Variables

Name Use Description Possible Values
improving DV Overall, has your life been improving in the last 6 months?

1 = Not at all

2 = Not really

3 = Neutral

4 = Mostly, yes

5 = Yes, very much

feedback_aware IV Are you aware of any way to provide feedback or complaints about assistance?

0 = No

1 = Yes

consulted IV In the last 6 months, have you been asked by a humanitarian organization what aid you need?

0 = No

1 = Yes

fem Control Gender

0 = Male

1 = Female

age Control Age Numeric
hoh Control Head of household?

0 = No

1 = Yes

Descriptive Statistics

Summary Statistics for Continuous & Ordinal Variables
Variable Mean Median Standard Deviation Minimum Maximum
Improving 4.14 5 1.22 1 5
Community_Level_Improvements 1.20 1 1.14 0 7
Individual_Level_Improvements 0.90 1 0.97 0 6
Institutional_Level_Improvements 1.26 1 0.79 0 5
Age 33.64 30 13.09 18 90
Proportions for Binary Variables
Proportion in Sample
Aware of Feedback 0.56
Consulted 0.54
Female 0.51
Head of Household 0.62

OLS Models

Awareness of Voice Opportunities

model_1 <- lm(improving ~ feedback_aware + fem + age + hoh, data = ds)

model_2 <- lm(improving ~ consulted + fem + age + hoh, data = ds)

model_3 <- lm(improving ~ feedback_aware + consulted + fem + age + hoh, data = ds)
modelsummary(
  list(model_1, model_2, model_3),
  title = "Awareness of Voice Opportunities",
  stars = c("*" = 0.05,"**" = 0.01,"***" = 0.001),
  statistic = c("std.error"),
  coef_map = c(
    "feedback_aware" = "Voice Opportunities Awareness",
    "consulted" = "Consulted by Humanitarian Org",
    "fem" = "Female",
    "age" = "Age",
    "hoh" = "Head of Household",
    "(Intercept)" = "Constant"),
  gof_omit = "AIC|BIC|Log.Lik.|RMSE",
  output = "html")
Awareness of Voice Opportunities
(1) (2) (3)
* p < 0.05, ** p < 0.01, *** p < 0.001
Voice Opportunities Awareness 0.401*** 0.337***
(0.081) (0.082)
Consulted by Humanitarian Org 0.378*** 0.311***
(0.082) (0.083)
Female 0.246** 0.278** 0.264**
(0.093) (0.094) (0.093)
Age 0.004 0.004 0.004
(0.003) (0.003) (0.003)
Head of Household 0.403*** 0.392*** 0.370***
(0.100) (0.101) (0.100)
Constant 3.403*** 3.407*** 3.274***
(0.140) (0.141) (0.143)
Num.Obs. 875 874 874
R2 0.055 0.052 0.070
R2 Adj. 0.050 0.048 0.065
F 12.605 11.998 13.121

Awareness of Different Voice Tools

model_4 <- lm(improving ~ feedback_typesaware_cmpln_box + feedback_typesaware_office_fic + feedback_typesaware_majhee + feedback_typesaware_leader + feedback_typesaware_ngo_staff + feedback_typesaware_gov_mil + feedback_typesaware_ngo_vol + feedback_typesaware_voice_rcrd + fem + age + hoh, data = ds)
modelsummary(
  list(model_4),
  title = "Awareness of Different Voice Tools",
  stars = c("*" = 0.05,"**" = 0.01,"***" = 0.001),
  statistic = c("std.error"),
  coef_map = c(
    "feedback_typesaware_cmpln_box" = "Complaint or Feedback Box",
    "feedback_typesaware_office_fic" = "Feedback at an Office",
    "feedback_typesaware_majhee" = "Speak with Majhi",
    "feedback_typesaware_leader" = "Community or Religious Leader",
    "feedback_typesaware_ngo_staff" = "Speak with NGO Staff",
    "feedback_typesaware_gov_mil" = "Government or Military",
    "feedback_typesaware_ngo_vol" = "NGO Volunteer, Mobiliser",
    "feedback_typesaware_voice_rcrd" = "Voice Recorder in Safe Space",
    "fem" = "Female",
    "age" = "Age",
    "hoh" = "Head of Household",
    "(Intercept)" = "Constant"),
  gof_omit = "AIC|BIC|Log.Lik.|RMSE",
  output = "html")
Awareness of Different Voice Tools
(1)
* p < 0.05, ** p < 0.01, *** p < 0.001
Complaint or Feedback Box 0.414
(0.244)
Feedback at an Office −0.498**
(0.165)
Speak with Majhi 0.659**
(0.216)
Community or Religious Leader 0.062
(0.114)
Speak with NGO Staff 0.117
(0.101)
Government or Military 0.343***
(0.098)
NGO Volunteer, Mobiliser 0.434**
(0.157)
Voice Recorder in Safe Space −0.433
(1.078)
Female 0.507***
(0.118)
Age 0.002
(0.004)
Head of Household 0.325**
(0.125)
Constant 2.903***
(0.269)
Num.Obs. 493
R2 0.117
R2 Adj. 0.096
F 5.773

Barriers

model_6_competence <- lm(improving ~ feedback_aware + feedback_barriers_no_skills + feedback_aware*feedback_barriers_no_skills + fem + age + hoh, data = ds)

model_6_empowerment <- lm(improving ~ feedback_aware + feedback_barriers_afraid + feedback_aware*feedback_barriers_afraid + fem + age + hoh, data = ds)

model_6_trust <- lm(improving ~ feedback_aware + feedback_barriers_no_trust + feedback_aware*feedback_barriers_no_trust + fem + age + hoh, data = ds)

model_6_effectiveness <- lm(improving ~ feedback_aware + feedback_barriers_no_action + feedback_aware*feedback_barriers_no_action + fem + age + hoh, data = ds)

model_7_competence <- lm(improving ~ consulted + feedback_barriers_no_skills + consulted*feedback_barriers_no_skills + fem + age + hoh, data = ds)

model_7_empowerment <- lm(improving ~ consulted + feedback_barriers_afraid + consulted*feedback_barriers_afraid + fem + age + hoh, data = ds)

model_7_trust <- lm(improving ~ consulted + feedback_barriers_no_trust + consulted*feedback_barriers_no_trust + fem + age + hoh, data = ds)

model_7_effectiveness <- lm(improving ~ consulted + feedback_barriers_no_action + consulted*feedback_barriers_no_action + fem + age + hoh, data = ds)

Overall, the barriers don’t have much of an effect, and they don’t change the effect that the other IVs have on the DV. In only 3 of the 8 models do the barriers have a significant relationship with perceptions of life improvements, and in two of these cases a barrier (that the refugees don’t think anything will change) actually has a positive relationship with the dv and in one case a barrier (that refugees don’t have the skills needed) has a negative relationship with the dv. In none of the models are the interaction terms significant.

I think it’s best to just leave these out.

Results for Types of Improvements

Factor analysis, MCA, and PCA all did not work very well with these variables. Accordingly, we will simply sum them within three categories: institutional, individual, and community improvements.

Community Level

model_8 <- lm(improve_community ~ feedback_aware + consulted + fem + age + hoh, data = ds)

summary(model_8)
## 
## Call:
## lm(formula = improve_community ~ feedback_aware + consulted + 
##     fem + age + hoh, data = ds)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5969 -0.7739 -0.1132  0.6877  5.4047 
## 
## Coefficients:
##                   Estimate  Std. Error t value             Pr(>|t|)    
## (Intercept)     1.11322517  0.13436444   8.285 0.000000000000000445 ***
## feedback_aware  0.19881906  0.07726559   2.573             0.010242 *  
## consulted       0.28391765  0.07756147   3.661             0.000267 ***
## fem            -0.33744136  0.08702277  -3.878             0.000113 ***
## age            -0.00008874  0.00299144  -0.030             0.976342    
## hoh             0.00266294  0.09382531   0.028             0.977364    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.107 on 868 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.054,  Adjusted R-squared:  0.04855 
## F-statistic:  9.91 on 5 and 868 DF,  p-value: 0.000000003127

Individual Level

model_9 <- lm(improve_individual ~ feedback_aware + consulted + fem + age + hoh, data = ds)

summary(model_9)
## 
## Call:
## lm(formula = improve_individual ~ feedback_aware + consulted + 
##     fem + age + hoh, data = ds)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3676 -0.6027 -0.2200  0.4841  4.8185 
## 
## Coefficients:
##                 Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)     1.148425   0.110969  10.349 < 0.0000000000000002 ***
## feedback_aware  0.065903   0.063812   1.033                0.302    
## consulted       0.126837   0.064056   1.980                0.048 *  
## fem            -0.578133   0.071870  -8.044  0.00000000000000284 ***
## age            -0.003436   0.002471  -1.391                0.165    
## hoh             0.095175   0.077488   1.228                0.220    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9142 on 868 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.1152, Adjusted R-squared:  0.1101 
## F-statistic:  22.6 on 5 and 868 DF,  p-value: < 0.00000000000000022

Institutional Level

model_10 <- lm(improve_institutional ~ feedback_aware + consulted + fem + age + hoh, data = ds)

summary(model_10)
## 
## Call:
## lm(formula = improve_institutional ~ feedback_aware + consulted + 
##     fem + age + hoh, data = ds)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5792 -0.4196 -0.1380  0.5949  3.4609 
## 
## Coefficients:
##                 Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)     1.176989   0.092848  12.677 < 0.0000000000000002 ***
## feedback_aware  0.152354   0.053392   2.854              0.00443 ** 
## consulted       0.128558   0.053596   2.399              0.01667 *  
## fem            -0.266236   0.060134  -4.427            0.0000108 ***
## age             0.001146   0.002067   0.554              0.57958    
## hoh             0.046828   0.064835   0.722              0.47033    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7649 on 868 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.05939,    Adjusted R-squared:  0.05397 
## F-statistic: 10.96 on 5 and 868 DF,  p-value: 0.0000000003009
stargazer(model_8, model_9, model_10, type = "text")
## 
## =========================================================================================
##                                                   Dependent variable:                    
##                                ----------------------------------------------------------
##                                improve_community improve_individual improve_institutional
##                                       (1)               (2)                  (3)         
## -----------------------------------------------------------------------------------------
## feedback_aware                      0.199**            0.066              0.152***       
##                                     (0.077)           (0.064)              (0.053)       
##                                                                                          
## consulted                          0.284***           0.127**              0.129**       
##                                     (0.078)           (0.064)              (0.054)       
##                                                                                          
## fem                                -0.337***         -0.578***            -0.266***      
##                                     (0.087)           (0.072)              (0.060)       
##                                                                                          
## age                                 -0.0001            -0.003               0.001        
##                                     (0.003)           (0.002)              (0.002)       
##                                                                                          
## hoh                                  0.003             0.095                0.047        
##                                     (0.094)           (0.077)              (0.065)       
##                                                                                          
## Constant                           1.113***           1.148***            1.177***       
##                                     (0.134)           (0.111)              (0.093)       
##                                                                                          
## -----------------------------------------------------------------------------------------
## Observations                          874               874                  874         
## R2                                   0.054             0.115                0.059        
## Adjusted R2                          0.049             0.110                0.054        
## Residual Std. Error (df = 868)       1.107             0.914                0.765        
## F Statistic (df = 5; 868)          9.910***          22.602***            10.961***      
## =========================================================================================
## Note:                                                         *p<0.1; **p<0.05; ***p<0.01

Appendix

Proportions for Variables Used to Make Leveled Improvements

prop_table_aid_well <- ds %>%
  summarize(
    aid_well_improved_sanitation = mean(aid_well_improved_sanitation, na.rm = TRUE),
    aid_well_clean_water = mean(aid_well_clean_water, na.rm = TRUE),
    aid_well_ngo_training = mean(aid_well_ngo_training, na.rm = TRUE),
    aid_well_prep_natural_disaster = mean(aid_well_prep_natural_disaster, na.rm = TRUE),
    aid_well_more_safespaces_c = mean(aid_well_more_safespaces_c, na.rm = TRUE),
    aid_well_more_safespaces_w = mean(aid_well_more_safespaces_w, na.rm = TRUE),
    aid_well_better_relationships = mean(aid_well_better_relationships, na.rm = TRUE),
    aid_well_psychosocial_support = mean(aid_well_psychosocial_support, na.rm = TRUE),
    aid_well_collect_firewood = mean(aid_well_collect_firewood, na.rm = TRUE),
    aid_well_diverse_food = mean(aid_well_diverse_food, na.rm = TRUE),
    aid_well_employment_access = mean(aid_well_employment_access, na.rm = TRUE),
    aid_well_community_groups = mean(aid_well_community_groups, na.rm = TRUE),
    aid_well_more_learning = mean(aid_well_more_learning, na.rm = TRUE),
    aid_well_id_card = mean(aid_well_id_card, na.rm = TRUE),
    aid_well_stronger_shelter_mater = mean(aid_well_stronger_shelter_mater, na.rm = TRUE),
    aid_well_health_services = mean(aid_well_health_services, na.rm = TRUE),
    aid_well_aid_organised = mean(aid_well_aid_organised, na.rm = TRUE),
    aid_well_structural_improvement = mean(aid_well_structural_improvement, na.rm = TRUE))

prop_table_aid_well <- t(prop_table_aid_well)

rownames(prop_table_aid_well) <- c("Improved Sanitation", "Clean Water", "NGO Training", "Natural Disaster Preparation", "More Safe Spaces for Children", "More Safe Spaces for Women", "Better Relationships", "Psychosocial Support", "Firewood Collection", "Food Diversity", "Employment Access", "Community Groups", "Learning Access", "ID Card", "Stronger Shelter Materials", "Health Services", "Aid More Organised", "Structural Improvements")

prop_table_aid_well %>% 
  kable(digits = 2, caption = "Proportions for Binary Variables", col.names = "Proportion in Sample", row.names = TRUE) %>%
  kable_styling(full_width = TRUE)
Proportions for Binary Variables
Proportion in Sample
Improved Sanitation 0.46
Clean Water 0.30
NGO Training 0.20
Natural Disaster Preparation 0.09
More Safe Spaces for Children 0.10
More Safe Spaces for Women 0.04
Better Relationships 0.01
Psychosocial Support 0.07
Firewood Collection 0.41
Food Diversity 0.13
Employment Access 0.07
Community Groups 0.14
Learning Access 0.09
ID Card 0.03
Stronger Shelter Materials 0.27
Health Services 0.10
Aid More Organised 0.07
Structural Improvements 0.81
allprops_df <- data.frame(
  Variable = rownames(prop_table_aid_well),
  Proportion = as.numeric(prop_table_aid_well[, 1]))

datasummary_df(allprops_df, 
               title = "Proportions for Binary Variables", 
               fmt = 2, 
               output = "/Users/corbinwalls/Library/CloudStorage/OneDrive-american.edu/Graduate Assistantship/Voice in Refugee Camps/Analysis/Appendix A.docx")
## NULL

SUR models for Different Levels of Outcomes

ds$improve_individual_scaled <- scale(ds$improve_individual, center = FALSE)
ds$improve_community_scaled <- scale(ds$improve_community, center = FALSE)
ds$improve_institutional_scaled <- scale(ds$improve_institutional, center = FALSE)

indiv <- improve_individual_scaled ~ feedback_aware + consulted + fem + age + hoh
comm <- improve_community_scaled ~ feedback_aware + consulted + fem + age + hoh
inst <- improve_institutional_scaled ~ feedback_aware + consulted + fem + age + hoh
fitsur <- systemfit(list(indivreg = indiv, commreg= comm, instreg = inst), data = ds, method = "SUR")
summary(fitsur)
## 
## systemfit results 
## method: SUR 
## 
##           N   DF     SSR detRCov   OLS-R2 McElroy-R2
## system 2622 2604 1031.41 0.04829 0.080666    0.05912
## 
##            N  DF     SSR      MSE     RMSE       R2   Adj R2
## indivreg 874 868 413.543 0.476432 0.690241 0.115198 0.110101
## commreg  874 868 388.913 0.448057 0.669370 0.054003 0.048554
## instreg  874 868 228.951 0.263769 0.513584 0.059389 0.053971
## 
## The covariance matrix of the residuals used for estimation
##           indivreg   commreg   instreg
## indivreg 0.4764321 0.1152565 0.0627804
## commreg  0.1152565 0.4480565 0.0926173
## instreg  0.0627804 0.0926173 0.2637687
## 
## The covariance matrix of the residuals
##           indivreg   commreg   instreg
## indivreg 0.4764321 0.1152565 0.0627804
## commreg  0.1152565 0.4480565 0.0926173
## instreg  0.0627804 0.0926173 0.2637687
## 
## The correlations of the residuals
##          indivreg  commreg  instreg
## indivreg 1.000000 0.249459 0.177097
## commreg  0.249459 1.000000 0.269410
## instreg  0.177097 0.269410 1.000000
## 
## 
## SUR estimates for 'indivreg' (equation 1)
## Model Formula: improve_individual_scaled ~ feedback_aware + consulted + fem + 
##     age + hoh
## 
##                   Estimate  Std. Error  t value               Pr(>|t|)    
## (Intercept)     0.86706646  0.08378208 10.34907 < 0.000000000000000222 ***
## feedback_aware  0.04975725  0.04817846  1.03277               0.301999    
## consulted       0.09576286  0.04836295  1.98009               0.048009 *  
## fem            -0.43649306  0.05426249 -8.04410  0.0000000000000028866 ***
## age            -0.00259389  0.00186529 -1.39060               0.164702    
## hoh             0.07185787  0.05850417  1.22825               0.219685    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.690241 on 868 degrees of freedom
## Number of observations: 874 Degrees of Freedom: 868 
## SSR: 413.543052 MSE: 0.476432 Root MSE: 0.690241 
## Multiple R-Squared: 0.115198 Adjusted R-Squared: 0.110101 
## 
## 
## SUR estimates for 'commreg' (equation 2)
## Model Formula: improve_community_scaled ~ feedback_aware + consulted + fem + 
##     age + hoh
## 
##                     Estimate    Std. Error  t value               Pr(>|t|)    
## (Intercept)     0.6731559604  0.0812488133  8.28512 0.00000000000000044409 ***
## feedback_aware  0.1202238643  0.0467217177  2.57319             0.01024159 *  
## consulted       0.1716821195  0.0469006354  3.66055             0.00026688 ***
## fem            -0.2040473646  0.0526217879 -3.87762             0.00011345 ***
## age            -0.0000536593  0.0018088939 -0.02966             0.97634172    
## hoh             0.0016102512  0.0567352154  0.02838             0.97736411    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.66937 on 868 degrees of freedom
## Number of observations: 874 Degrees of Freedom: 868 
## SSR: 388.913074 MSE: 0.448057 Root MSE: 0.66937 
## Multiple R-Squared: 0.054003 Adjusted R-Squared: 0.048554 
## 
## 
## SUR estimates for 'instreg' (equation 3)
## Model Formula: improve_institutional_scaled ~ feedback_aware + consulted + fem + 
##     age + hoh
## 
##                    Estimate   Std. Error  t value               Pr(>|t|)    
## (Intercept)     0.790248205  0.062339351 12.67655 < 0.000000000000000222 ***
## feedback_aware  0.102292980  0.035847927  2.85353              0.0044266 ** 
## consulted       0.086315829  0.035985204  2.39865              0.0166658 *  
## fem            -0.178755227  0.040374843 -4.42739            0.000010754 ***
## age             0.000769181  0.001387901  0.55420              0.5795814    
## hoh             0.031440730  0.043530931  0.72226              0.4703280    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.513584 on 868 degrees of freedom
## Number of observations: 874 Degrees of Freedom: 868 
## SSR: 228.951261 MSE: 0.263769 Root MSE: 0.513584 
## Multiple R-Squared: 0.059389 Adjusted R-Squared: 0.053971
comm_indiv_feedback <- glht(fitsur,linfct = c("commreg_feedback_aware - indivreg_feedback_aware = 0"))
summary(comm_indiv_feedback) 
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: systemfit(formula = list(indivreg = indiv, commreg = comm, instreg = inst), 
##     method = "SUR", data = ds)
## 
## Linear Hypotheses:
##                                                       Estimate Std. Error z value Pr(>|z|)
## commreg_feedback_aware - indivreg_feedback_aware == 0  0.07047    0.05815   1.212    0.226
## (Adjusted p values reported -- single-step method)
inst_indiv_feedback <- glht(fitsur,linfct = c("instreg_feedback_aware - indivreg_feedback_aware = 0"))
summary(inst_indiv_feedback) 
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: systemfit(formula = list(indivreg = indiv, commreg = comm, instreg = inst), 
##     method = "SUR", data = ds)
## 
## Linear Hypotheses:
##                                                       Estimate Std. Error z value Pr(>|z|)
## instreg_feedback_aware - indivreg_feedback_aware == 0  0.05254    0.05472    0.96    0.337
## (Adjusted p values reported -- single-step method)
comm_inst_feedback <- glht(fitsur,linfct = c("commreg_feedback_aware - instreg_feedback_aware = 0"))
summary(comm_inst_feedback) 
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: systemfit(formula = list(indivreg = indiv, commreg = comm, instreg = inst), 
##     method = "SUR", data = ds)
## 
## Linear Hypotheses:
##                                                      Estimate Std. Error z value Pr(>|z|)
## commreg_feedback_aware - instreg_feedback_aware == 0  0.01793    0.05065   0.354    0.723
## (Adjusted p values reported -- single-step method)
comm_indiv_consulted <- glht(fitsur,linfct = c("commreg_consulted - indivreg_consulted = 0"))
summary(comm_indiv_consulted)
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: systemfit(formula = list(indivreg = indiv, commreg = comm, instreg = inst), 
##     method = "SUR", data = ds)
## 
## Linear Hypotheses:
##                                             Estimate Std. Error z value Pr(>|z|)
## commreg_consulted - indivreg_consulted == 0  0.07592    0.05837   1.301    0.193
## (Adjusted p values reported -- single-step method)
inst_indiv_consulted <- glht(fitsur,linfct = c("instreg_consulted - indivreg_consulted = 0"))
summary(inst_indiv_consulted) 
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: systemfit(formula = list(indivreg = indiv, commreg = comm, instreg = inst), 
##     method = "SUR", data = ds)
## 
## Linear Hypotheses:
##                                              Estimate Std. Error z value Pr(>|z|)
## instreg_consulted - indivreg_consulted == 0 -0.009447   0.054932  -0.172    0.863
## (Adjusted p values reported -- single-step method)
comm_inst_consulted <- glht(fitsur,linfct = c("commreg_consulted - instreg_consulted = 0"))
summary(comm_inst_consulted) # significant at alpha = 0.10
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: systemfit(formula = list(indivreg = indiv, commreg = comm, instreg = inst), 
##     method = "SUR", data = ds)
## 
## Linear Hypotheses:
##                                            Estimate Std. Error z value Pr(>|z|)  
## commreg_consulted - instreg_consulted == 0  0.08537    0.05085   1.679   0.0932 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)

Mediation Analysis

Here, I will use the lavaan package and will estimate the indirect effect via the product of coefficients approach. To test for significance, I will use both the Sobel test and the percentile based bootstrapping method.

Specify Path Analyses

mediation_path_1a <- "
# Path c' (direct effect)
improving ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*feedback_aware + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_1b <- "
# Path c' (direct effect)
improving ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*feedback_aware + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_1c <- "
# Path c' (direct effect)
improving ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*feedback_aware + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_1d <- "
# Path c' (direct effect)
improving ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*feedback_aware + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_2a <- "
# Path c' (direct effect)
improving ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*consulted + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_2b <- "
# Path c' (direct effect)
improving ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*consulted + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_2c <- "
# Path c' (direct effect)
improving ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*consulted + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_2d <- "
# Path c' (direct effect)
improving ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*consulted + fem + age + hoh

# Path b
improving ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_3a <- "
# Path c' (direct effect)
improve_community ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*feedback_aware + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_3b <- "
# Path c' (direct effect)
improve_community ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*feedback_aware + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_3c <- "
# Path c' (direct effect)
improve_community ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*feedback_aware + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_3d <- "
# Path c' (direct effect)
improve_community ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*feedback_aware + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_4a <- "
# Path c' (direct effect)
improve_community ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*consulted + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_4b <- "
# Path c' (direct effect)
improve_community ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*consulted + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_4c <- "
# Path c' (direct effect)
improve_community ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*consulted + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_4d <- "
# Path c' (direct effect)
improve_community ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*consulted + fem + age + hoh

# Path b
improve_community ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_5a <- "
# Path c' (direct effect)
improve_individual ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*feedback_aware + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_5b <- "
# Path c' (direct effect)
improve_individual ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*feedback_aware + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_5c <- "
# Path c' (direct effect)
improve_individual ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*feedback_aware + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_5d <- "
# Path c' (direct effect)
improve_individual ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*feedback_aware + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_6a <- "
# Path c' (direct effect)
improve_individual ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*consulted + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_6b <- "
# Path c' (direct effect)
improve_individual ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*consulted + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_6c <- "
# Path c' (direct effect)
improve_individual ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*consulted + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_6d <- "
# Path c' (direct effect)
improve_individual ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*consulted + fem + age + hoh

# Path b
improve_individual ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_7a <- "
# Path c' (direct effect)
improve_institutional ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*feedback_aware + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_7b <- "
# Path c' (direct effect)
improve_institutional ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*feedback_aware + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_7c <- "
# Path c' (direct effect)
improve_institutional ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*feedback_aware + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_7d <- "
# Path c' (direct effect)
improve_institutional ~ c*feedback_aware + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*feedback_aware + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_8a <- "
# Path c' (direct effect)
improve_institutional ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_skills ~ a*consulted + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_no_skills + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_8b <- "
# Path c' (direct effect)
improve_institutional ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_afraid ~ a*consulted + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_afraid + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_8c <- "
# Path c' (direct effect)
improve_institutional ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_trust ~ a*consulted + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_no_trust + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

mediation_path_8d <- "
# Path c' (direct effect)
improve_institutional ~ c*consulted + fem + age + hoh

# Path a
feedback_barriers_no_action ~ a*consulted + fem + age + hoh

# Path b
improve_institutional ~ b*feedback_barriers_no_action + fem + age + hoh

# Indirect Effect (a*b)
ab := a*b
"

Fit Models

mediation_model_1a <- sem(mediation_path_1a, data = ds)

mediation_model_1b <- sem(mediation_path_1b, data = ds)

mediation_model_1c <- sem(mediation_path_1c, data = ds)
## Warning: lavaan->lav_data_full():  
##    some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate
mediation_model_1d <- sem(mediation_path_1d, data = ds)

mediation_model_2a <- sem(mediation_path_2a, data = ds)

mediation_model_2b <- sem(mediation_path_2b, data = ds)

mediation_model_2c <- sem(mediation_path_2c, data = ds)
## Warning: lavaan->lav_data_full():  
##    some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate
mediation_model_2d <- sem(mediation_path_2d, data = ds)

mediation_model_3a <- sem(mediation_path_3a, data = ds)

mediation_model_3b <- sem(mediation_path_3b, data = ds)

mediation_model_3c <- sem(mediation_path_3c, data = ds)
## Warning: lavaan->lav_data_full():  
##    some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate
mediation_model_3d <- sem(mediation_path_3d, data = ds)

mediation_model_4a <- sem(mediation_path_4a, data = ds)

mediation_model_4b <- sem(mediation_path_4b, data = ds)

mediation_model_4c <- sem(mediation_path_4c, data = ds)
## Warning: lavaan->lav_data_full():  
##    some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate
mediation_model_4d <- sem(mediation_path_4d, data = ds)

mediation_model_5a <- sem(mediation_path_5a, data = ds)

mediation_model_5b <- sem(mediation_path_5b, data = ds)

mediation_model_5c <- sem(mediation_path_5c, data = ds)

mediation_model_5d <- sem(mediation_path_5d, data = ds)

mediation_model_6a <- sem(mediation_path_6a, data = ds)

mediation_model_6b <- sem(mediation_path_6b, data = ds)

mediation_model_6c <- sem(mediation_path_6c, data = ds)

mediation_model_6d <- sem(mediation_path_6d, data = ds)

mediation_model_7a <- sem(mediation_path_7a, data = ds)

mediation_model_7b <- sem(mediation_path_7b, data = ds)

mediation_model_7c <- sem(mediation_path_7c, data = ds)

mediation_model_7d <- sem(mediation_path_7d, data = ds)

mediation_model_8a <- sem(mediation_path_8a, data = ds)

mediation_model_8b <- sem(mediation_path_8b, data = ds)

mediation_model_8c <- sem(mediation_path_8c, data = ds)

mediation_model_8d <- sem(mediation_path_8d, data = ds)

Summarize Models

summary(mediation_model_1a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                90.287
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1209.359
##   Loglikelihood unrestricted model (H1)      -1209.359
##                                                       
##   Akaike (AIC)                                2440.719
##   Bayesian (BIC)                              2493.235
##   Sample-size adjusted Bayesian (SABIC)       2458.302
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                      
##     feedbck_wr (c)                 0.420    0.081    5.163    0.000
##     fem                            0.212    0.094    2.251    0.024
##     age                            0.004    0.003    1.196    0.232
##     hoh                            0.384    0.100    3.840    0.000
##   feedback_barriers_no_skills ~                                    
##     feedbck_wr (a)                -0.044    0.013   -3.234    0.001
##     fem                            0.079    0.015    5.123    0.000
##     age                            0.000    0.001    0.911    0.362
##     hoh                            0.046    0.017    2.748    0.006
##   improving ~                                                      
##     fdbck_br__ (b)                 0.429    0.203    2.113    0.035
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.400    0.067   20.917    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.060
##     fdbck_brrrs_n_    0.041
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.019    0.011   -1.769    0.077
summary(mediation_model_1b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                59.626
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -569.553
##   Loglikelihood unrestricted model (H1)       -569.553
##                                                       
##   Akaike (AIC)                                1161.106
##   Bayesian (BIC)                              1213.623
##   Sample-size adjusted Bayesian (SABIC)       1178.689
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                   
##     feedbck_wr (c)              0.400    0.081    4.936    0.000
##     fem                         0.241    0.093    2.589    0.010
##     age                         0.004    0.003    1.127    0.260
##     hoh                         0.407    0.100    4.085    0.000
##   feedback_barriers_afraid ~                                    
##     feedbck_wr (a)              0.002    0.006    0.382    0.703
##     fem                         0.008    0.007    1.065    0.287
##     age                         0.001    0.000    2.401    0.016
##     hoh                        -0.006    0.008   -0.694    0.488
##   improving ~                                                   
##     fdbck_brr_ (b)              0.672    0.423    1.590    0.112
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.404    0.067   20.917    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.058
##     fdbck_brrrs_fr    0.009
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.002    0.004    0.371    0.710
summary(mediation_model_1c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                52.481
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                333.112
##   Loglikelihood unrestricted model (H1)        333.112
##                                                       
##   Akaike (AIC)                                -644.224
##   Bayesian (BIC)                              -591.708
##   Sample-size adjusted Bayesian (SABIC)       -626.641
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                     
##     feedbck_wr (c)                0.402    0.081    4.955    0.000
##     fem                           0.245    0.093    2.638    0.008
##     age                           0.004    0.003    1.248    0.212
##     hoh                           0.404    0.100    4.047    0.000
##   feedback_barriers_no_trust ~                                    
##     feedbck_wr (a)                0.002    0.002    0.845    0.398
##     fem                          -0.002    0.003   -0.684    0.494
##     age                          -0.000    0.000   -1.130    0.258
##     hoh                           0.002    0.003    0.550    0.582
##   improving ~                                                     
##     fdbck_br__ (b)               -0.298    1.189   -0.250    0.802
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.407    0.067   20.917    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.055
##     fdbck_brrrs_n_    0.004
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.002   -0.240    0.810
summary(mediation_model_1d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                65.112
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -892.020
##   Loglikelihood unrestricted model (H1)       -892.020
##                                                       
##   Akaike (AIC)                                1806.040
##   Bayesian (BIC)                              1858.556
##   Sample-size adjusted Bayesian (SABIC)       1823.623
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                      
##     feedbck_wr (c)                 0.400    0.081    4.944    0.000
##     fem                            0.227    0.093    2.440    0.015
##     age                            0.004    0.003    1.218    0.223
##     hoh                            0.407    0.099    4.088    0.000
##   feedback_barriers_no_action ~                                    
##     feedbck_wr (a)                 0.003    0.009    0.269    0.788
##     fem                            0.028    0.011    2.557    0.011
##     age                            0.000    0.000    0.550    0.582
##     hoh                           -0.005    0.012   -0.409    0.682
##   improving ~                                                      
##     fdbck_br__ (b)                 0.685    0.291    2.352    0.019
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.399    0.067   20.917    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.061
##     fdbck_brrrs_n_    0.012
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.002    0.006    0.267    0.789
summary(mediation_model_2a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                82.987
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1212.304
##   Loglikelihood unrestricted model (H1)      -1212.304
##                                                       
##   Akaike (AIC)                                2446.609
##   Bayesian (BIC)                              2499.113
##   Sample-size adjusted Bayesian (SABIC)       2464.179
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                      
##     consulted  (c)                 0.369    0.082    4.504    0.000
##     fem                            0.260    0.095    2.746    0.006
##     age                            0.004    0.003    1.304    0.192
##     hoh                            0.384    0.101    3.807    0.000
##   feedback_barriers_no_skills ~                                    
##     consulted  (a)                 0.040    0.014    2.960    0.003
##     fem                            0.079    0.016    5.105    0.000
##     age                            0.001    0.001    0.984    0.325
##     hoh                            0.036    0.017    2.146    0.032
##   improving ~                                                      
##     fdbck_br__ (b)                 0.223    0.203    1.094    0.274
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.410    0.067   20.905    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.054
##     fdbck_brrrs_n_    0.039
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.009    0.009    1.027    0.305
summary(mediation_model_2b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                64.449
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -567.202
##   Loglikelihood unrestricted model (H1)       -567.202
##                                                       
##   Akaike (AIC)                                1156.405
##   Bayesian (BIC)                              1208.909
##   Sample-size adjusted Bayesian (SABIC)       1173.975
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                   
##     consulted  (c)              0.368    0.082    4.498    0.000
##     fem                         0.273    0.093    2.926    0.003
##     age                         0.004    0.003    1.236    0.216
##     hoh                         0.396    0.101    3.936    0.000
##   feedback_barriers_afraid ~                                    
##     consulted  (a)              0.019    0.006    2.901    0.004
##     fem                         0.009    0.007    1.157    0.247
##     age                         0.001    0.000    2.470    0.013
##     hoh                        -0.008    0.008   -1.011    0.312
##   improving ~                                                   
##     fdbck_brr_ (b)              0.513    0.426    1.204    0.228
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.410    0.067   20.905    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.054
##     fdbck_brrrs_fr    0.018
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.010    0.009    1.112    0.266
summary(mediation_model_2c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                50.051
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                330.796
##   Loglikelihood unrestricted model (H1)        330.796
##                                                       
##   Akaike (AIC)                                -639.592
##   Bayesian (BIC)                              -587.089
##   Sample-size adjusted Bayesian (SABIC)       -622.022
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                     
##     consulted  (c)                0.379    0.082    4.638    0.000
##     fem                           0.277    0.093    2.968    0.003
##     age                           0.004    0.003    1.331    0.183
##     hoh                           0.392    0.101    3.898    0.000
##   feedback_barriers_no_trust ~                                    
##     consulted  (a)                0.002    0.002    0.780    0.436
##     fem                          -0.002    0.003   -0.640    0.522
##     age                          -0.000    0.000   -1.116    0.264
##     hoh                           0.001    0.003    0.512    0.609
##   improving ~                                                     
##     fdbck_br__ (b)               -0.273    1.191   -0.229    0.819
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.412    0.068   20.905    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.052
##     fdbck_brrrs_n_    0.003
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.000    0.002   -0.220    0.826
summary(mediation_model_2d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                75.127
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -886.697
##   Loglikelihood unrestricted model (H1)       -886.697
##                                                       
##   Akaike (AIC)                                1795.394
##   Bayesian (BIC)                              1847.897
##   Sample-size adjusted Bayesian (SABIC)       1812.964
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                      
##     consulted  (c)                 0.359    0.082    4.370    0.000
##     fem                            0.262    0.094    2.803    0.005
##     age                            0.004    0.003    1.304    0.192
##     hoh                            0.397    0.100    3.952    0.000
##   feedback_barriers_no_action ~                                    
##     consulted  (a)                 0.036    0.009    3.848    0.000
##     fem                            0.029    0.011    2.684    0.007
##     age                            0.000    0.000    0.634    0.526
##     hoh                           -0.010    0.012   -0.850    0.395
##   improving ~                                                      
##     fdbck_br__ (b)                 0.533    0.295    1.808    0.071
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.407    0.067   20.905    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.056
##     fdbck_brrrs_n_    0.028
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.019    0.012    1.637    0.102
summary(mediation_model_3a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                71.295
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1154.903
##   Loglikelihood unrestricted model (H1)      -1154.903
##                                                       
##   Akaike (AIC)                                2331.806
##   Bayesian (BIC)                              2384.323
##   Sample-size adjusted Bayesian (SABIC)       2349.389
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                              
##     feedbck_wr (c)                 0.255    0.076    3.337    0.001
##     fem                           -0.348    0.088   -3.929    0.000
##     age                           -0.000    0.003   -0.113    0.910
##     hoh                            0.044    0.094    0.465    0.642
##   feedback_barriers_no_skills ~                                    
##     feedbck_wr (a)                -0.044    0.013   -3.234    0.001
##     fem                            0.079    0.015    5.123    0.000
##     age                            0.000    0.001    0.911    0.362
##     hoh                            0.046    0.017    2.748    0.006
##   improve_community ~                                              
##     fdbck_br__ (b)                 0.084    0.191    0.441    0.659
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.237    0.059   20.917    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.039
##     fdbck_brrrs_n_    0.041
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.004    0.008   -0.437    0.662
summary(mediation_model_3b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                42.370
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -514.229
##   Loglikelihood unrestricted model (H1)       -514.229
##                                                       
##   Akaike (AIC)                                1050.458
##   Bayesian (BIC)                              1102.974
##   Sample-size adjusted Bayesian (SABIC)       1068.041
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                           
##     feedbck_wr (c)              0.252    0.076    3.308    0.001
##     fem                        -0.341    0.087   -3.908    0.000
##     age                        -0.000    0.003   -0.099    0.921
##     hoh                         0.047    0.094    0.507    0.612
##   feedback_barriers_afraid ~                                    
##     feedbck_wr (a)              0.002    0.006    0.382    0.703
##     fem                         0.008    0.007    1.065    0.287
##     age                         0.001    0.000    2.401    0.016
##     hoh                        -0.006    0.008   -0.694    0.488
##   improve_community ~                                           
##     fdbck_brr_ (b)             -0.002    0.397   -0.006    0.996
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.237    0.059   20.917    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.039
##     fdbck_brrrs_fr    0.009
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.000    0.001   -0.006    0.996
summary(mediation_model_3c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                37.895
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                389.771
##   Loglikelihood unrestricted model (H1)        389.771
##                                                       
##   Akaike (AIC)                                -757.542
##   Bayesian (BIC)                              -705.026
##   Sample-size adjusted Bayesian (SABIC)       -739.959
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                             
##     feedbck_wr (c)                0.253    0.076    3.321    0.001
##     fem                          -0.342    0.087   -3.920    0.000
##     age                          -0.000    0.003   -0.117    0.907
##     hoh                           0.048    0.094    0.516    0.606
##   feedback_barriers_no_trust ~                                    
##     feedbck_wr (a)                0.002    0.002    0.845    0.398
##     fem                          -0.002    0.003   -0.684    0.494
##     age                          -0.000    0.000   -1.130    0.258
##     hoh                           0.002    0.003    0.550    0.582
##   improve_community ~                                             
##     fdbck_br__ (b)               -0.510    1.115   -0.457    0.647
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.236    0.059   20.917    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.039
##     fdbck_brrrs_n_    0.004
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.002   -0.402    0.688
summary(mediation_model_3d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                45.020
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -838.114
##   Loglikelihood unrestricted model (H1)       -838.114
##                                                       
##   Akaike (AIC)                                1698.227
##   Bayesian (BIC)                              1750.744
##   Sample-size adjusted Bayesian (SABIC)       1715.810
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                              
##     feedbck_wr (c)                 0.251    0.076    3.305    0.001
##     fem                           -0.344    0.088   -3.930    0.000
##     age                           -0.000    0.003   -0.107    0.915
##     hoh                            0.048    0.094    0.513    0.608
##   feedback_barriers_no_action ~                                    
##     feedbck_wr (a)                 0.003    0.009    0.269    0.788
##     fem                            0.028    0.011    2.557    0.011
##     age                            0.000    0.000    0.550    0.582
##     hoh                           -0.005    0.012   -0.409    0.682
##   improve_community ~                                              
##     fdbck_br__ (b)                 0.108    0.274    0.396    0.692
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.237    0.059   20.917    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.039
##     fdbck_brrrs_n_    0.012
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.000    0.001    0.222    0.824
summary(mediation_model_4a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                76.802
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1151.203
##   Loglikelihood unrestricted model (H1)      -1151.203
##                                                       
##   Akaike (AIC)                                2324.406
##   Bayesian (BIC)                              2376.910
##   Sample-size adjusted Bayesian (SABIC)       2341.976
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                              
##     consulted  (c)                 0.326    0.076    4.269    0.000
##     fem                           -0.324    0.088   -3.672    0.000
##     age                           -0.000    0.003   -0.017    0.987
##     hoh                            0.018    0.094    0.190    0.850
##   feedback_barriers_no_skills ~                                    
##     consulted  (a)                 0.040    0.014    2.960    0.003
##     fem                            0.079    0.016    5.105    0.000
##     age                            0.001    0.001    0.984    0.325
##     hoh                            0.036    0.017    2.146    0.032
##   improve_community ~                                              
##     fdbck_br__ (b)                -0.065    0.190   -0.341    0.733
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.226    0.059   20.905    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.047
##     fdbck_brrrs_n_    0.039
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.003    0.008   -0.339    0.735
summary(mediation_model_4b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                58.043
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -506.212
##   Loglikelihood unrestricted model (H1)       -506.212
##                                                       
##   Akaike (AIC)                                1034.425
##   Bayesian (BIC)                              1086.928
##   Sample-size adjusted Bayesian (SABIC)       1051.995
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                           
##     consulted  (c)              0.326    0.076    4.273    0.000
##     fem                        -0.328    0.087   -3.767    0.000
##     age                         0.000    0.003    0.004    0.997
##     hoh                         0.014    0.094    0.152    0.879
##   feedback_barriers_afraid ~                                    
##     consulted  (a)              0.019    0.006    2.901    0.004
##     fem                         0.009    0.007    1.157    0.247
##     age                         0.001    0.000    2.470    0.013
##     hoh                        -0.008    0.008   -1.011    0.312
##   improve_community ~                                           
##     fdbck_brr_ (b)             -0.151    0.397   -0.382    0.703
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.226    0.059   20.905    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.047
##     fdbck_brrrs_fr    0.018
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.003    0.008   -0.378    0.705
summary(mediation_model_4c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                45.124
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                392.526
##   Loglikelihood unrestricted model (H1)        392.526
##                                                       
##   Akaike (AIC)                                -763.053
##   Bayesian (BIC)                              -710.549
##   Sample-size adjusted Bayesian (SABIC)       -745.482
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                             
##     consulted  (c)                0.325    0.076    4.267    0.000
##     fem                          -0.330    0.087   -3.795    0.000
##     age                          -0.000    0.003   -0.046    0.963
##     hoh                           0.016    0.094    0.174    0.862
##   feedback_barriers_no_trust ~                                    
##     consulted  (a)                0.002    0.002    0.780    0.436
##     fem                          -0.002    0.003   -0.640    0.522
##     age                          -0.000    0.000   -1.116    0.264
##     hoh                           0.001    0.003    0.512    0.609
##   improve_community ~                                             
##     fdbck_br__ (b)               -0.531    1.110   -0.479    0.632
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.226    0.059   20.905    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.047
##     fdbck_brrrs_n_    0.003
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.002   -0.408    0.683
summary(mediation_model_4d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                66.775
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -826.679
##   Loglikelihood unrestricted model (H1)       -826.679
##                                                       
##   Akaike (AIC)                                1675.358
##   Bayesian (BIC)                              1727.862
##   Sample-size adjusted Bayesian (SABIC)       1692.929
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_community ~                                              
##     consulted  (c)                 0.325    0.077    4.236    0.000
##     fem                           -0.328    0.087   -3.758    0.000
##     age                           -0.000    0.003   -0.025    0.980
##     hoh                            0.015    0.094    0.162    0.872
##   feedback_barriers_no_action ~                                    
##     consulted  (a)                 0.036    0.009    3.848    0.000
##     fem                            0.029    0.011    2.684    0.007
##     age                            0.000    0.000    0.634    0.526
##     hoh                           -0.010    0.012   -0.850    0.395
##   improve_community ~                                              
##     fdbck_br__ (b)                -0.034    0.275   -0.125    0.901
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_cmmnty    1.226    0.059   20.905    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_cmmnty    0.047
##     fdbck_brrrs_n_    0.028
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.010   -0.125    0.901
summary(mediation_model_5a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               141.049
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -981.332
##   Loglikelihood unrestricted model (H1)       -981.332
##                                                       
##   Akaike (AIC)                                1984.665
##   Bayesian (BIC)                              2037.181
##   Sample-size adjusted Bayesian (SABIC)       2002.248
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                             
##     feedbck_wr (c)                 0.082    0.063    1.315    0.188
##     fem                           -0.567    0.073   -7.820    0.000
##     age                           -0.003    0.002   -1.398    0.162
##     hoh                            0.121    0.077    1.571    0.116
##   feedback_barriers_no_skills ~                                    
##     feedbck_wr (a)                -0.044    0.013   -3.234    0.001
##     fem                            0.079    0.015    5.123    0.000
##     age                            0.000    0.001    0.911    0.362
##     hoh                            0.046    0.017    2.748    0.006
##   improve_individual ~                                             
##     fdbck_br__ (b)                -0.185    0.156   -1.183    0.237
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.832    0.040   20.917    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.113
##     fdbck_brrrs_n_    0.041
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.008    0.007    1.111    0.266
summary(mediation_model_5b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               110.929
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -341.256
##   Loglikelihood unrestricted model (H1)       -341.256
##                                                       
##   Akaike (AIC)                                 704.512
##   Bayesian (BIC)                               757.028
##   Sample-size adjusted Bayesian (SABIC)        722.095
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                          
##     feedbck_wr (c)              0.090    0.062    1.450    0.147
##     fem                        -0.582    0.072   -8.133    0.000
##     age                        -0.004    0.002   -1.437    0.151
##     hoh                         0.113    0.077    1.468    0.142
##   feedback_barriers_afraid ~                                    
##     feedbck_wr (a)              0.002    0.006    0.382    0.703
##     fem                         0.008    0.007    1.065    0.287
##     age                         0.001    0.000    2.401    0.016
##     hoh                        -0.006    0.008   -0.694    0.488
##   improve_individual ~                                          
##     fdbck_brr_ (b)              0.031    0.326    0.096    0.924
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.833    0.040   20.917    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.111
##     fdbck_brrrs_fr    0.009
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.000    0.001    0.093    0.926
summary(mediation_model_5c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               106.360
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                562.697
##   Loglikelihood unrestricted model (H1)        562.697
##                                                       
##   Akaike (AIC)                               -1103.395
##   Bayesian (BIC)                             -1050.879
##   Sample-size adjusted Bayesian (SABIC)      -1085.812
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                            
##     feedbck_wr (c)                0.091    0.062    1.461    0.144
##     fem                          -0.583    0.072   -8.142    0.000
##     age                          -0.004    0.002   -1.446    0.148
##     hoh                           0.113    0.077    1.473    0.141
##   feedback_barriers_no_trust ~                                    
##     feedbck_wr (a)                0.002    0.002    0.845    0.398
##     fem                          -0.002    0.003   -0.684    0.494
##     age                          -0.000    0.000   -1.130    0.258
##     hoh                           0.002    0.003    0.550    0.582
##   improve_individual ~                                            
##     fdbck_br__ (b)               -0.324    0.915   -0.354    0.723
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.833    0.040   20.917    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.111
##     fdbck_brrrs_n_    0.004
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.002   -0.326    0.744
summary(mediation_model_5d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               114.738
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -664.561
##   Loglikelihood unrestricted model (H1)       -664.561
##                                                       
##   Akaike (AIC)                                1351.123
##   Bayesian (BIC)                              1403.639
##   Sample-size adjusted Bayesian (SABIC)       1368.706
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                             
##     feedbck_wr (c)                 0.091    0.062    1.463    0.144
##     fem                           -0.575    0.072   -8.012    0.000
##     age                           -0.003    0.002   -1.413    0.158
##     hoh                            0.111    0.077    1.452    0.147
##   feedback_barriers_no_action ~                                    
##     feedbck_wr (a)                 0.003    0.009    0.269    0.788
##     fem                            0.028    0.011    2.557    0.011
##     age                            0.000    0.000    0.550    0.582
##     hoh                           -0.005    0.012   -0.409    0.682
##   improve_individual ~                                             
##     fdbck_br__ (b)                -0.259    0.225   -1.151    0.250
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.832    0.040   20.917    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.113
##     fdbck_brrrs_n_    0.012
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.002   -0.262    0.793
summary(mediation_model_6a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               143.155
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -980.050
##   Loglikelihood unrestricted model (H1)       -980.050
##                                                       
##   Akaike (AIC)                                1982.100
##   Bayesian (BIC)                              2034.604
##   Sample-size adjusted Bayesian (SABIC)       1999.670
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                             
##     consulted  (c)                 0.150    0.063    2.384    0.017
##     fem                           -0.556    0.073   -7.662    0.000
##     age                           -0.003    0.002   -1.343    0.179
##     hoh                            0.108    0.077    1.400    0.161
##   feedback_barriers_no_skills ~                                    
##     consulted  (a)                 0.040    0.014    2.960    0.003
##     fem                            0.079    0.016    5.105    0.000
##     age                            0.001    0.001    0.984    0.325
##     hoh                            0.036    0.017    2.146    0.032
##   improve_individual ~                                             
##     fdbck_br__ (b)                -0.244    0.156   -1.567    0.117
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.829    0.040   20.905    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.117
##     fdbck_brrrs_n_    0.039
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.010    0.007   -1.385    0.166
summary(mediation_model_6b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               121.925
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -336.294
##   Loglikelihood unrestricted model (H1)       -336.294
##                                                       
##   Akaike (AIC)                                 694.588
##   Bayesian (BIC)                               747.092
##   Sample-size adjusted Bayesian (SABIC)        712.159
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                          
##     consulted  (c)              0.141    0.063    2.236    0.025
##     fem                        -0.575    0.072   -8.024    0.000
##     age                        -0.003    0.002   -1.380    0.167
##     hoh                         0.099    0.077    1.284    0.199
##   feedback_barriers_afraid ~                                    
##     consulted  (a)              0.019    0.006    2.901    0.004
##     fem                         0.009    0.007    1.157    0.247
##     age                         0.001    0.000    2.470    0.013
##     hoh                        -0.008    0.008   -1.011    0.312
##   improve_individual ~                                          
##     fdbck_brr_ (b)             -0.034    0.327   -0.104    0.917
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.831    0.040   20.905    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.114
##     fdbck_brrrs_fr    0.018
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.006   -0.104    0.917
summary(mediation_model_6c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               109.051
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                562.467
##   Loglikelihood unrestricted model (H1)        562.467
##                                                       
##   Akaike (AIC)                               -1102.933
##   Bayesian (BIC)                             -1050.429
##   Sample-size adjusted Bayesian (SABIC)      -1085.363
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                            
##     consulted  (c)                0.141    0.063    2.245    0.025
##     fem                          -0.576    0.072   -8.041    0.000
##     age                          -0.003    0.002   -1.407    0.159
##     hoh                           0.100    0.077    1.295    0.195
##   feedback_barriers_no_trust ~                                    
##     consulted  (a)                0.002    0.002    0.780    0.436
##     fem                          -0.002    0.003   -0.640    0.522
##     age                          -0.000    0.000   -1.116    0.264
##     hoh                           0.001    0.003    0.512    0.609
##   improve_individual ~                                            
##     fdbck_br__ (b)               -0.340    0.914   -0.372    0.710
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.831    0.040   20.905    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.114
##     fdbck_brrrs_n_    0.003
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.001    0.002   -0.336    0.737
summary(mediation_model_6d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                               132.851
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -655.664
##   Loglikelihood unrestricted model (H1)       -655.664
##                                                       
##   Akaike (AIC)                                1333.329
##   Bayesian (BIC)                              1385.833
##   Sample-size adjusted Bayesian (SABIC)       1350.899
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_individual ~                                             
##     consulted  (c)                 0.152    0.063    2.406    0.016
##     fem                           -0.566    0.072   -7.881    0.000
##     age                           -0.003    0.002   -1.364    0.172
##     hoh                            0.096    0.077    1.248    0.212
##   feedback_barriers_no_action ~                                    
##     consulted  (a)                 0.036    0.009    3.848    0.000
##     fem                            0.029    0.011    2.684    0.007
##     age                            0.000    0.000    0.634    0.526
##     hoh                           -0.010    0.012   -0.850    0.395
##   improve_individual ~                                             
##     fdbck_br__ (b)                -0.326    0.226   -1.441    0.150
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improve_indvdl    0.829    0.040   20.905    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improve_indvdl    0.116
##     fdbck_brrrs_n_    0.028
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.012    0.009   -1.349    0.177
summary(mediation_model_7a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                99.287
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -819.883
##   Loglikelihood unrestricted model (H1)       -819.883
##                                                       
##   Akaike (AIC)                                1661.766
##   Bayesian (BIC)                              1714.283
##   Sample-size adjusted Bayesian (SABIC)       1679.349
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     feedbck_wr (c)                 0.201    0.052    3.853    0.000
##     fem                           -0.314    0.060   -5.200    0.000
##     age                            0.001    0.002    0.387    0.699
##     hoh                            0.037    0.064    0.582    0.561
##   feedback_barriers_no_skills ~                                    
##     feedbck_wr (a)                -0.044    0.013   -3.234    0.001
##     fem                            0.079    0.015    5.123    0.000
##     age                            0.000    0.001    0.911    0.362
##     hoh                            0.046    0.017    2.748    0.006
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.500    0.130    3.841    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.575    0.027   20.917    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.069
##     fdbck_brrrs_n_    0.041
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.022    0.009   -2.474    0.013
summary(mediation_model_7b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                58.303
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -185.238
##   Loglikelihood unrestricted model (H1)       -185.238
##                                                       
##   Akaike (AIC)                                 392.476
##   Bayesian (BIC)                               444.992
##   Sample-size adjusted Bayesian (SABIC)        410.059
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                       
##     feedbck_wr (c)              0.178    0.052    3.412    0.001
##     fem                        -0.277    0.060   -4.632    0.000
##     age                         0.001    0.002    0.376    0.707
##     hoh                         0.062    0.064    0.970    0.332
##   feedback_barriers_afraid ~                                    
##     feedbck_wr (a)              0.002    0.006    0.382    0.703
##     fem                         0.008    0.007    1.065    0.287
##     age                         0.001    0.000    2.401    0.016
##     hoh                        -0.006    0.008   -0.694    0.488
##   improve_institutional ~                                       
##     fdbck_brr_ (b)              0.420    0.272    1.543    0.123
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.583    0.028   20.917    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.056
##     fdbck_brrrs_fr    0.009
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.001    0.003    0.371    0.711
summary(mediation_model_7c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                51.685
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                717.691
##   Loglikelihood unrestricted model (H1)        717.691
##                                                       
##   Akaike (AIC)                               -1413.381
##   Bayesian (BIC)                             -1360.865
##   Sample-size adjusted Bayesian (SABIC)      -1395.798
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                         
##     feedbck_wr (c)                0.178    0.052    3.408    0.001
##     fem                          -0.273    0.060   -4.558    0.000
##     age                           0.001    0.002    0.527    0.598
##     hoh                           0.059    0.064    0.921    0.357
##   feedback_barriers_no_trust ~                                    
##     feedbck_wr (a)                0.002    0.002    0.845    0.398
##     fem                          -0.002    0.003   -0.684    0.494
##     age                          -0.000    0.000   -1.130    0.258
##     hoh                           0.002    0.003    0.550    0.582
##   improve_institutional ~                                         
##     fdbck_br__ (b)                0.510    0.766    0.665    0.506
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.584    0.028   20.917    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.054
##     fdbck_brrrs_n_    0.004
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.001    0.002    0.522    0.601
summary(mediation_model_7d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                69.670
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -504.765
##   Loglikelihood unrestricted model (H1)       -504.765
##                                                       
##   Akaike (AIC)                                1031.529
##   Bayesian (BIC)                              1084.046
##   Sample-size adjusted Bayesian (SABIC)       1049.112
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     feedbck_wr (c)                 0.178    0.052    3.419    0.001
##     fem                           -0.291    0.060   -4.876    0.000
##     age                            0.001    0.002    0.442    0.658
##     hoh                            0.063    0.064    0.986    0.324
##   feedback_barriers_no_action ~                                    
##     feedbck_wr (a)                 0.003    0.009    0.269    0.788
##     fem                            0.028    0.011    2.557    0.011
##     age                            0.000    0.000    0.550    0.582
##     hoh                           -0.005    0.012   -0.409    0.682
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.630    0.187    3.365    0.001
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.577    0.028   20.917    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.066
##     fdbck_brrrs_n_    0.012
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.002    0.006    0.268    0.789
summary(mediation_model_8a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                89.939
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -824.103
##   Loglikelihood unrestricted model (H1)       -824.103
##                                                       
##   Akaike (AIC)                                1670.207
##   Bayesian (BIC)                              1722.710
##   Sample-size adjusted Bayesian (SABIC)       1687.777
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     consulted  (c)                 0.143    0.053    2.712    0.007
##     fem                           -0.292    0.061   -4.815    0.000
##     age                            0.001    0.002    0.454    0.650
##     hoh                            0.042    0.065    0.650    0.516
##   feedback_barriers_no_skills ~                                    
##     consulted  (a)                 0.040    0.014    2.960    0.003
##     fem                            0.079    0.016    5.105    0.000
##     age                            0.001    0.001    0.984    0.325
##     hoh                            0.036    0.017    2.146    0.032
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.409    0.131    3.136    0.002
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.580    0.028   20.905    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.061
##     fdbck_brrrs_n_    0.039
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.016    0.008    2.153    0.031
summary(mediation_model_8b, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                63.044
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -183.180
##   Loglikelihood unrestricted model (H1)       -183.180
##                                                       
##   Akaike (AIC)                                 388.360
##   Bayesian (BIC)                               440.863
##   Sample-size adjusted Bayesian (SABIC)        405.930
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                              Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                       
##     consulted  (c)              0.152    0.053    2.885    0.004
##     fem                        -0.263    0.060   -4.372    0.000
##     age                         0.001    0.002    0.446    0.656
##     hoh                         0.060    0.065    0.919    0.358
##   feedback_barriers_afraid ~                                    
##     consulted  (a)              0.019    0.006    2.901    0.004
##     fem                         0.009    0.007    1.157    0.247
##     age                         0.001    0.000    2.470    0.013
##     hoh                        -0.008    0.008   -1.011    0.312
##   improve_institutional ~                                       
##     fdbck_brr_ (b)              0.355    0.274    1.295    0.195
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.585    0.028   20.905    0.000
##    .fdbck_brrrs_fr    0.009    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.052
##     fdbck_brrrs_fr    0.018
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.007    0.006    1.183    0.237
summary(mediation_model_8c, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                48.833
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                714.912
##   Loglikelihood unrestricted model (H1)        714.912
##                                                       
##   Akaike (AIC)                               -1407.825
##   Bayesian (BIC)                             -1355.321
##   Sample-size adjusted Bayesian (SABIC)      -1390.254
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                         
##     consulted  (c)                0.158    0.053    3.004    0.003
##     fem                          -0.259    0.060   -4.306    0.000
##     age                           0.001    0.002    0.581    0.561
##     hoh                           0.056    0.065    0.862    0.389
##   feedback_barriers_no_trust ~                                    
##     consulted  (a)                0.002    0.002    0.780    0.436
##     fem                          -0.002    0.003   -0.640    0.522
##     age                          -0.000    0.000   -1.116    0.264
##     hoh                           0.001    0.003    0.512    0.609
##   improve_institutional ~                                         
##     fdbck_br__ (b)                0.524    0.767    0.683    0.494
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.586    0.028   20.905    0.000
##    .fdbck_brrrs_n_    0.001    0.000   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.051
##     fdbck_brrrs_n_    0.003
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.001    0.002    0.514    0.607
summary(mediation_model_8d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                79.308
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -499.881
##   Loglikelihood unrestricted model (H1)       -499.881
##                                                       
##   Akaike (AIC)                                1021.761
##   Bayesian (BIC)                              1074.265
##   Sample-size adjusted Bayesian (SABIC)       1039.332
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     consulted  (c)                 0.138    0.053    2.623    0.009
##     fem                           -0.276    0.060   -4.599    0.000
##     age                            0.001    0.002    0.493    0.622
##     hoh                            0.062    0.065    0.965    0.334
##   feedback_barriers_no_action ~                                    
##     consulted  (a)                 0.036    0.009    3.848    0.000
##     fem                            0.029    0.011    2.684    0.007
##     age                            0.000    0.000    0.634    0.526
##     hoh                           -0.010    0.012   -0.850    0.395
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.572    0.189    3.021    0.003
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.580    0.028   20.905    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.060
##     fdbck_brrrs_n_    0.028
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.021    0.009    2.376    0.017
summary(mediation_model_1a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                90.287
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -1209.359
##   Loglikelihood unrestricted model (H1)      -1209.359
##                                                       
##   Akaike (AIC)                                2440.719
##   Bayesian (BIC)                              2493.235
##   Sample-size adjusted Bayesian (SABIC)       2458.302
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improving ~                                                      
##     feedbck_wr (c)                 0.420    0.081    5.163    0.000
##     fem                            0.212    0.094    2.251    0.024
##     age                            0.004    0.003    1.196    0.232
##     hoh                            0.384    0.100    3.840    0.000
##   feedback_barriers_no_skills ~                                    
##     feedbck_wr (a)                -0.044    0.013   -3.234    0.001
##     fem                            0.079    0.015    5.123    0.000
##     age                            0.000    0.001    0.911    0.362
##     hoh                            0.046    0.017    2.748    0.006
##   improving ~                                                      
##     fdbck_br__ (b)                 0.429    0.203    2.113    0.035
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improving         1.400    0.067   20.917    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improving         0.060
##     fdbck_brrrs_n_    0.041
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.019    0.011   -1.769    0.077
summary(mediation_model_7a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           875         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                99.287
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -819.883
##   Loglikelihood unrestricted model (H1)       -819.883
##                                                       
##   Akaike (AIC)                                1661.766
##   Bayesian (BIC)                              1714.283
##   Sample-size adjusted Bayesian (SABIC)       1679.349
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     feedbck_wr (c)                 0.201    0.052    3.853    0.000
##     fem                           -0.314    0.060   -5.200    0.000
##     age                            0.001    0.002    0.387    0.699
##     hoh                            0.037    0.064    0.582    0.561
##   feedback_barriers_no_skills ~                                    
##     feedbck_wr (a)                -0.044    0.013   -3.234    0.001
##     fem                            0.079    0.015    5.123    0.000
##     age                            0.000    0.001    0.911    0.362
##     hoh                            0.046    0.017    2.748    0.006
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.500    0.130    3.841    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.575    0.027   20.917    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.917    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.069
##     fdbck_brrrs_n_    0.041
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab               -0.022    0.009   -2.474    0.013
summary(mediation_model_8a, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                89.939
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -824.103
##   Loglikelihood unrestricted model (H1)       -824.103
##                                                       
##   Akaike (AIC)                                1670.207
##   Bayesian (BIC)                              1722.710
##   Sample-size adjusted Bayesian (SABIC)       1687.777
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     consulted  (c)                 0.143    0.053    2.712    0.007
##     fem                           -0.292    0.061   -4.815    0.000
##     age                            0.001    0.002    0.454    0.650
##     hoh                            0.042    0.065    0.650    0.516
##   feedback_barriers_no_skills ~                                    
##     consulted  (a)                 0.040    0.014    2.960    0.003
##     fem                            0.079    0.016    5.105    0.000
##     age                            0.001    0.001    0.984    0.325
##     hoh                            0.036    0.017    2.146    0.032
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.409    0.131    3.136    0.002
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.580    0.028   20.905    0.000
##    .fdbck_brrrs_n_    0.039    0.002   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.061
##     fdbck_brrrs_n_    0.039
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.016    0.008    2.153    0.031
summary(mediation_model_8d, fit.measures = TRUE, rsquare = TRUE)
## lavaan 0.6-19 ended normally after 1 iteration
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        11
## 
##                                                   Used       Total
##   Number of observations                           874         876
## 
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                                79.308
##   Degrees of freedom                                 9
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -499.881
##   Loglikelihood unrestricted model (H1)       -499.881
##                                                       
##   Akaike (AIC)                                1021.761
##   Bayesian (BIC)                              1074.265
##   Sample-size adjusted Bayesian (SABIC)       1039.332
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value H_0: RMSEA <= 0.050                       NA
##   P-value H_0: RMSEA >= 0.080                       NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                                 Estimate  Std.Err  z-value  P(>|z|)
##   improve_institutional ~                                          
##     consulted  (c)                 0.138    0.053    2.623    0.009
##     fem                           -0.276    0.060   -4.599    0.000
##     age                            0.001    0.002    0.493    0.622
##     hoh                            0.062    0.065    0.965    0.334
##   feedback_barriers_no_action ~                                    
##     consulted  (a)                 0.036    0.009    3.848    0.000
##     fem                            0.029    0.011    2.684    0.007
##     age                            0.000    0.000    0.634    0.526
##     hoh                           -0.010    0.012   -0.850    0.395
##   improve_institutional ~                                          
##     fdbck_br__ (b)                 0.572    0.189    3.021    0.003
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)
##    .improv_nstttnl    0.580    0.028   20.905    0.000
##    .fdbck_brrrs_n_    0.019    0.001   20.905    0.000
## 
## R-Square:
##                    Estimate
##     improv_nstttnl    0.060
##     fdbck_brrrs_n_    0.028
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)
##     ab                0.021    0.009    2.376    0.017

7a, 8a, 8d