Prospective Relations between Parents’ Depressive Symptoms and Children’s Attributional Style

Parents’ Psychopathology

We used the Structured Clinical Interview for DSM-IV Axis I Disorders (SCID-I; First et al., 1997) to evaluate psychopathology in parents. A randomly selected subset (N=23, 10%) of taped interviews was used to assess inter-rater reliability, yielding kappa coefficients ≥ .80.

Beck Depression Inventory, Second Edition (BDI-II;

Beck et al., 1996; Beck, Steer, & Garbin, 1988) is a 21-item self-report measure rated on a scale ranging from 0 (absence of symptoms) to 3 (most severe level of the symptom). Scores can range from 0 to 63; higher scores indicate more depression. Coefficient alpha of the BDI-II in this sample was ≥ .91 across all time points.

Children’s Measures

We assessed children’s explanatory style with the 24-item Children’s Attributional Style Questionnaire-Revised (CASQ-R, Thompson, Kaslow, Weiss, & Nolen-Hoeksema, 1998), which measures children’s beliefs about the causes of 12 positive and 12 negative events. Children select one of two possible causes for each event, either internal or external, stable or unstable, or global or specific. Lower total scores indicated a more depressive explanatory style, such that negative events were explained using internal, global, and stable attributions, and positive events were explained using external, specific, and unstable attributions. For example, “a good friend tells you that he hates you because” either (a) “My friend was in a bad mood that day” (external); or (b) “I wasn’t nice to my friend that day” (internal). Composite total scores ranged from −.50 to 1.00, with higher scores indicating a more positive attributional style. McDonald’s omega coefficients for the total score in this sample ranged from .68–.82 (McDonald, 2013; Dunn, Baguley, & Brunsden, 2014). Because internal consistency reliabilities of the CASQ-R tend to be low (Gladstone & Kaslow, 1995; Seligman et al., 1984; Thompson et al., 1998), we used an alternative index of reliability for this scale – McDonald’s omega coefficient. A problem with alpha is that it assumes that all items in the scale are equally good indicators of the underlying construct (tau equivalence). That is, no item is any better or worse than any other item in discriminating the latent construct (i.e., all have equal factor loadings), which is not likely the case for the CASQ. Omega estimates the proportion of variance in the items that is attributable to the common latent factor (the thing we care about) as opposed to error variance. This is the classic definition of reliability. Omega does not assume that each item is interchangeable.

The Children’s Depression Inventory (CDI; Kovacs, 1992) is a 27-item self-report measure of children’s symptoms of depression rated on a 3-point scale. Total scores can range from 0 to 54, with higher scores indicating more depression. Coefficient alpha for the CDI in this sample across all time points was ≥ .84.

Latent difference score models.

Latent difference score (LDS) modeling (McArdle & Hamagami, 2001) was used to capture change in parents’ depressive symptoms and in children’s explanatory style over time. The LDS approach is a highly general strategy for capturing dynamic change, subsuming both latent growth curve models and cross-lagged panel models. LDS modeling is particularly well suited to addressing hypotheses that involve predicting change in one time-varying process from prior levels of a parallel time-varying process (McArdle, 2009). At each measurement occasion (t) the variance of the measured dependent variable (DV, $y_t^M$) is decomposed into a true score ($y_t^T$) and a unique (error) score ( $e_t$). Change is modeled in the true scores rather than the measured variables, which has the advantage of removing the error variance from the measurement of the dependent variable.

In the LDS approach, we estimated latent difference scores (${[\Delta y]}_l^T$) representing the rate of change in the latent true score between adjacent measurement occasions, where l represents a specific time lag between adjacent time points. The latent difference score can be a function of multiple processes. In a dual change score (DCS) model, the latent difference score is a function of a constant latent slope ($\alpha \times \varsigma$) and the true score at the prior measurement occasion $\beta y{(t-1)}^T$), such that${[\Delta y]}_l^T=\alpha \times \zeta +\beta \times y{(t-1)}^T$. The unconditional DCS model estimates a mean starting value (${\mu }_0$), a mean constant rate of change (${\mu }_{\zeta }$), a proportional change coefficient (β), and error variance (${[ϵ]}_t$), which is presumed to be constant over time. Additionally, the models allow for individual differences in starting levels ($y_1^T$) and in the rate of constant change ($\varsigma$) by estimating parameters ${\sigma }_0^2\text{and}{\sigma }_{\varsigma }^2$, respectively, and their covariance ($\rho (0,\zeta )$. Thus, the model estimates seven parameters total.

LDS analyses also can accommodate multiple change processes simultaneously, allowing for flexible dynamic associations between time-varying constructs. In bivariate LDS models, levels of change in one time-varying construct affects levels of change in another time-varying construct. These can be unidirectional effects, where one time-varying process affects another, or they can be bidirectional between the two time-varying constructs. For example, in a bivariate dual change score model (BDCS), separate DCS models are specified for two time-varying processes. These models are then combined and allowed to influence one another. The rate of change at a specific time-lag for the first construct could be regressed on levels of the other time-varying process at the prior time point. Simultaneously, the latent rate of change in the second could be regressed on levels of the first time-varying construct at the prior time point. Cross-process regressions are referred to as “coupling” parameters and their estimates are expressed using γ coefficients.

Modeling sequence.

We first fit DCS models for depressive symptoms and children’s explanatory style, separately. We also tested whether the assumptions of common error variance (${ϵ}_t$) over time and constant proportional change coefficients (β) were tenable, relaxing these assumptions as needed. Then we combined the LDS models for parental depressive symptoms and children’s explanatory style into a BDCS model, allowing reciprocal effects whereby levels of one process at time t-1 predicted the rate of change in the other time-varying process at the subsequent time lag, and vice versa. Constant slopes ($\varsigma$) for both processes were regressed on to the intercept (representing baseline levels) of the other process. Covariances between the two intercepts and constant slopes were freely estimated. Finally, covariates representing characteristics of the parent and child assessed at Time 1 were added as predictors of the latent intercepts and slopes for both processes.

Latent Difference Score Model.

For children’s attributional style (CASQ), the dual change score (DCS) model provided a close fit to the data: χ²(12) = 17.69, p = .13; root mean square error of approximation (RMSEA) = .05, 90% confidence interval (CI) [.00, .09]; comparative fit index (CFI) = .99; standardized RMS residual (SRMR) = .04. For parental depressive symptoms, the DCS model provided a reasonably close fit to the data: χ²(12) = 22.43, p = .03; RMSEA = .06, 90% CI [.02, .10]; CFI = .98; SRMR = .03. The final bivariate LDS model (Figure 1) combined the DCS models for the BDI and CASQ.

We estimated bidirectional cross-process (coupling) parameters such that the latent difference score for the Beck Depression Inventory (BDI) at each time point was regressed onto levels of the CASQ at the prior time point, and latent difference scores for the CASQ at each time point were regressed onto levels of the BDI at the prior time point. The intercept and constant slope for both the BDI and CASQ were regressed onto parental depression status (i.e., whether the parent was depressed currently), and children’s age and sex. Inspection of residual variance plots indicated that the assumption of constant residual variance over time was not tenable for either the BDI or CASQ, particularly for the last time point. In the final model, residual variances for both the BDI and CASQ at the final time point were freely estimated rather than being constrained to be equal to the residual variances at prior time points. This model provided a close fit to the data: χ² = 35.22, df = 30, p = .24, CFI = .995; RMSEA = .028, 90% CI = .000 and .060; SRMR = .024. The final model parameter estimates are in Table 3.

Cross-process associations.

At each time lag, the rate of change in children’s attributional style (captured by latent difference scores) was negatively associated with parents’ levels of depressive symptoms at the prior time point. Higher parental depressive symptoms predicted accelerated decreases in attribution (CASQ) scores (increasing pessimism) from one time point to the next. In contrast, there was no association between children’s levels of attributional style and changes in parents’ depressive symptoms at subsequent time points.

Sensitivity Analyses.

We conducted a sensitivity analysis to eliminate an alternative model that observed associations between parental BDI and subsequent change in children’s CASQ were attributable to children’s depressive symptoms. This sensitivity analysis also addressed whether children’s current depression was a confounder or simpler explanation for associations between children’s attributions and parents’ depressive symptoms. Results of this sensitivity model were identical to the final bivariate dual change score model (BDCS), except that CASQ true scores were regressed onto children’s depressive symptom scores (CDI) at each time point. Because of some missing CDI data, we used multiple imputation and ran the sensitivity model in 50 imputed data sets, combining the results using Rubin’s (1996) rules. This did not alter the conclusions. There were still negative prospective associations between parents’ depressive symptom levels and the rate of change in children’s attributions at the subsequent time lag, and children’s attribution scores did not predict subsequent change in parents’ depressive symptoms. Thus, the prospective associations between parents’ depressive symptoms and change in children’s attributions were not merely due to children’s levels of depressive symptoms.