]	33.090
Mean of (ADS)[T7]		2.304	[2.284, 2.323]	31.931
Mean of (ADS)[T8]		2.279	[2.261, 2.297]	33.897
Mean of (ADS)[T9]		2.305	[2.286, 2.324]	32.937
Mean of (ADS)[T10]		2.300	[2.281, 2.319]	32.986
Mean of (NFC)[T1]		4.368	[4.349, 4.387]	62.307
Mean of (NFC)[T2]		4.347	[4.328, 4.366]	62.219
Mean of (NFC)[T3]		4.318	[4.284, 4.352]	34.357
Mean of (NFC)[T4]		4.324	[4.305, 4.343]	61.908
Mean of (NFC)[T5]		4.347	[4.316, 4.378]	37.428
Mean of (NFC)[T6]		4.306	[4.287, 4.325]	60.463
Mean of (NFC)[T7]		4.318	[4.300, 4.337]	62.864
Mean of (NFC)[T8]		4.296	[4.242, 4.350]	21.564
Mean of (NFC)[T9]		4.304	[4.285, 4.323]	61.025
Mean of (NFC)[T10]		4.344	[4.291, 4.397]	22.065
Variances
Variance of RI(ADS)[T1-T10]		0.382	[0.369, 0.395]	7.686
Variance of RI(NFC)[T1-T10]		0.641	[0.623, 0.658]	9.946
Variance of (ADS)[T1]		0.340	[0.318, 0.362]	4.117
Variance of (NFC)[T1]		0.233	[0.218, 0.247]	4.229
Variance of (ADS)[T2-T10]		0.191	[0.185, 0.197]	9.708
Variance of (NFC)[T2-T10]		0.291	[0.283, 0.300]	8.642

Note. CI = confidence interval; ADS = anxiety and depression symptoms; NFC = need for cognition; RI = random intercept.

Model fit indices: χ²(df = 199) = 1656.254, p < .001, CFI = .965, RMSEA = .025, SRMR = .042. Within-person cross-lagged effects refer to level in ADS at a prior time-point (T-1) predicting (→) future Δ in NFC at the next adjacent time-point (T) (and vice versa). Within-person coupling effects and proportional effects, residual covariances between ADS and NFC, as well as variances of ADS and NFC were each uniquely fixed to be equal across all 9 time-lags.

Table 2.

Bivariate dual latent change score model of ADS and NFC across 10 time-points

		Estimate	95% CI	Cohen’s d
Within-person coupling effects
Δ(ADS)[ΔT-1] → Δ(NFC)[ΔT]		0.095	[−0.094, 0.284]	0.136
Δ(NFC)[ΔT-1] → Δ(ADS)[ΔT]		−1.342	[−2.488, −0.197]	−0.316
Within-person proportional effects
Δ(ADS)[ΔT-1] → Δ(ADS)[ΔT]		0	–	–
Δ(NFC)[ΔT-1] → Δ(NFC)[ΔT]		0	–	–
Between-person covariances
(ADS)[T-1] ↔ Δ(ADS)[ΔT]		−0.011	[−0.015, −0.008]	−0.865
(NFC)[T-1] ↔ Δ(NFC)[ΔT]		−0.011	[−0.013, −0.008]	−1.158
(NFC)[T-1] ↔ (ADS)[T-1]		−0.076	[−0.092, −0.061]	−1.345
Δ(NFC)[ΔT] ↔ Δ(ADS)[ΔT]		0.003	[−0.000, 0.006]	0.232
(ADS)[T-1] ↔ Δ(NFC)[ΔT]		0.001	[−0.002, 0.005]	0.118
(NFC)[T-1] ↔ Δ(ADS)[ΔT]		−0.011	[−0.022, 0.001]	−0.251
(NFC)[T] ↔ Δ(ADS)[T]		−0.004	[−0.007, −0.000]	−0.277
Between-person Intercepts
Mean of (ADS)[T1]		2.380	[2.365, 2.396]	40.360
Mean of Δ(ADS)[T]		−0.016	[−0.023, −0.009]	−0.642
Mean of (NFC)[T1]		4.350	[4.333, 4.367]	68.930
Mean of Δ(NFC)[T]		−0.005	[−0.007, −0.002]	−0.448
Variances
Variance of (ADS)[T1]		0.408	[0.388, 0.428]	5.484
Residuals of Δ(ADS)[T]		0.273	[0.266, 0.281]	10.000
Variance of Δ(ADS)[T]		0.007	[0.000, 0.014]	0.270
Variance of (NFC)[T1]		0.671	[0.648, 0.693]	8.133
Residuals of Δ(NFC)[T]		0.177	[0.172, 0.183]	8.658
Variance of Δ(NFC)[T]		0.003	[0.003, 0.004]	1.539

Note. CI = confidence interval; ADS = anxiety and depression symptoms; NFC = need for cognition.

Model fit indices: χ²(df = 211) = 840.417, CFI = .985, RMSEA = .016, SRMR = .040. Within-person coupling effects refer to change (Δ) in ADS at a prior time-lag (ΔT – 1) predicting (→) future Δ in NFC at the next adjacent time-lag (ΔT; and vice versa). Within-person coupling effects and proportional effects, residual covariances between ADS and NFC, and variances of ADS and NFC were each uniquely fixed to be equal across all 9 time-lags.

The BDLCS model similarly displayed good model fit (χ²(df = 211) = 840.417, CFI = .985, RMSEA = .016, SRMR = .040). Within persons, change in ADS at a previous time-lag did not significantly predict change in NFC at the next time-lag (β = 0.095, 95% CI [−0.094, 0.284], d = 0.136). However, within-person reduction in NFC at a prior time-lag significantly predicted a rise in ADS at the future adjacent time-lag (β = −1.342, 95% CI [−2.488, −0.197], d = −0.316). Equations 1 to 4 present the new set of equations. Thus, our findings no longer paralleled the bidirectional results on the relations between change-to-future change in NFC and ADS reported in our original set of analyses that adjusted for initial NFC and ADS levels. However, Equation 2, in particular, shows that the change-to-future change relations representing the effect of NFC on future ADS remained negative across all time-lags of the current study. In addition, Figures 1 and 2 illustrate path diagrams reflecting our revised set of RI-CLPM and BLCS analyses, respectively.

Figure 1. Random-intercepts cross-lagged panel model of MHI and NFC across 10 time-points.

Note. ^*** p < .001.

MHI = mental health symptom severity; NFC = need for cognition; Cohen’s d parameter estimates were displayed. Within-person cross-lagged effects refer to the level in MHI at a prior time-point (T-1) predicting (→) future Δ in NFC at the next adjacent time-point (T) (and vice versa) across 10 years. Each unique within-person coupling effect and proportional effects, residual covariances between MHI and NFC, and variances of MHI and NFC were fixed to be equal across all nine time-lags. A subset of the 10 time-points was shown due to space constraints.

Figure 2. Bivariate dual latent change score model of MHI and NFC across 10 time-points.

Note. ^*** p < .001.

MHI = mental health symptom severity; NFC = need for cognition. Cohen’s d parameter estimates were displayed. Within-person coupling effects refer to change (Δ) in MHI at a prior time-lag (ΔT – 1) predicting (→) future Δ in NFC at the next adjacent time-lag (ΔT; and vice versa) across 10 years. Each unique within-person coupling effect and proportional effects, residual covariances between MHI and NFC, and variances of MHI and NFC were fixed to be equal across all 9 time-lags.

$$\mathrm{\Delta }\mathrm{N}\mathrm{F}{\mathrm{C}}_{\mathrm{T},\mathrm{T}+1}=-0.005+0\times \mathrm{N}\mathrm{F}{\mathrm{C}}_{\mathrm{T}}+0.095\times \mathrm{\Delta }\mathrm{A}\mathrm{D}{\mathrm{S}}_{\mathrm{T}-1,\mathrm{T}}$$ (1)

$$\mathrm{\Delta }\mathrm{A}\mathrm{D}{\mathrm{S}}_{\mathrm{T},\mathrm{T}+1}=-0.016+0\times \mathrm{A}\mathrm{D}{\mathrm{S}}_{\mathrm{T}}-1.342\times \mathrm{\Delta }\mathrm{N}\mathrm{F}{\mathrm{C}}_{\mathrm{T}-1,\mathrm{T}}$$ (2)

$$\mathrm{N}\mathrm{F}{\mathrm{C}}_{\mathrm{T}+1}=\mathrm{N}\mathrm{F}{\mathrm{C}}_{\mathrm{T}}+\mathrm{\Delta }\mathrm{N}\mathrm{F}{\mathrm{C}}_{\mathrm{T},\mathrm{T}+1}$$ (3)

$$\mathrm{A}\mathrm{D}{\mathrm{S}}_{\mathrm{T}+1}=\mathrm{A}\mathrm{D}{\mathrm{S}}_{\mathrm{T}}+\mathrm{\Delta }\mathrm{A}\mathrm{D}{\mathrm{S}}_{\mathrm{T},\mathrm{T}+1}$$ (4)

Our reanalysis highlights the importance of following recommendations (Sorjonen, Nilsonne, & Melin, 2021) to conduct a sensitivity analysis of testing longitudinal SEM models with and without regressing latent change outcomes on their baseline scores as covariates. It is consistent with the critique (Sorjonen, Nilsonne, et al., 2022) that parameter estimates derived from RI-CLPM and BDLCS models may not converge. Since the RI-CLPM results remained similar, this gives us confidence that our inferences drawn from RI-CLPM-derived level-to-future level parameter estimates and reported in our original manuscript were robust.

Importantly, our revised BDLCS analysis suggests that a lower NFC reduction would predict future elevated ADS but not the opposite. Since we replicated the same pattern of BDLCS-derived results in our original and revised set of analyses, it is unlikely that the potentially protective effect of NFC on ADS was a spurious relationship (Sorjonen & Melin, 2022). Noteworthy is that our results derived from the actual data were inconsistent with the simulation-based findings and inferred conclusions by Sorjonen, Nilsonne, et al. (2022). These results can be retrieved in the updated OSF page (https://osf.io/srt3n/). Therefore, we maintain our original theoretical and clinical interpretations that increased NFC and related concepts could protect against heightened future ADS and be considered when fine-tuning evidence-based therapies for depression and anxiety disorders. Further, NFC deficits could be instrumental in the etiology of common mental health problems. These assertions are consistent with ample published evidence on the essential role of NFC in various psychological issues beyond ADS, such as executive dysfunction (Hui et al., in press), quarantine-related thoughts and feelings (Wu et al., 2021), repetitive negative thinking (Lachlan et al., 2021), addictive behaviors (Shim et al., 2018), and treatment adherence (Hadj-Abo et al., 2020).

However, the change-to-future change effect of ADS on NFC was spurious and is an example of Lord’s paradox, i.e., the relation between a shift in X and a future shift in Y changes sign or direction after controlling for the baseline value of Y (Sorjonen, Melin, et al., 2022). This discrepancy is likely because adjusting for outcomes at baseline when using change scores as a predictor can inflate false positive errors, especially for studies with large sample sizes, as shown in a simulation study (Sorjonen et al., 2019). Thus, we urge readers to interpret with caution change-to-future change relations indicating the effect of ADS on NFC in our original paper. Overall, our findings offer more support for the vulnerability model (i.e., NFC predicting ADS) instead of the scar theory (ADS predicting NFC).