As clarified before, a first aim of the present study was to apply a Latent State-Trait (LST) analysis approach to extract the stable component of maternal depression, as measured by the SCL-90/R across three different occasions of measurement (respectively at child age 2, 5 and 8 years). In order to analyze LST models, two test-halves of the maternal depression score were computed. Table 1 shows the descriptive statistics of these test-halves and also the internal consistency (i.e., split-half reliability with Spearman–Brown correction) of SCL-90/R maternal depression across the three measurement occasions. As can be seen, all test-halves of maternal depression showed a substantial normal distribution with slight deviations only for kurtosis (< − 1). To assess longitudinal mean differences across the three assessment waves, repeated-measures ANOVAs were conducted, separately for the two test-halves. Results of these analyses showed a significant multivariate effect for both the first test-half [F(2, 158) = 8.39, p < .001] and the second test-half [F(2, 158) = 12.40, p < .001]. In particular, post-hoc Sidak tests revealed that, for both test-halves, the mean scores for maternal depression at both T2 and T3 were significantly lower than those observed at T1 (p < .001 and p < .01 respectively), indicating a significant reduction of maternal depression overtime.
Table 2 reports the intercorrelations among maternal depression test-halves across the different occasions of measurement. Results showed significant and large correlations among all measures and across all observations, a necessary condition for the application of LST models.
With regards to the children’s symptoms, Table 3 shows the descriptive statistics (i.e., mean, SD, skewness and kurtosis) and Crobach’s alpha values of the CBCL general and specific scales, as measured at T3 (at child age of 8 years—see inside brackets) and T4 (at child age of 12 years—see outside brackets) occasions of measurement. As can be seen from Table 3, some moderate deviations from normality (especially at T4) emerged for some scales (i.e., anxiety, withdrawal, internalizing disorders, thought problems, rule breaking, aggressive behaviors, externalizing behaviors), with skewness and kurtosis values not included within ± 1 interval. Interestingly, apart from the withdrawal scale, mean scores of all scales were significantly lower in the third measurement than in the fourth one, (see the last two columns of Table 3 to examine t test values and the corresponding probabilities), indicating that children’s symptoms tended to increase from 8 to 12 years of age (applying non-parametric tests, not assuming normal distribution of the scales, similar results emerged). Considering the large number of statistical comparisons conducted (eleven t tests), a correction was applied to conventional alpha level (.05) using Benjamini–Hochberg procedure. The Benjamini–Hochberg corrected analyses’ did not show substantial differences when compared with the analyses using conventional alpha levels.
Extracting stable, occasion and error components of maternal depression across three measurement occasions (at age 2, 5 and 8 of the children) applying LST analysis
In order to disentangle consistency, occasion-specificity, and error variance of maternal depression during children’s development, a Latent State-Trait [LST; 28] analysis approach was applied across three different occasions of measurement (i.e., at age 2, 5 and 8 of the children).
As shown in Fig. 1, a No Method (NM) model with three latent occasion factors, one stable factor, no method factors, and six casual error components were analyzed, including SCL-90/R test-halves of depression scale as observed variables. As shown in Table 4, this model was tested and compared with both a model that also included method latent factors to account for the variability due to test-halves differences, and a model that included only the general stable factor of maternal depression with no occasion and no method factors (NMNO). Regarding the former, recently different approaches that account for method effects in LST models were compared using simulation studies and actual data sets . The model with M − 1 method factors , that includes one method factor less than methods used in the study, and the model with no method factors (NM), have both shown unbiased parameter estimates, even for more complex models than the one conducted in the present study (≈ 20 estimated parameters), and also for smaller sample sizes (≈ 100). For these reasons, in the present study a comparison among NM, M-1, and NMNO was conducted to identify the best fitting model (see Table 4).
Since some of the measures showed slight deviations from normal distribution, we used maximum likelihood estimation robust to non-normality (MLR). Moreover, we fixed to 1 all factor loadings for each latent factor in order to increase the ratio between number of participants and number of estimated parameters . Finally, we constrained the occasion-specificities and the error variances to be equal.
Results showed that the NM model displayed an adequate fit with a non-significant chi square (see Table 4) and excellent levels for the other indices (RMSEA = .00; CFI = 1.00; TLI = 1.00; SRMR = .01). Similar results were found for the less restricted M-1 model that also revealed a non-significant chi square (see Table 4), and optimal levels for the other indices (RMSEA = .00; CFI = 1.00; TLI = 1.00; SRMR = .01). Finally, the NMNO model, that included only the general depression factor (excluding both occasion and method factors), showed a close to significant chi square (see Table 4), non-optimal levels for the RMSEA (.06), and adequate levels for the other indices (CFI = .99; TLI = .99; SRMR = .01). In order compare the fit of these models, the NM model was compared with both the M-1 and the NMNO ones applying the Δχ2 test. Results of these tests revealed that the NM model fitted better than the NMNO one [Δχ2(1) = 9.08, p < .01], and fitted similarly to the less parsimonious M-1 model [Δχ2(1) = .09, p = .76], indicating that the NM model was the best fitting one. As illustrated in Table 4, consistency was much higher than occasion-specificity, suggesting that maternal depression as measured by the SCL-90/R was highly stable overtime. It is worth noting that, when aggregating results of the two halves, excellent reliability was found for the SCL-90/R depression scale. Since, in the final NM model, for each latent factor all loadings were fixed to 1, and occasion-specificities and the error variances were constrained to be equal, a further statistical test was conducted to evaluate the adequacy of these restrictions. In particular, the NM model was compared to a model that relaxed these restrictions. No significant differences were found [Δχ2(3) = 4.32, p = .23], indicating that the more parsimonious restricted model was the best fitting one.
The stable component of maternal depression as a predictor of children’s symptoms
In order to investigate the predictive power of the stable-component of maternal depression on children’s symptom levels, the NM model was used including two additional observed variables (see Fig. 2): the CBCL scales as measured at O3 (at 8 age of the children) and at O4 (at age 12 of the children). The model proposed in Fig. 2 included both a Latent State-Trait approach (LST) —referring to the factorial estimation of the stable component of maternal depression across the different occasions of measurement—and a Cross Lagged Panel analysis (CLPM) —referring to the path analysis aimed to estimate the effect of maternal depression stable component on children's symptomatic scales at O4 controlling for children's symptomatic scales at O3.
More specifically, in a first set of three LST models, the stable-component of maternal depression estimated at O1, O2, and O3 (i.e., child age 2, 5, and 8 respectively), was included as a predictor, the O4 measure of each of the three general CBCL scale (i.e., Internalizing/Externalizing problems, and Emotional Dysregulation scales) was included as criterion, and the corresponding O3 measure of CBCL scale was included as a control variable. As shown in Table 5, each LST analysis (i.e., 1, 2, 3 models including as criterion, respectively, Internalizing, Externalizing and Emotional Dysregulation scale) fitted the data well, with no significant chi-square, and with adequate levels for the other indices (RMSEA ≤ .05; CFI, TLI ≥ .99; SRMR ≤ .01). Moreover, as expected, the stable-component of maternal depressive symptoms showed significant predictive power for each CBCL general scale at age 12, even when the corresponding CBCL scale at age 8 was controlled for. In particular, as shown in Table 5, in each model both the standardized structural coefficient of maternal depression (SSCMD) and the standardized coefficient of autoregression (SSCA) of CBCL general scales were significant, with a higher effect size for the latter. In order to confirm the validity of each model tested, these models were compared with analogous models in which the path between maternal depression and the CBCL scale was fixed to 0. The differences between the chi-square, computed for each pair of models, corrected with the appropriate formula for MLR parameter estimation , were all significant, confirming the relevance of the stable component of maternal depression in the prediction of the CBCL general scales (see Table 5). Interestingly, the unique contribution of the stable component of maternal depression was particularly strong for children’s internalizing symptoms scores, with respect to externalizing and emotional dysregulation ones.
In order to estimate the unique predictive contribution of the stable component of maternal depression on specific CBCL scales, a second set of eight LST models were conducted including the fourth occasion of measurement of each specific CBCL scale (i.e., Anxiety, Withdrawal, Somatization, Social Problems, Thought Problems, Attention problems, Rule Breaking behaviors, Aggressive behaviors) as criterion, and the third occasion of measurement of the corresponding CBCL scale as a covariate. As shown in Table 6, each LST analysis (i.e., 1, 2, 3, 4, 5, 6, 7, 8 models including as criterion respectively Anxiety, Withdrawal, Somatization, Social Problems, Thought Problems, Attention problems, Rule Breaking behaviors, Aggressive behaviors scale) fitted data well, with no significant chi square and adequate levels for the other indices (RMSEA ≤ .05; CFI, TLI ≥ .99; SRMR ≤ .01). The stable component of maternal depression showed significant predictive power on each of the CBCL specific scales at age 12, even when the corresponding CBCL scale at age 8 was controlled for. As shown in Table 6, in each model both the standardized structural coefficient of maternal depression (SSCMD) and the standardized coefficient of autoregression (SSCA) were significant, with higher effect size for the latter. As for previous analyses, to confirm the validity of each solution tested, the models were compared with analogous models in which the path between maternal depressive symptoms and CBCL scale was fixed to 0. The differences between chi-square, computed for each pair of models, corrected with the appropriate formula for MLR parameter estimation , were all significant (except for the model that includes Thought Problems as a criterion), confirming the relevance of the stable component of maternal depressive symptoms in the prediction of the CBCL specific scales (see Table 6). The stable-component of maternal depression was particularly predictive of children’s depression scores if compared with the other CBCL symptoms scales. Considering the large number of statistical tests conducted, to test the significance of parameters estimated (i.e., SSCMS, SSCA and Δχ2), a correction was applied to conventional alpha level (.05) using Benjamini–Hochberg procedure, but no differences emerged when compared with the conventional testing procedure.