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First, direct pathways from each type of self-reported problematic substance use (alcohol and drug) to a service referral at wave 1 while controlling for child age, child gender, household poverty, and presence of prior reports on family were tested. For both the alcohol and drug models, there was no significant direct relationship from the problematic substance use to a service referral at wave 1 when the control variables were included in the model.

Single mediator models examining each of the hypothesized mediators (emotional maltreatment, harsh discipline, parental monitoring, and exposure to violence) for all

combinations of problematic substance use by baseline service referral were conducted next.

Emotional maltreatment, parental monitoring, and exposure to violence did not mediate the relationship from caregiver problematic alcohol use or caregiver problematic drug use to baseline service referral. However, harsh discipline fully mediated both the relationship from problematic

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drug use to baseline service referral and the relationship from problematic alcohol use to baseline service referral. See Appendix 18 for indirect parameter estimates and model fit statistics.

For each significant pathway, both direct and mediated, moderation was tested with each of the three hypothesized moderators (caregiver criminal involvement, domestic violence, and caregiver depression). When assessing for a moderating relationship, an interaction term (e.g., emotional maltreatment*depression) is created with the moderating variable and the variable involved in the direct or mediating pathway. When testing a moderating pathway, it is necessary to include the moderating variable as a mediator in the analysis to control for its individual impact on the relationship separate from the interaction term. If the interaction term (but not the moderating variable as a mediator) is a significant pathway then moderation alone is occurring.

If the moderating variable put in as a mediator is a significant pathway then the hypothesized moderator may be functioning as a mediator and should be examined as a mediator separate from the interaction term.

For the direct pathway from caregiver self-reported problematic alcohol use to referral for services at baseline, caregiver depression both moderated the relationship and served as a significant mediator in the relationship from problematic alcohol use to referral for services at baseline (Figure 24). The model indicates that increased problematic alcohol use was associated with meeting criteria for depression. Meeting criteria for depression was associated with

baseline services. The significant moderation indicated that problematic alcohol use levels were similar in both the groups that received services and the group that did not receive services when there was no caregiver depression. When there was caregiver depression, there were higher levels of problematic alcohol use in the group without baseline services compared to the group with baseline services. See Appendix 19 for indirect parameter estimates and model fit statistics.

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Domestic violence also moderated the direct relationship from problematic alcohol use to referral for services at baseline. Criminal involvement did not moderate the direct pathway. Consistent with the direct model from problematic alcohol use to referral for services at baseline, major depression served as a mediator and moderator in the relationship from problematic alcohol use to referral for services at baseline when included in the model mediated by harsh discipline.

Criminal involvement and domestic violence were not moderators in the indirect relationship through harsh discipline.

For the direct pathway from caregiver self-reported problematic drug use to referral for services at baseline, caregiver depression served as a significant mediator in the relationship but did not moderate the relationship (Figure 25). The model indicates that the path from self-reported problematic drug use to baseline services is through caregiver depression such that higher problematic drug use is related to the presence of caregiver depression which is associated with baseline services. See Appendix 20 for indirect parameter estimates and model fit statistics.

For this reason, caregiver depression was then tested separately as single mediator model.

Caregiver depression was a significant fully mediating pathway in the single mediator model.

Criminal involvement and domestic violence did not moderate the direct pathway from problematic drug use to referral for services at baseline. Again, major depression served as a mediator and moderator in the relationship from problematic drug use to referral for services at baseline when included in the model mediated by harsh discipline. Criminal involvement and domestic violence were not moderators in the indirect relationship through harsh discipline.

For problematic alcohol use to baseline services, the final model is a mediation and moderation model with caregiver depression both serving as mediator and a moderator in the direct path from problematic alcohol use to baseline services model (Figure 24). All fit indices

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for this model are strong and indicate that the model fits the data very well. The final model for problematic drug use to baseline services is a single mediator model with caregiver depression fully mediating the relationship from problematic drug use to baseline services (Figure 25).

Again, all fit indices indicate that the model is a very strong fit with the data.

Figure 24

Figure 25

92 Referrals for Services at Wave 2

To examine the direct pathways from problematic substance use to each type of service referral at wave 2, direct models were run that regressed each type of service referral (any services, services to caregiver, services to child, concrete services, or child welfare services) on each type of problematic substance use (alcohol or drug) while controlling for child age, child gender, household poverty, and presence of prior reports on family. For both the alcohol and drug models, there were no significant direct relationships from the problematic substance use to services to child when the control variables were included in the model. There were no direct relationships from problematic alcohol use to any services, services to caregiver, concrete services, or child welfare services. There were direct relationships from problematic drug use to any services (μ=0.10, p < .05), services to caregiver (μ=0.14, p < .01), concrete services (μ=0.10, p < .05), and child welfare services (μ=0.10, p < .05).

Next, single mediator models were run with each of the hypothesized mediators (emotional maltreatment, harsh discipline, parental monitoring, and exposure to violence) for all

combinations of problematic substance use by type of service referral. None of the hypothesized mediators was a significant mediator in the relationship from caregiver self-reported problematic alcohol or drug use to any of the service referral variables at wave 2. See Appendices 21-25 for indirect parameter estimates and model fit statistics.

For the significant direct pathways from caregiver self-reported problematic drug use to any services, services to the caregiver, concrete services, and child welfare services at wave 2, moderation was tested with each of the three hypothesized moderators (caregiver criminal involvement, domestic violence, and caregiver depression). None of the hypothesized moderators moderated the direct relationship.

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There are no final models reported for the relationship from problematic alcohol use to any of the services at wave 2 variables or for problematic drug use to services to child at wave 2 because there were no direct relationships after including the control variables in the model. The final models for problematic drug use to any services, caregiver services, concrete services, and child welfare services at wave 2 were direct models (Figure 26-29). These models indicate that self-report of problematic drug use is positively associated with services at wave 2. The direct models were just identified. Therefore, fit indices are not produced for these models.

Figure 26

Figure 27

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Figure 29

Subsequent CPS Reports by Wave 2

After including the control variables in the model, there were no significant direct pathways from caregiver self-reported problematic alcohol or drug use to a subsequent CPS report by wave 2.

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Single mediator models examined the four hypothesized mediators for all both types of problematic substance use with subsequent CPS reports. None of the hypothesized mediators were significant mediators in that relationship. See Appendix 26 for indirect parameter estimates and model fit statistics.

Case Outcomes at Wave 1

After including the control variables in the model, there were no significant direct pathways from caregiver self-reported problematic alcohol or drug use to case outcomes at wave 1.

Single mediator models examined the four hypothesized mediators for all both types of problematic substance use with case outcomes at wave 1. None of the hypothesized mediators were significant mediators in those relationships. See Appendix 27 for indirect parameter estimates and model fit statistics.

Case Outcomes at Wave 2

Consistent with the results for case outcomes at wave 1, there were no significant direct pathways from caregiver self-reported problematic alcohol and drug use to case outcomes at wave 2. There were also no significant single mediators in these models. See Appendix 27 for indirect parameter estimates and model fit statistics.

Out-of-Home Placement between Baseline and Wave 2

In the direct models regressing out-of-home (OOH) placements occurring between baseline and 18-month follow-up on caregiver self-reported problematic substance use (alcohol and drug), there were no significant direct relationships from problematic alcohol use to OOH placement or from problematic drug use to OOH placement after the inclusion of the control variables.

In the single mediator models, emotional maltreatment, parental monitoring, and exposure to violence were not significant pathways from either problematic alcohol use or problematic drug

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use to OOH placement. Harsh discipline was a significant pathway which fully mediated the relationship from both problematic drug use and problematic alcohol use to OOH placement.

See Appendix 28 for indirect parameter estimates and model fit statistics.

For the direct pathway from caregiver self-reported problematic alcohol use to OOH placement, moderation was tested with each of the three hypothesized moderators (caregiver criminal involvement, domestic violence, and caregiver depression). See Appendix 29 for indirect parameter estimates and model fit statistics. Criminal involvement and domestic violence did not moderate the relationship. In the model examining caregiver depression as moderator in the direct relationship from problematic alcohol use to OOH placement, caregiver depression was not found to be moderator but it was a significant mediating pathway. For this reason, caregiver depression was examined in a separate single mediator model. The single mediator model with caregiver depression indicated it is a significant pathway which fully mediates the relationship from problematic alcohol use to OOH placement. The two significant single mediators (harsh discipline, caregiver depression) were tested in a double mediator model.

For the mediated pathway from caregiver problematic alcohol use to OOH placement by wave 2 through harsh discipline, only caregiver depression was a significant moderator. Caregiver depression served as both a significant moderator in the mediating pathway from problematic alcohol use to OOH placement and a significant mediating pathway. Harsh discipline also remained a significant pathway in the model. Combinations of the significant mediators (harsh discipline, caregiver depression) and significant moderators (caregiver depression) were

examined.

For the direct pathway from caregiver self-reported problematic drug use to OOH placement at wave 2, none of the hypothesized moderators moderated the relationship but major criminal

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involvement fully mediated the relationship. A single mediator model with criminal involvement was then tested and found to have strong fit. For the mediated pathway from caregiver

problematic drug use to OOH placement by wave 2 through harsh discipline, caregiver

depression was found to both mediate and moderate the relationship. Caregiver depression was then examined separately in a single mediator model. See Appendix 30 for indirect parameter estimates and model fit statistics.

For problematic alcohol use to OOH placement, the final model is a mediation model with caregiver depression fully mediating the relationship from problematic alcohol use to OOH placement (Figure 30). The model indicates that the path from self-reported problematic alcohol use to child OOH placement is through caregiver depression such that higher problematic

alcohol use is associated with the presence of caregiver depression which is associated with OOH placement. Another model, examining depression as both a mediator and a moderator in the direct relationship, had strong χ² test of model fit and RMSEA fit indices but weak CFI, TLI, and WRMR fit indices. See Appendix 29 for indirect parameter estimates and model fit

statistics. The single mediator model (Figure 30) was chosen because of its consistently strong fit statistics on all fit indicators.

For problematic drug use to OOH placement, the final model is a mediation model with criminal involvement fully mediating the relationship from problematic drug use to OOH placement (Figure 31). The model indicates that the path from self-reported problematic drug use to child OOH placement is through caregiver criminal involvement such that higher problematic alcohol use is associated with having one or more convictions which is associated with not having a child placed OOH. Several alternative models also had strong fit indices and could arguably serve as the final model for this relationship. The single mediator model with

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caregiver depression had very strong fit indices but pathway through caregiver depression was not significant, indicating a strong relationship between the variables but little explanatory power. The two mediator model contacting harsh discipline and criminal involvement had acceptable fit indices but did not indicate as strong a fit as the single mediator model containing only criminal involvement. Finally, the two mediator model containing depression and criminal involvement had strong fit indices. However, only criminal involvement was a significant pathway when both paths were included in the model. Therefore, the single mediator model (Figure 31) provides both strong fit and the same explanatory paths as the larger models. See Appendix 29 for indirect parameter estimates and model fit statistics.

Figure 30

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Child Depression at Wave 1

After including the control variables in the model, there were no significant direct pathways from caregiver self-reported problematic alcohol or drug use to child depression at wave 1.

Single mediator models examined the four hypothesized mediators for both types of problematic substance use with child depression at wave 1. Emotional maltreatment and harsh discipline were not significant mediators from caregiver self-reported problematic alcohol use or from self-reported problematic drug use to child depression at wave 1. In only the problematic alcohol use to child depression at wave 1 single mediator models, parental monitoring and exposure to violence each fully mediated the pathway from problematic alcohol use to child depression at wave 1. Parental monitoring and exposure to violence were not mediators in the

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relationship from problematic drug use to child depression at wave 1. See Appendices 31-32 for indirect parameter estimates and model fit statistics.

Next, a double mediator model was conducted to determine if including both significant single mediators (parental monitoring and exposure to violence) in a parallel double mediator model better fit the data than single mediator models. For the model examining the pathway from problematic alcohol use to child depression at wave 1, parental monitoring was a significant mediator that fully mediated the pathway. Exposure to violence was no longer a significant pathway in the double mediator model. See Appendix 31 for indirect parameter estimates and model fit statistics.

For the direct pathway from caregiver problematic alcohol use to child depression at wave 1, none of the hypothesized moderators moderated the relationship. For the mediated pathway from caregiver problematic alcohol use to child depression at wave 1 through parental

monitoring, none of the hypothesized moderators moderated the relationship. For the mediated pathway from caregiver problematic alcohol use to child depression at wave 1 through exposure to violence, none of the hypothesized moderators moderated the relationship.

For problematic alcohol use to child depression at wave 1, the final model is a mediation model with parental monitoring fully mediating the relationship from problematic alcohol use to child depression at wave 1 (Figure 32). The model indicates that the path from self-reported problematic alcohol use to child depression is through parental monitoring such that higher problematic alcohol use is associated with better monitoring which is associated with lower reported child depression. The model had strong fit on all fit indices. The single mediator model with exposure to violence had acceptable fit but was not as good a fit to the data as the chosen final model. See Appendix 33 for indirect parameter estimates and model fit statistics. There is

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no final model for the relationship from problematic drug use to child depression at wave 1 because there were no significant direct or mediating pathways.

Figure 32

Child Depression at Wave 2

After including the control variables in the model, there was no significant direct pathway from caregiver self-reported problematic alcohol or drug use to child depression at wave 2.

Single mediator models examined the four hypothesized mediators for both types of problematic substance use with child depression at wave 2. Results were consistent with the single mediator results seen in the child depression at wave 1 models. Emotional maltreatment and harsh discipline were not significant mediators from caregiver self-reported problematic alcohol use or from self-reported problematic drug use to child depression at wave 2. In only the problematic alcohol use to child depression at wave 2 single mediator models, parental

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monitoring and exposure to violence each fully mediated the pathway from problematic alcohol use to child depression at wave 2. Parental monitoring and exposure to violence were not mediators in the relationship from problematic drug use to child depression at wave 2. See Appendices 31-32 for indirect parameter estimates and model fit statistics.

As was conducted in the caregiver depression at wave 1 models, a double mediator model was conducted that included both significant single mediators (parental monitoring and exposure to violence) in a parallel double mediator model. For the model examining the pathway from problematic alcohol use to child depression at wave 2, neither parental monitoring nor exposure to violence were significant pathways in the double mediator model. See Appendix 31 for indirect parameter estimates and model fit statistics.

For the direct pathway from caregiver problematic alcohol use to child depression at wave 2, none of the hypothesized moderators moderated the relationship. For the mediated pathway from caregiver problematic alcohol use to child depression at wave 2 through parental

monitoring, none of the hypothesized moderators moderated the relationship. For the mediated pathway from caregiver problematic alcohol use to child depression at wave 2 through exposure to violence, depression was a significant moderator but the model fit was very poor.

For problematic alcohol use to child depression at wave 2, the final model is a mediation model with parental monitoring fully mediating the relationship from problematic alcohol use to child depression at wave 2 (Figure 33). The model indicates that the path from self-reported problematic alcohol use to child depression at wave 2 is again through parental monitoring such that higher problematic alcohol use is associated with better monitoring which is associated with lower reported child depression. The model had strong fit on all fit indices except the TLI. The single mediator model with exposure to violence had acceptable fit on all indices but the TLI but

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was not as good a fit to the data as the chosen final model. See Appendix 34 for indirect parameter estimates and model fit statistics. There is no final model for the relationship from problematic drug use to child depression at wave 2 because there were no significant direct or

was not as good a fit to the data as the chosen final model. See Appendix 34 for indirect parameter estimates and model fit statistics. There is no final model for the relationship from problematic drug use to child depression at wave 2 because there were no significant direct or