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Study 1

Confirmatory Factor Analysis

Three-Factor Model (Efficacy Scales)

ThreeFactor_model <- '
  # Factor 1: Bias-Awareness Efficacy
  Awareness =~ DSE_Aware_1_t2 + DSE_Aware_2_t2 + DSE_Aware_3_t2

  # Factor 2: Self-Regulation Efficacy
  Regulation =~ DSE_Regulate_1_t2 + DSE_Regulate_2_t2 + DSE_Regulate_3_t2 +
                DSE_Regulate_4_t2 + DSE_Regulate_5_t2

  # Factor 3: Intergroup-Management Efficacy
  Management =~ DSE_Management_1_t2 + DSE_Management_2_t2 + DSE_Management_3_t2 +
                DSE_Management_4_t2 + DSE_Management_5_t2
'

ThreeFactor_fit <- cfa(ThreeFactor_model, Study_1_CFA, estimator = "ML")

# plot CFA results
semPaths(ThreeFactor_fit, "std", weighted = FALSE, nCharNodes = 7, 
         shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5)

## Fit Indices:
## 
##   chisq      df  pvalue     cfi    srmr 
## 178.794  62.000   0.000   0.957   0.042
## Standardized Factor Loadings:
## 
##                     Awrnss Regltn Mngmnt
## DSE_Aware_1_t2       0.894  0.000  0.000
## DSE_Aware_2_t2       0.866  0.000  0.000
## DSE_Aware_3_t2       0.912  0.000  0.000
## DSE_Regulate_1_t2    0.000  0.784  0.000
## DSE_Regulate_2_t2    0.000  0.847  0.000
## DSE_Regulate_3_t2    0.000  0.807  0.000
## DSE_Regulate_4_t2    0.000  0.814  0.000
## DSE_Regulate_5_t2    0.000  0.870  0.000
## DSE_Management_1_t2  0.000  0.000  0.891
## DSE_Management_2_t2  0.000  0.000  0.879
## DSE_Management_3_t2  0.000  0.000  0.912
## DSE_Management_4_t2  0.000  0.000  0.916
## DSE_Management_5_t2  0.000  0.000  0.866
## 
## 
## Explained Variance (R²):
## 
##      DSE_Aware_1_t2      DSE_Aware_2_t2      DSE_Aware_3_t2   DSE_Regulate_1_t2 
##               0.799               0.750               0.832               0.614 
##   DSE_Regulate_2_t2   DSE_Regulate_3_t2   DSE_Regulate_4_t2   DSE_Regulate_5_t2 
##               0.717               0.651               0.662               0.757 
## DSE_Management_1_t2 DSE_Management_2_t2 DSE_Management_3_t2 DSE_Management_4_t2 
##               0.793               0.773               0.831               0.839 
## DSE_Management_5_t2 
##               0.751

One-Factor Model (Efficacy Scales)

OneFactor_model <- '
  # One Factor: Bias-Awareness, Self-Regulation, & Intergroup-Management Efficacy
  OneFactor =~ DSE_Aware_1_t2 + DSE_Aware_2_t2 + DSE_Aware_3_t2 + 
               DSE_Regulate_1_t2 + DSE_Regulate_2_t2 + DSE_Regulate_3_t2 +
               DSE_Regulate_4_t2 + DSE_Regulate_5_t2 +
               DSE_Management_1_t2 + DSE_Management_2_t2 + DSE_Management_3_t2 +
                DSE_Management_4_t2 + DSE_Management_5_t2
'

OneFactor_fit <- cfa(OneFactor_model, Study_1_CFA, estimator = "ML")
## Fit Indices:
## 
##   chisq      df  pvalue     cfi    srmr 
## 783.767  65.000   0.000   0.738   0.125
## Standardized Factor Loadings:
## 
##                     OnFctr
## DSE_Aware_1_t2       0.782
## DSE_Aware_2_t2       0.799
## DSE_Aware_3_t2       0.794
## DSE_Regulate_1_t2    0.495
## DSE_Regulate_2_t2    0.580
## DSE_Regulate_3_t2    0.640
## DSE_Regulate_4_t2    0.589
## DSE_Regulate_5_t2    0.645
## DSE_Management_1_t2  0.885
## DSE_Management_2_t2  0.864
## DSE_Management_3_t2  0.871
## DSE_Management_4_t2  0.881
## DSE_Management_5_t2  0.865
## 
## 
## Explained Variance (R²):
## 
##      DSE_Aware_1_t2      DSE_Aware_2_t2      DSE_Aware_3_t2   DSE_Regulate_1_t2 
##               0.611               0.639               0.631               0.245 
##   DSE_Regulate_2_t2   DSE_Regulate_3_t2   DSE_Regulate_4_t2   DSE_Regulate_5_t2 
##               0.337               0.410               0.347               0.416 
## DSE_Management_1_t2 DSE_Management_2_t2 DSE_Management_3_t2 DSE_Management_4_t2 
##               0.783               0.746               0.758               0.777 
## DSE_Management_5_t2 
##               0.748
## 
## 
##  Three-Factor vs One-Factor Model:
## 
## Chi-Squared Difference Test
## 
##                 Df    AIC    BIC  Chisq Chisq diff   RMSEA Df diff Pr(>Chisq)
## ThreeFactor_fit 62 6180.3 6279.1 178.79                                      
## OneFactor_fit   65 6779.3 6867.8 783.77     604.97 0.94858       3  < 2.2e-16
##                    
## ThreeFactor_fit    
## OneFactor_fit   ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Seven-Factor Measurement Model (All Seven Multi-Item Scales)

SevenFactor_model <- '
  # Factor 1: Bias-Awareness Efficacy
  Awareness =~ DSE_Aware_1_t2 + DSE_Aware_2_t2 + DSE_Aware_3_t2

  # Factor 2: Self-Regulation Efficacy
  Regulation =~ DSE_Regulate_1_t2 + DSE_Regulate_2_t2 + DSE_Regulate_3_t2 +
                DSE_Regulate_4_t2 + DSE_Regulate_5_t2

  # Factor 3: Intergroup-Management Efficacy
  Management =~ DSE_Management_1_t2 + DSE_Management_2_t2 + DSE_Management_3_t2 +
                DSE_Management_4_t2 + DSE_Management_5_t2

  # Factor 4: Leader Diversity Advocacy
  InclusiveLeadership =~ Inclusive_Leader_1_t1 + Inclusive_Leader_2_t1 +
                         Inclusive_Leader_3_t1 + Inclusive_Leader_4_t1

  # Factor 5: Pro-Diversity Attitudes
  ProDiversity =~ ProDiversity_1_t1 + ProDiversity_2_t1 +
                  ProDiversity_3_t1 + ProDiversity_4_t1

  # Factor 6: Relational Allyship
  RelationalAlly =~ Relational_Allyship_1_t3 + Relational_Allyship_2_t3 +
                    Relational_Allyship_3_t3 + Relational_Allyship_4_t3 +
                    Relational_Allyship_5_t3 + Relational_Allyship_6_t3 +
                    Relational_Allyship_7_t3

  # Factor 7: Organizational Allyship
  OrgAlly =~ Org_Allyship_1_t3 + Org_Allyship_2_t3 + Org_Allyship_3_t3 +
             Org_Allyship_4_t3 + Org_Allyship_5_t3 + Org_Allyship_6_t3 +
             Org_Allyship_7_t3 + Org_Allyship_8_t3 + Org_Allyship_9_t3
'

SevenFactor_fit <- cfa(SevenFactor_model, Study_1_CFA, estimator = "ML")
## Fit Indices:
## 
##    chisq       df   pvalue      cfi     srmr 
## 1263.032  608.000    0.000    0.936    0.046
## Standardized Factor Loadings:
## 
##                          Awrnss Regltn Mngmnt InclsL PrDvrs RltnlA OrgAll
## DSE_Aware_1_t2            0.895  0.000  0.000  0.000  0.000  0.000  0.000
## DSE_Aware_2_t2            0.865  0.000  0.000  0.000  0.000  0.000  0.000
## DSE_Aware_3_t2            0.912  0.000  0.000  0.000  0.000  0.000  0.000
## DSE_Regulate_1_t2         0.000  0.791  0.000  0.000  0.000  0.000  0.000
## DSE_Regulate_2_t2         0.000  0.855  0.000  0.000  0.000  0.000  0.000
## DSE_Regulate_3_t2         0.000  0.790  0.000  0.000  0.000  0.000  0.000
## DSE_Regulate_4_t2         0.000  0.805  0.000  0.000  0.000  0.000  0.000
## DSE_Regulate_5_t2         0.000  0.878  0.000  0.000  0.000  0.000  0.000
## DSE_Management_1_t2       0.000  0.000  0.890  0.000  0.000  0.000  0.000
## DSE_Management_2_t2       0.000  0.000  0.878  0.000  0.000  0.000  0.000
## DSE_Management_3_t2       0.000  0.000  0.915  0.000  0.000  0.000  0.000
## DSE_Management_4_t2       0.000  0.000  0.919  0.000  0.000  0.000  0.000
## DSE_Management_5_t2       0.000  0.000  0.870  0.000  0.000  0.000  0.000
## Inclusive_Leader_1_t1     0.000  0.000  0.000  0.884  0.000  0.000  0.000
## Inclusive_Leader_2_t1     0.000  0.000  0.000  0.948  0.000  0.000  0.000
## Inclusive_Leader_3_t1     0.000  0.000  0.000  0.932  0.000  0.000  0.000
## Inclusive_Leader_4_t1     0.000  0.000  0.000  0.936  0.000  0.000  0.000
## ProDiversity_1_t1         0.000  0.000  0.000  0.000  0.901  0.000  0.000
## ProDiversity_2_t1         0.000  0.000  0.000  0.000  0.932  0.000  0.000
## ProDiversity_3_t1         0.000  0.000  0.000  0.000  0.864  0.000  0.000
## ProDiversity_4_t1         0.000  0.000  0.000  0.000  0.902  0.000  0.000
## Relational_Allyship_1_t3  0.000  0.000  0.000  0.000  0.000  0.879  0.000
## Relational_Allyship_2_t3  0.000  0.000  0.000  0.000  0.000  0.877  0.000
## Relational_Allyship_3_t3  0.000  0.000  0.000  0.000  0.000  0.918  0.000
## Relational_Allyship_4_t3  0.000  0.000  0.000  0.000  0.000  0.924  0.000
## Relational_Allyship_5_t3  0.000  0.000  0.000  0.000  0.000  0.907  0.000
## Relational_Allyship_6_t3  0.000  0.000  0.000  0.000  0.000  0.820  0.000
## Relational_Allyship_7_t3  0.000  0.000  0.000  0.000  0.000  0.852  0.000
## Org_Allyship_1_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.929
## Org_Allyship_2_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.920
## Org_Allyship_3_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.933
## Org_Allyship_4_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.917
## Org_Allyship_5_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.930
## Org_Allyship_6_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.930
## Org_Allyship_7_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.918
## Org_Allyship_8_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.921
## Org_Allyship_9_t3         0.000  0.000  0.000  0.000  0.000  0.000  0.934
## 
## 
## Explained Variance (R²):
## 
##           DSE_Aware_1_t2           DSE_Aware_2_t2           DSE_Aware_3_t2 
##                    0.801                    0.748                    0.831 
##        DSE_Regulate_1_t2        DSE_Regulate_2_t2        DSE_Regulate_3_t2 
##                    0.625                    0.732                    0.624 
##        DSE_Regulate_4_t2        DSE_Regulate_5_t2      DSE_Management_1_t2 
##                    0.648                    0.771                    0.792 
##      DSE_Management_2_t2      DSE_Management_3_t2      DSE_Management_4_t2 
##                    0.770                    0.837                    0.844 
##      DSE_Management_5_t2    Inclusive_Leader_1_t1    Inclusive_Leader_2_t1 
##                    0.758                    0.782                    0.899 
##    Inclusive_Leader_3_t1    Inclusive_Leader_4_t1        ProDiversity_1_t1 
##                    0.869                    0.875                    0.812 
##        ProDiversity_2_t1        ProDiversity_3_t1        ProDiversity_4_t1 
##                    0.868                    0.746                    0.813 
## Relational_Allyship_1_t3 Relational_Allyship_2_t3 Relational_Allyship_3_t3 
##                    0.773                    0.769                    0.843 
## Relational_Allyship_4_t3 Relational_Allyship_5_t3 Relational_Allyship_6_t3 
##                    0.853                    0.823                    0.672 
## Relational_Allyship_7_t3        Org_Allyship_1_t3        Org_Allyship_2_t3 
##                    0.725                    0.864                    0.846 
##        Org_Allyship_3_t3        Org_Allyship_4_t3        Org_Allyship_5_t3 
##                    0.870                    0.841                    0.865 
##        Org_Allyship_6_t3        Org_Allyship_7_t3        Org_Allyship_8_t3 
##                    0.865                    0.842                    0.848 
##        Org_Allyship_9_t3 
##                    0.872

Six-Factor Alternative Model #1 (Combine outcomes into single factor)

SixFactor_model <- '
  # Factor 1: Bias-Awareness Efficacy
  Awareness =~ DSE_Aware_1_t2 + DSE_Aware_2_t2 + DSE_Aware_3_t2

  # Factor 2: Self-Regulation Efficacy
  Regulation =~ DSE_Regulate_1_t2 + DSE_Regulate_2_t2 + DSE_Regulate_3_t2 +
                DSE_Regulate_4_t2 + DSE_Regulate_5_t2

  # Factor 3: Intergroup-Management Efficacy
  Management =~ DSE_Management_1_t2 + DSE_Management_2_t2 + DSE_Management_3_t2 +
                DSE_Management_4_t2 + DSE_Management_5_t2

  # Factor 4: Leader Diversity Advocacy
  InclusiveLeadership =~ Inclusive_Leader_1_t1 + Inclusive_Leader_2_t1 +
                         Inclusive_Leader_3_t1 + Inclusive_Leader_4_t1

  # Factor 5: Pro-Diversity Attitudes
  ProDiversity =~ ProDiversity_1_t1 + ProDiversity_2_t1 +
                  ProDiversity_3_t1 + ProDiversity_4_t1

  # Factor 6: Relational Allyship & Organizational Allyship
  Outcomes =~ Relational_Allyship_1_t3 + Relational_Allyship_2_t3 +
                    Relational_Allyship_3_t3 + Relational_Allyship_4_t3 +
                    Relational_Allyship_5_t3 + Relational_Allyship_6_t3 +
                    Relational_Allyship_7_t3 +
                    Org_Allyship_1_t3 + Org_Allyship_2_t3 + Org_Allyship_3_t3 +
                    Org_Allyship_4_t3 + Org_Allyship_5_t3 + Org_Allyship_6_t3 +
                    Org_Allyship_7_t3 + Org_Allyship_8_t3 + Org_Allyship_9_t3
'

SixFactor_fit1 <- cfa(SixFactor_model, Study_1_CFA, estimator = "ML")

Six-Factor Alternative Model #2 (Combine predictors into single factor)

SixFactor2_model <- '
  # Factor 1: Bias-Awareness Efficacy
  Awareness =~ DSE_Aware_1_t2 + DSE_Aware_2_t2 + DSE_Aware_3_t2

  # Factor 2: Self-Regulation Efficacy
  Regulation =~ DSE_Regulate_1_t2 + DSE_Regulate_2_t2 + DSE_Regulate_3_t2 +
                DSE_Regulate_4_t2 + DSE_Regulate_5_t2

  # Factor 3: Intergroup-Management Efficacy
  Management =~ DSE_Management_1_t2 + DSE_Management_2_t2 + DSE_Management_3_t2 +
                DSE_Management_4_t2 + DSE_Management_5_t2

  # Factor 4: Leader Diversity Advocacy & Pro-Diversity Attitudes
  Predictors =~ Inclusive_Leader_1_t1 + Inclusive_Leader_2_t1 +
                         Inclusive_Leader_3_t1 + Inclusive_Leader_4_t1 +
                         ProDiversity_1_t1 + ProDiversity_2_t1 +
                         ProDiversity_3_t1 + ProDiversity_4_t1

  # Factor 5: Relational Allyship
  RelationalAlly =~ Relational_Allyship_1_t3 + Relational_Allyship_2_t3 +
                    Relational_Allyship_3_t3 + Relational_Allyship_4_t3 +
                    Relational_Allyship_5_t3 + Relational_Allyship_6_t3 +
                    Relational_Allyship_7_t3

  # Factor 6: Organizational Allyship
  OrgAlly =~ Org_Allyship_1_t3 + Org_Allyship_2_t3 + Org_Allyship_3_t3 +
             Org_Allyship_4_t3 + Org_Allyship_5_t3 + Org_Allyship_6_t3 +
             Org_Allyship_7_t3 + Org_Allyship_8_t3 + Org_Allyship_9_t3 
'

SixFactor_fit2 <- cfa(SixFactor2_model, Study_1_CFA, estimator = "ML")

Five-Factor Alternative Model #3 (Combine predictors/outcomes into single factor)

FiveFactor_model <- '
  # Factor 1: Bias-Awareness Efficacy
  Awareness =~ DSE_Aware_1_t2 + DSE_Aware_2_t2 + DSE_Aware_3_t2

  # Factor 2: Self-Regulation Efficacy
  Regulation =~ DSE_Regulate_1_t2 + DSE_Regulate_2_t2 + DSE_Regulate_3_t2 +
                DSE_Regulate_4_t2 + DSE_Regulate_5_t2

  # Factor 3: Intergroup-Management Efficacy
  Management =~ DSE_Management_1_t2 + DSE_Management_2_t2 + DSE_Management_3_t2 +
                DSE_Management_4_t2 + DSE_Management_5_t2

  # Factor 4: Leader Diversity Advocacy & Pro-Diversity Attitudes
  Predictors =~ Inclusive_Leader_1_t1 + Inclusive_Leader_2_t1 +
                         Inclusive_Leader_3_t1 + Inclusive_Leader_4_t1 +
                         ProDiversity_1_t1 + ProDiversity_2_t1 +
                         ProDiversity_3_t1 + ProDiversity_4_t1

  # Factor 5: Relational Allyship & Organizational Allyship
  Outcomes =~ Relational_Allyship_1_t3 + Relational_Allyship_2_t3 +
                    Relational_Allyship_3_t3 + Relational_Allyship_4_t3 +
                    Relational_Allyship_5_t3 + Relational_Allyship_6_t3 +
                    Relational_Allyship_7_t3 +
                    Org_Allyship_1_t3 + Org_Allyship_2_t3 + Org_Allyship_3_t3 +
                    Org_Allyship_4_t3 + Org_Allyship_5_t3 + Org_Allyship_6_t3 +
                    Org_Allyship_7_t3 + Org_Allyship_8_t3 + Org_Allyship_9_t3
'

FiveFactor_fit <- cfa(FiveFactor_model, Study_1_CFA, estimator = "ML")

Table 1: Model Comparison

## 
## Chi-Squared Difference Test
## 
##                  Df   AIC   BIC  Chisq Chisq diff   RMSEA Df diff Pr(>Chisq)
## SevenFactor_fit 608 16468 16790 1263.0                                      
## SixFactor_fit1  614 17510 17812 2317.5    1054.45 0.89122       6  < 2.2e-16
## SixFactor_fit2  614 17177 17479 1984.4     721.39 0.73618       6  < 2.2e-16
## FiveFactor_fit  619 18201 18486 3018.2    1755.13 0.84895      11  < 2.2e-16
##                    
## SevenFactor_fit    
## SixFactor_fit1  ***
## SixFactor_fit2  ***
## FiveFactor_fit  ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##                       cfi       srmr
## SevenFactor     0.9360565 0.04608307
## SixFactor_Alt1  0.8337080 0.10531765
## SixFactor_Alt2  0.8662205 0.09155365
## FiveFactor_Alt3 0.7657961 0.13010189

Reliability Estimates (Cronbach Alpha) - Study 1 Measures

## Alpha for bias-awareness efficacy:     0.9173952 
##  Alpha for self-regulation efficacy:    0.9139933 
##  Alpha for intergroup-management efficacy: 0.9512536
## Alpha for relational ally work: 0.9608815 
##  Alpha for organizational ally work: 0.9817662
## Alpha for leader diversity advocacy: 0.9596095 
##  Alpha for pro-diversity attitudes: 0.9409475

Table 1: Descriptives & Correlations

## 
## 
## Means, standard deviations, and correlations with confidence intervals
##  
## 
##   Variable    M    SD   1            2           3            4         
##   1. Male     0.59 0.49                                                 
##                                                                         
##   2. White    0.71 0.46 -.06                                            
##                         [-.19, .07]                                     
##                                                                         
##   3. Ideology 3.31 1.88 .15*         .10                                
##                         [.02, .28]   [-.03, .23]                        
##                                                                         
##   4. LdrDivAd 3.27 1.23 -.11         -.11        -.06                   
##                         [-.24, .02]  [-.24, .02] [-.19, .07]            
##                                                                         
##   5. PDB      4.32 0.98 -.24**       -.08        -.48**       .45**     
##                         [-.36, -.12] [-.20, .06] [-.57, -.37] [.34, .55]
##                                                                         
##   6. Aware    3.69 1.08 -.14*        .00         -.23**       .38**     
##                         [-.26, -.01] [-.13, .13] [-.35, -.10] [.26, .48]
##                                                                         
##   7. Regulate 4.28 0.77 -.15*        .08         -.16*        .29**     
##                         [-.27, -.02] [-.05, .21] [-.28, -.03] [.17, .41]
##                                                                         
##   8. Manage   3.41 1.20 -.12         -.03        -.19**       .51**     
##                         [-.24, .01]  [-.16, .11] [-.31, -.06] [.41, .61]
##                                                                         
##   9. OrgAlly  2.56 1.28 -.09         -.03        -.12         .56**     
##                         [-.22, .04]  [-.17, .10] [-.25, .01]  [.46, .64]
##                                                                         
##   10. RelAlly 3.55 0.95 -.16*        -.03        -.27**       .55**     
##                         [-.29, -.03] [-.16, .10] [-.38, -.14] [.45, .63]
##                                                                         
##   5          6          7          8          9         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##                                                         
##   .41**                                                 
##   [.30, .51]                                            
##                                                         
##   .37**      .58**                                      
##   [.26, .48] [.49, .66]                                 
##                                                         
##   .41**      .77**      .57**                           
##   [.30, .52] [.72, .82] [.48, .65]                      
##                                                         
##   .41**      .48**      .25**      .59**                
##   [.30, .52] [.38, .58] [.12, .37] [.50, .67]           
##                                                         
##   .61**      .51**      .51**      .54**      .68**     
##   [.51, .68] [.41, .60] [.41, .60] [.44, .63] [.61, .75]
##                                                         
## 
## Note. M and SD are used to represent mean and standard deviation, respectively.
## Values in square brackets indicate the 95% confidence interval.
## The confidence interval is a plausible range of population correlations 
## that could have caused the sample correlation (Cumming, 2014).
##  * indicates p < .05. ** indicates p < .01.
## 

Run Mplus Path Models

Table 3 (Model 1): Path Model for Relational Ally Work

## Mplus VERSION 8.11 (Mac)
## MUTHEN & MUTHEN
## 09/04/2025  11:42 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Study 1
##   DATA: FILE = "Study1.dat";
##   VARIABLE:
##     NAMES = Male White Ideology LdrDivAd PDB Aware Regulate Manage OrgAlly RelAlly;
##   MISSING = ALL (999);
## 
##   USEVARIABLES LdrDivAd PDB Aware Regulate RelAlly
##           PolID;
## 
##   DEFINE:
##   ! Political Ideology centered at the scale midpoint (= 4)
##   PolID = Ideology - 4;
## 
##   ! Grand-mean center Leader Diversity Advocacy and Pro-Diversity Attitudes
##   CENTER LdrDivAd PDB (GRANDMEAN);
## 
##   ANALYSIS:
##     ESTIMATOR = ML;
## 
##   MODEL:
##     Aware    ON PDB LdrDivAd;
##     Regulate ON PDB LdrDivAd;
## 
##     RelAlly  ON PolID PDB LdrDivAd Aware Regulate;
## 
## 
##     ! Covariances among predictors
##     PDB WITH LdrDivAd PolID;
##     LdrDivAd WITH PolID;
##     Aware WITH Regulate;
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Study 1
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                         224
## 
## Number of dependent variables                                    3
## Number of independent variables                                  3
## Number of continuous latent variables                            0
## 
## Observed dependent variables
## 
##   Continuous
##    AWARE       REGULATE    RELALLY
## 
## Observed independent variables
##    LDRDIVAD    PDB         POLID
## 
## Variables with special functions
## 
##   Centering (GRANDMEAN)
##    LDRDIVAD    PDB
## 
## 
## Estimator                                                       ML
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Study1.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns             1
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               AWARE         REGULATE      RELALLY       LDRDIVAD      PDB
##               ________      ________      ________      ________      ________
##  AWARE          1.000
##  REGULATE       1.000         1.000
##  RELALLY        1.000         1.000         1.000
##  LDRDIVAD       1.000         1.000         1.000         1.000
##  PDB            1.000         1.000         1.000         1.000         1.000
##  POLID          1.000         1.000         1.000         1.000         1.000
## 
## 
##            Covariance Coverage
##               POLID
##               ________
##  POLID          1.000
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      AWARE                 3.690      -0.610       1.000    1.79%       2.667      3.667      4.000
##              224.000       1.164      -0.498       5.000   20.09%       4.000      4.667
##      REGULATE              4.278      -1.277       1.400    0.45%       3.800      4.200      4.400
##              224.000       0.591       1.382       5.000   29.91%       4.600      5.000
##      RELALLY               3.548      -0.668       1.250    3.12%       2.875      3.375      3.750
##              224.000       0.890      -0.233       5.000    0.45%       3.875      4.500
##      LDRDIVAD              0.000      -0.436      -2.269   12.05%      -1.019     -0.269     -0.019
##              224.000       1.503      -0.730       1.731   12.05%       0.481      0.981
##      PDB                   0.000      -1.748      -3.318    1.34%      -0.568      0.182      0.432
##              224.000       0.947       2.453       0.682   45.98%       0.682      0.682
##      POLID                -0.688       0.488      -3.000   19.20%      -2.000     -2.000     -1.000
##              224.000       3.509      -0.878       3.000    8.04%       0.000      1.000
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       25
## 
## Loglikelihood
## 
##           H0 Value                       -1809.288
##           H1 Value                       -1808.224
## 
## Information Criteria
## 
##           Akaike (AIC)                    3668.576
##           Bayesian (BIC)                  3753.867
##           Sample-Size Adjusted BIC        3674.638
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                              2.129
##           Degrees of Freedom                     2
##           P-Value                           0.3450
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.017
##           90 Percent C.I.                    0.000  0.135
##           Probability RMSEA <= .05           0.525
## 
## CFI/TLI
## 
##           CFI                                1.000
##           TLI                                0.998
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                            331.308
##           Degrees of Freedom                    12
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.013
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  AWARE    ON
##     PDB                0.335      0.073      4.559      0.000
##     LDRDIVAD           0.212      0.058      3.636      0.000
## 
##  REGULATE ON
##     PDB                0.240      0.054      4.435      0.000
##     LDRDIVAD           0.099      0.043      2.300      0.021
## 
##  RELALLY  ON
##     POLID             -0.013      0.027     -0.475      0.635
##     PDB                0.318      0.059      5.401      0.000
##     LDRDIVAD           0.215      0.041      5.254      0.000
##     AWARE              0.115      0.051      2.234      0.026
##     REGULATE           0.281      0.069      4.054      0.000
## 
##  PDB      WITH
##     LDRDIVAD           0.536      0.087      6.131      0.000
##     POLID             -0.869      0.135     -6.444      0.000
## 
##  LDRDIVAD WITH
##     POLID             -0.149      0.154     -0.968      0.333
## 
##  AWARE    WITH
##     REGULATE           0.329      0.050      6.561      0.000
## 
##  Means
##     LDRDIVAD           0.000      0.082      0.000      1.000
##     PDB                0.000      0.065      0.000      1.000
##     POLID             -0.688      0.125     -5.493      0.000
## 
##  Intercepts
##     AWARE              3.690      0.064     57.767      0.000
##     REGULATE           4.278      0.047     90.881      0.000
##     RELALLY            1.913      0.266      7.181      0.000
## 
##  Variances
##     LDRDIVAD           1.503      0.142     10.583      0.000
##     PDB                0.947      0.089     10.583      0.000
##     POLID              3.509      0.332     10.583      0.000
## 
##  Residual Variances
##     AWARE              0.914      0.086     10.583      0.000
##     REGULATE           0.496      0.047     10.583      0.000
##     RELALLY            0.407      0.038     10.583      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.703E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
##      Beginning Time:  11:42:55
##         Ending Time:  11:42:55
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2024 Muthen & Muthen

Hypothesis 1a: Mediation Analysis

res <- readModels("Mplus Syntax/Study1_Mediation_RelAlly.out")

# Extract coefficients
a_est <- res$parameters$unstandardized$est[2]  # Effect of X on M (a-path)
b_est <- res$parameters$unstandardized$est[8]  # Effect of M on Y (b-path)

# Extract standard errors
a_se <- res$parameters$unstandardized$se[2]
b_se <- res$parameters$unstandardized$se[8]

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_est, mu.y = b_est, se.x = a_se, se.y = b_se,
               rho = 0, alpha = .05, sims = 10000, method = "parametric")
## Indirect effect estimate: 0.02438
## Indirect effect standard error: 0.0130437
## Monte Carlo 95% CI: [ 0.002680119 , 0.05340348 ]

Hypothesis 2: Mediation Analysis

# Extract coefficients
a_est <- res$parameters$unstandardized$est[4]  # Effect of X on M (a-path)
b_est <- res$parameters$unstandardized$est[9]  # Effect of M on Y (b-path)

# Extract standard errors
a_se <- res$parameters$unstandardized$se[4]
b_se <- res$parameters$unstandardized$se[9]

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_est, mu.y = b_est, se.x = a_se, se.y = b_se,
               rho = 0, alpha = .05, sims = 10000, method = "parametric")
## Indirect effect estimate: 0.027819
## Indirect effect standard error: 0.01419382
## Monte Carlo 95% CI: [ 0.003669805 , 0.05903483 ]

Table 3 (Model 2): Conditional Path Model for Relational Ally Work

## Mplus VERSION 8.11 (Mac)
## MUTHEN & MUTHEN
## 09/04/2025  11:42 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Study 1: Moderated Mediation Models
##   DATA: FILE = "Study1.dat";
##   VARIABLE:
##     NAMES = Male White Ideology LdrDivAd PDB Aware Regulate Manage OrgAlly RelAlly;
##   MISSING = ALL (999);
## 
##   USEVARIABLES LdrDivAd PDB Aware Regulate RelAlly
##           PolID LDA_PDB
## 
##   DEFINE:
##   ! Political Ideology centered at the scale midpoint (= 4)
##   PolID = Ideology - 4;
## 
##   ! Grand-mean center Leader Diversity Advocacy and Pro-Diversity Attitudes
##   CENTER LdrDivAd PDB (GRANDMEAN);
## 
##   ! Create interaction term
##   LDA_PDB = LdrDivAd * PDB;
## 
##   ANALYSIS:
##     ESTIMATOR = ML;
## 
##   MODEL:
##     Aware    ON PDB (a2)
##                 LdrDivAd (a1)
##                 LDA_PDB (a3);
## 
##     Regulate ON PDB (b2)
##                 LdrDivAd (b1)
##                 LDA_PDB (b3);
## 
##     RelAlly  ON PolID
##                 PDB
##                 LdrDivAd
##                 Aware (aw)
##                 Regulate (rg);
## 
##     PDB WITH LdrDivAd PolID;
##   LdrDivAd WITH PolID;
##     Aware WITH Regulate;
## 
##   MODEL CONSTRAINT:
## 
##           LOOP(PDB, -1.96, 1.96, .98); ! Two Standard Deviations Below/Above Mean
##           PLOT(
##                ! LdrDivAd_aw
##                LdrDivAd_rg
##                );
##           ! LdrDivAd_aw = (a1 + a3*PDB)*aw;
##           LdrDivAd_rg = (b1 + b3*PDB)*rg;
## 
##   PLOT: TYPE = PLOT2;
## 
## 
## 
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Study 1: Moderated Mediation Models
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                         224
## 
## Number of dependent variables                                    3
## Number of independent variables                                  4
## Number of continuous latent variables                            0
## 
## Observed dependent variables
## 
##   Continuous
##    AWARE       REGULATE    RELALLY
## 
## Observed independent variables
##    LDRDIVAD    PDB         POLID       LDA_PDB
## 
## Variables with special functions
## 
##   Centering (GRANDMEAN)
##    LDRDIVAD    PDB
## 
## 
## Estimator                                                       ML
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Study1.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns             1
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               AWARE         REGULATE      RELALLY       LDRDIVAD      PDB
##               ________      ________      ________      ________      ________
##  AWARE          1.000
##  REGULATE       1.000         1.000
##  RELALLY        1.000         1.000         1.000
##  LDRDIVAD       1.000         1.000         1.000         1.000
##  PDB            1.000         1.000         1.000         1.000         1.000
##  POLID          1.000         1.000         1.000         1.000         1.000
##  LDA_PDB        1.000         1.000         1.000         1.000         1.000
## 
## 
##            Covariance Coverage
##               POLID         LDA_PDB
##               ________      ________
##  POLID          1.000
##  LDA_PDB        1.000         1.000
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      AWARE                 3.690      -0.610       1.000    1.79%       2.667      3.667      4.000
##              224.000       1.164      -0.498       5.000   20.09%       4.000      4.667
##      REGULATE              4.278      -1.277       1.400    0.45%       3.800      4.200      4.400
##              224.000       0.591       1.382       5.000   29.91%       4.600      5.000
##      RELALLY               3.548      -0.668       1.250    3.12%       2.875      3.375      3.750
##              224.000       0.890      -0.233       5.000    0.45%       3.875      4.500
##      LDRDIVAD              0.000      -0.436      -2.269   12.05%      -1.019     -0.269     -0.019
##              224.000       1.503      -0.730       1.731   12.05%       0.481      0.981
##      PDB                   0.000      -1.748      -3.318    1.34%      -0.568      0.182      0.432
##              224.000       0.947       2.453       0.682   45.98%       0.682      0.682
##      POLID                -0.688       0.488      -3.000   19.20%      -2.000     -2.000     -1.000
##              224.000       3.509      -0.878       3.000    8.04%       0.000      1.000
##      LDA_PDB               0.536       2.556      -2.282    0.45%      -0.183      0.088      0.222
##              224.000       2.016       8.309       7.529    0.45%       0.437      1.010
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       27
## 
## Loglikelihood
## 
##           H0 Value                       -1803.499
##           H1 Value                       -1744.261
## 
## Information Criteria
## 
##           Akaike (AIC)                    3660.998
##           Bayesian (BIC)                  3753.113
##           Sample-Size Adjusted BIC        3667.545
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                            118.476
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.289
##           90 Percent C.I.                    0.245  0.336
##           Probability RMSEA <= .05           0.000
## 
## CFI/TLI
## 
##           CFI                                0.658
##           TLI                                0.146
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                            344.071
##           Degrees of Freedom                    15
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.170
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  AWARE    ON
##     PDB                0.531      0.092      5.791      0.000
##     LDRDIVAD           0.172      0.058      2.968      0.003
##     LDA_PDB            0.194      0.057      3.425      0.001
## 
##  REGULATE ON
##     PDB                0.325      0.069      4.723      0.000
##     LDRDIVAD           0.082      0.043      1.878      0.060
##     LDA_PDB            0.084      0.042      1.969      0.049
## 
##  RELALLY  ON
##     POLID             -0.013      0.027     -0.475      0.635
##     PDB                0.318      0.059      5.401      0.000
##     LDRDIVAD           0.215      0.041      5.254      0.000
##     AWARE              0.115      0.051      2.234      0.026
##     REGULATE           0.281      0.069      4.054      0.000
## 
##  PDB      WITH
##     LDRDIVAD           0.536      0.087      6.131      0.000
##     POLID             -0.869      0.135     -6.444      0.000
## 
##  LDRDIVAD WITH
##     POLID             -0.149      0.154     -0.968      0.333
## 
##  AWARE    WITH
##     REGULATE           0.309      0.048      6.417      0.000
## 
##  Means
##     LDRDIVAD           0.000      0.082      0.000      1.000
##     PDB                0.000      0.065      0.000      1.000
##     POLID             -0.688      0.125     -5.493      0.000
## 
##  Intercepts
##     AWARE              3.587      0.069     51.772      0.000
##     REGULATE           4.233      0.052     81.540      0.000
##     RELALLY            1.913      0.266      7.182      0.000
## 
##  Variances
##     LDRDIVAD           1.503      0.142     10.583      0.000
##     PDB                0.947      0.089     10.583      0.000
##     POLID              3.509      0.332     10.583      0.000
## 
##  Residual Variances
##     AWARE              0.869      0.082     10.583      0.000
##     REGULATE           0.488      0.046     10.583      0.000
##     RELALLY            0.407      0.038     10.583      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.522E-04
##        (ratio of smallest to largest eigenvalue)
## 
## 
## PLOT INFORMATION
## 
## The following plots are available:
## 
##   Loop plots
## 
##      Beginning Time:  11:42:56
##         Ending Time:  11:42:56
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2024 Muthen & Muthen

Hypothesis 4a: Moderated Mediation (Bias-Awareness Efficacy and Relational Ally Work)

res <- readModels("Mplus Syntax/Study1_Moderated Mediation_RelAlly.out")

# Extract coefficients
a_int <- res$parameters$unstandardized$est[3]  # Effect of XW on M (a-path)
b_est <- res$parameters$unstandardized$est[10]  # Effect of M on Y (b-path)

# Extract standard errors
a_int_se <- res$parameters$unstandardized$se[3]
b_se <- res$parameters$unstandardized$se[10]

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_int, mu.y = b_est, se.x = a_int_se, se.y = b_se,
               rho = 0, alpha = .05, sims = 10000, method = "parametric")
## 
## --- Index of Moderated Mediation ---
## Estimate: 0.02231
## Standard error: 0.01221924
## Monte Carlo 95% CI: [ 0.002302669 , 0.04970842 ]
# Conditional Indirect Effect for High and Low Pro-Diversity Attitudes
# Set moderator values (e.g., ±1 SD)
PDB_low <- -0.98  # 1 SD below mean
PDB_high <- 0.98  # 1 SD above mean

# Extract coefficient and standard error for leader diversity advocacy
a_main <- res$parameters$unstandardized$est[2]  # Effect of X on M (a-path)         
a_main_se <- res$parameters$unstandardized$se[2]

# Compute conditional a-paths
a_low  <- a_main + a_int * PDB_low
a_high <- a_main + a_int * PDB_high

# Compute SEs of conditional a-paths
a_low_se  <- sqrt(a_main_se^2 + (PDB_low^2 * a_int_se^2))
a_high_se <- sqrt(a_main_se^2 + (PDB_high^2 * a_int_se^2))

# Compute Monte Carlo CI for indirect effect at low PDB
mc_ci_low <- medci(mu.x = a_low, mu.y = b_est,
                   se.x = a_low_se, se.y = b_se,
                   rho = 0, alpha = 0.10, sims = 10000, method = "parametric")

# Compute Monte Carlo CI for indirect effect at high PDB
mc_ci_high <- medci(mu.x = a_high, mu.y = b_est,
                    se.x = a_high_se, se.y = b_se,
                    rho = 0, alpha = 0.05, sims = 10000, method = "parametric")
## 
## --- Conditional Indirect Effects ---
## At LOW PDB (-1 SD):
## Indirect effect estimate: -0.002
## Standard error (LOW PDB): 0.01
## Monte Carlo 90% CI: [ -0.019 , 0.014 ]
## At HIGH PDB (+1 SD):
## Indirect effect estimate: 0.042
## Standard error (HIGH PDB): 0.021
## Monte Carlo 95% CI: [ 0.005 , 0.087 ]

Hypothesis 4b: Moderated Mediation (Self-Regulation Efficacy and Relational Ally Work)

# Extract coefficients
a_int <- res$parameters$unstandardized$est[6]  # Effect of XW on M (a-path)
b_est <- res$parameters$unstandardized$est[11]  # Effect of M on Y (b-path)

# Extract standard errors
a_int_se <- res$parameters$unstandardized$se[6]
b_se <- res$parameters$unstandardized$se[11] 

# Compute Monte Carlo confidence interval (alpha = .10)
mc_ci <- medci(mu.x = a_int, mu.y = b_est, se.x = a_int_se, se.y = b_se,
               rho = 0, alpha = .05, sims = 10000, method = "parametric")
## 
## --- Index of Moderated Mediation ---
## Estimate: 0.023604
## Standard error: 0.013464
## Monte Carlo 95% CI: [ 0.0004302779 , 0.05311739 ]
# Conditional Indirect Effect for High and Low Pro-Diversity Attitudes
# Set moderator values (e.g., ±1 SD)
PDB_low <- -0.98  # 1 SD below mean
PDB_high <- 0.98  # 1 SD above mean

# Extract coefficient and standard error for leader diversity advocacy
a_main <- res$parameters$unstandardized$est[5]  # Effect of X on M (a-path)         
a_main_se <- res$parameters$unstandardized$se[5]

# Compute conditional a-paths
a_low  <- a_main + a_int * PDB_low
a_high <- a_main + a_int * PDB_high

# Compute SEs of conditional a-paths
a_low_se  <- sqrt(a_main_se^2 + (PDB_low^2 * a_int_se^2))
a_high_se <- sqrt(a_main_se^2 + (PDB_high^2 * a_int_se^2))

# Compute Monte Carlo CI for indirect effect at low PDB
mc_ci_low <- medci(mu.x = a_low, mu.y = b_est,
                   se.x = a_low_se, se.y = b_se,
                   rho = 0, alpha = 0.10, sims = 10000, method = "parametric")

# Compute Monte Carlo CI for indirect effect at high PDB
mc_ci_high <- medci(mu.x = a_high, mu.y = b_est,
                    se.x = a_high_se, se.y = b_se,
                    rho = 0, alpha = 0.05, sims = 10000, method = "parametric")
## 
## --- Conditional Indirect Effects ---
## At LOW PDB (-1 SD):
## Indirect effect estimate: -9e-05
## Standard error (LOW PDB): 0.017
## Monte Carlo 90% CI: [ -0.028 , 0.028 ]
## At HIGH PDB (+1 SD):
## Indirect effect estimate: 0.046
## Standard error (HIGH PDB): 0.021
## Monte Carlo 95% CI: [ 0.011 , 0.092 ]

View Johnson-Neyman Plots for Conditional Indirect Effects

Figure 1: Conditional Indirect Effect on Relationally Ally Work via Bias-Awareness Self-Efficacy

Figure 2: Conditional Indirect Effect on Relationally Ally Work via Self-Regulation Self-Efficacy

Table 3 (Model 1): Path Model for Organizational Ally Work

## Mplus VERSION 8.11 (Mac)
## MUTHEN & MUTHEN
## 09/04/2025  11:42 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Study 1
##   DATA: FILE = "Study1.dat";
##   VARIABLE:
##     NAMES = Male White Ideology LdrDivAd PDB Aware Regulate Manage OrgAlly RelAlly;
##   MISSING = ALL (999);
## 
##   USEVARIABLES LdrDivAd PDB Aware Manage OrgAlly
##           PolID;
## 
##   DEFINE:
##   ! Political Ideology centered at the scale midpoint (= 4)
##   PolID = Ideology - 4;
## 
##   ! Grand-mean center Leader Diversity Advocacy and Pro-Diversity Attitudes
##   CENTER LdrDivAd PDB (GRANDMEAN);
## 
##   ANALYSIS:
##     ESTIMATOR = ML;
## 
##   MODEL:
##     Aware    ON PDB LdrDivAd;
##     Manage   ON PDB LdrDivAd;
## 
##     OrgAlly  ON PolID PDB LdrDivAd Aware Manage;
## 
## 
##     ! Covariances among predictors
##     PDB WITH LdrDivAd PolID;
##     LdrDivAd WITH PolID;
##     Aware WITH Manage;
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Study 1
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                         224
## 
## Number of dependent variables                                    3
## Number of independent variables                                  3
## Number of continuous latent variables                            0
## 
## Observed dependent variables
## 
##   Continuous
##    AWARE       MANAGE      ORGALLY
## 
## Observed independent variables
##    LDRDIVAD    PDB         POLID
## 
## Variables with special functions
## 
##   Centering (GRANDMEAN)
##    LDRDIVAD    PDB
## 
## 
## Estimator                                                       ML
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Study1.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns             1
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               AWARE         MANAGE        ORGALLY       LDRDIVAD      PDB
##               ________      ________      ________      ________      ________
##  AWARE          1.000
##  MANAGE         1.000         1.000
##  ORGALLY        1.000         1.000         1.000
##  LDRDIVAD       1.000         1.000         1.000         1.000
##  PDB            1.000         1.000         1.000         1.000         1.000
##  POLID          1.000         1.000         1.000         1.000         1.000
## 
## 
##            Covariance Coverage
##               POLID
##               ________
##  POLID          1.000
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      AWARE                 3.690      -0.610       1.000    1.79%       2.667      3.667      4.000
##              224.000       1.164      -0.498       5.000   20.09%       4.000      4.667
##      MANAGE                3.409      -0.422       1.000    4.02%       2.200      3.200      3.600
##              224.000       1.439      -0.893       5.000   13.84%       4.000      4.600
##      ORGALLY               2.558       0.306       1.000   21.43%       1.000      2.000      2.556
##              224.000       1.627      -1.041       5.000    6.70%       3.000      3.778
##      LDRDIVAD              0.000      -0.436      -2.269   12.05%      -1.019     -0.269     -0.019
##              224.000       1.503      -0.730       1.731   12.05%       0.481      0.981
##      PDB                   0.000      -1.748      -3.318    1.34%      -0.568      0.182      0.432
##              224.000       0.947       2.453       0.682   45.98%       0.682      0.682
##      POLID                -0.688       0.488      -3.000   19.20%      -2.000     -2.000     -1.000
##              224.000       3.509      -0.878       3.000    8.04%       0.000      1.000
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       25
## 
## Loglikelihood
## 
##           H0 Value                       -1927.517
##           H1 Value                       -1926.653
## 
## Information Criteria
## 
##           Akaike (AIC)                    3905.035
##           Bayesian (BIC)                  3990.326
##           Sample-Size Adjusted BIC        3911.097
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                              1.728
##           Degrees of Freedom                     2
##           P-Value                           0.4214
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.000
##           90 Percent C.I.                    0.000  0.127
##           Probability RMSEA <= .05           0.596
## 
## CFI/TLI
## 
##           CFI                                1.000
##           TLI                                1.000
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                            428.964
##           Degrees of Freedom                    12
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.017
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  AWARE    ON
##     PDB                0.335      0.073      4.559      0.000
##     LDRDIVAD           0.212      0.058      3.636      0.000
## 
##  MANAGE   ON
##     PDB                0.281      0.077      3.661      0.000
##     LDRDIVAD           0.404      0.061      6.623      0.000
## 
##  ORGALLY  ON
##     POLID              0.024      0.039      0.622      0.534
##     PDB                0.165      0.086      1.916      0.055
##     LDRDIVAD           0.318      0.065      4.900      0.000
##     AWARE              0.077      0.094      0.812      0.417
##     MANAGE             0.358      0.090      3.964      0.000
## 
##  PDB      WITH
##     LDRDIVAD           0.536      0.087      6.131      0.000
##     POLID             -0.869      0.135     -6.444      0.000
## 
##  LDRDIVAD WITH
##     POLID             -0.149      0.154     -0.968      0.333
## 
##  AWARE    WITH
##     MANAGE             0.680      0.078      8.679      0.000
## 
##  Means
##     LDRDIVAD           0.000      0.082      0.000      1.000
##     PDB                0.000      0.065      0.000      1.000
##     POLID             -0.688      0.125     -5.493      0.000
## 
##  Intercepts
##     AWARE              3.690      0.064     57.767      0.000
##     MANAGE             3.409      0.067     51.076      0.000
##     ORGALLY            1.071      0.260      4.125      0.000
## 
##  Variances
##     LDRDIVAD           1.503      0.142     10.583      0.000
##     PDB                0.947      0.089     10.583      0.000
##     POLID              3.509      0.332     10.583      0.000
## 
##  Residual Variances
##     AWARE              0.914      0.086     10.583      0.000
##     MANAGE             0.998      0.094     10.583      0.000
##     ORGALLY            0.899      0.085     10.583      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.194E-02
##        (ratio of smallest to largest eigenvalue)
## 
## 
##      Beginning Time:  11:42:55
##         Ending Time:  11:42:55
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2024 Muthen & Muthen

Hypothesis 1b: Mediation Analysis

res <- readModels("Mplus Syntax/Study1_Mediation_OrgAlly.out")

# Extract coefficients
a_est <- res$parameters$unstandardized$est[2]  # Effect of X on M (a-path)
b_est <- res$parameters$unstandardized$est[8]  # Effect of M on Y (b-path)

# Extract standard errors
a_se <- res$parameters$unstandardized$se[2]
b_se <- res$parameters$unstandardized$se[8] 

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_est, mu.y = b_est, se.x = a_se, se.y = b_se,
               rho = 0, alpha = .10, sims = 10000, method = "parametric")
## Indirect effect estimate: 0.016324
## Indirect effect standard error: 0.02113752
## Monte Carlo 90% CI: [ -0.01618396 , 0.05287173 ]

Hypothesis 3: Mediation Analysis

# Extract coefficients
a_est <- res$parameters$unstandardized$est[4]  # Effect of X on M (a-path)
b_est <- res$parameters$unstandardized$est[9]   # Effect of M on Y (b-path)

# Extract standard errors
a_se <- res$parameters$unstandardized$se[4]
b_se <- res$parameters$unstandardized$se[9]

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_est, mu.y = b_est, se.x = a_se, se.y = b_se,
               rho = 0, alpha = .01, sims = 10000, method = "parametric")
## Indirect effect estimate: 0.144632
## Indirect effect standard error: 0.04276784
## Monte Carlo 99% CI: [ 0.04717184 , 0.268454 ]

Table 3 (Model 2): Conditional Path Model for Organizational Ally Work

## Mplus VERSION 8.11 (Mac)
## MUTHEN & MUTHEN
## 09/04/2025  11:42 AM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Study 1: Moderated Mediation Models
##   DATA: FILE = "Study1.dat";
##   VARIABLE:
##     NAMES = Male White Ideology LdrDivAd PDB Aware Regulate Manage OrgAlly RelAlly;
##   MISSING = ALL (999);
## 
##   USEVARIABLES LdrDivAd PDB Aware Manage OrgAlly
##           PolID LDA_PDB;
## 
##   DEFINE:
##   ! Political Ideology centered at the scale midpoint (= 4)
##   PolID = Ideology - 4;
## 
##   ! Grand-mean center Leader Diversity Advocacy and Pro-Diversity Attitudes
##   CENTER LdrDivAd PDB (GRANDMEAN);
## 
##   ! Create interaction term
##   LDA_PDB = LdrDivAd * PDB;
## 
##   ANALYSIS:
##     ESTIMATOR = ML;
## 
##   MODEL:
##     Aware    ON PDB (a2)
##                 LdrDivAd (a1)
##                 LDA_PDB (a3);
## 
##     Manage   ON PDB (c2)
##                 LdrDivAd (c1)
##                 LDA_PDB (c3);
## 
##     OrgAlly  ON PolID
##                 PDB
##                 LdrDivAd
##                 Aware
##                 Manage (mg);
## 
##     PDB WITH LdrDivAd PolID;
##   LdrDivAd WITH PolID;
##     Aware WITH Manage;
## 
##   MODEL CONSTRAINT:
## 
##           LOOP(PDB, -1.96, 1.96, .98); ! Two Standard Deviations Below/Above Mean
##           PLOT(LdrDivAd_mg);
##           LdrDivAd_mg = (c1 + c3*PDB)*mg;
## 
##   PLOT: TYPE = PLOT2;
## 
## 
## 
## 
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Study 1: Moderated Mediation Models
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                         224
## 
## Number of dependent variables                                    3
## Number of independent variables                                  4
## Number of continuous latent variables                            0
## 
## Observed dependent variables
## 
##   Continuous
##    AWARE       MANAGE      ORGALLY
## 
## Observed independent variables
##    LDRDIVAD    PDB         POLID       LDA_PDB
## 
## Variables with special functions
## 
##   Centering (GRANDMEAN)
##    LDRDIVAD    PDB
## 
## 
## Estimator                                                       ML
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Study1.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns             1
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               AWARE         MANAGE        ORGALLY       LDRDIVAD      PDB
##               ________      ________      ________      ________      ________
##  AWARE          1.000
##  MANAGE         1.000         1.000
##  ORGALLY        1.000         1.000         1.000
##  LDRDIVAD       1.000         1.000         1.000         1.000
##  PDB            1.000         1.000         1.000         1.000         1.000
##  POLID          1.000         1.000         1.000         1.000         1.000
##  LDA_PDB        1.000         1.000         1.000         1.000         1.000
## 
## 
##            Covariance Coverage
##               POLID         LDA_PDB
##               ________      ________
##  POLID          1.000
##  LDA_PDB        1.000         1.000
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      AWARE                 3.690      -0.610       1.000    1.79%       2.667      3.667      4.000
##              224.000       1.164      -0.498       5.000   20.09%       4.000      4.667
##      MANAGE                3.409      -0.422       1.000    4.02%       2.200      3.200      3.600
##              224.000       1.439      -0.893       5.000   13.84%       4.000      4.600
##      ORGALLY               2.558       0.306       1.000   21.43%       1.000      2.000      2.556
##              224.000       1.627      -1.041       5.000    6.70%       3.000      3.778
##      LDRDIVAD              0.000      -0.436      -2.269   12.05%      -1.019     -0.269     -0.019
##              224.000       1.503      -0.730       1.731   12.05%       0.481      0.981
##      PDB                   0.000      -1.748      -3.318    1.34%      -0.568      0.182      0.432
##              224.000       0.947       2.453       0.682   45.98%       0.682      0.682
##      POLID                -0.688       0.488      -3.000   19.20%      -2.000     -2.000     -1.000
##              224.000       3.509      -0.878       3.000    8.04%       0.000      1.000
##      LDA_PDB               0.536       2.556      -2.282    0.45%      -0.183      0.088      0.222
##              224.000       2.016       8.309       7.529    0.45%       0.437      1.010
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       27
## 
## Loglikelihood
## 
##           H0 Value                       -1920.363
##           H1 Value                       -1861.599
## 
## Information Criteria
## 
##           Akaike (AIC)                    3894.726
##           Bayesian (BIC)                  3986.840
##           Sample-Size Adjusted BIC        3901.273
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                            117.528
##           Degrees of Freedom                     6
##           P-Value                           0.0000
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.288
##           90 Percent C.I.                    0.244  0.335
##           Probability RMSEA <= .05           0.000
## 
## CFI/TLI
## 
##           CFI                                0.740
##           TLI                                0.350
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                            443.910
##           Degrees of Freedom                    15
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.167
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  AWARE    ON
##     PDB                0.531      0.092      5.791      0.000
##     LDRDIVAD           0.172      0.058      2.968      0.003
##     LDA_PDB            0.194      0.057      3.425      0.001
## 
##  MANAGE   ON
##     PDB                0.498      0.096      5.214      0.000
##     LDRDIVAD           0.360      0.060      5.949      0.000
##     LDA_PDB            0.215      0.059      3.636      0.000
## 
##  ORGALLY  ON
##     POLID              0.024      0.039      0.621      0.535
##     PDB                0.165      0.086      1.916      0.055
##     LDRDIVAD           0.317      0.065      4.900      0.000
##     AWARE              0.077      0.094      0.812      0.417
##     MANAGE             0.358      0.090      3.964      0.000
## 
##  PDB      WITH
##     LDRDIVAD           0.536      0.087      6.131      0.000
##     POLID             -0.870      0.135     -6.444      0.000
## 
##  LDRDIVAD WITH
##     POLID             -0.149      0.154     -0.968      0.333
## 
##  AWARE    WITH
##     MANAGE             0.630      0.074      8.548      0.000
## 
##  Means
##     LDRDIVAD           0.000      0.082      0.000      1.000
##     PDB                0.000      0.065      0.000      1.000
##     POLID             -0.688      0.125     -5.493      0.000
## 
##  Intercepts
##     AWARE              3.587      0.069     51.772      0.000
##     MANAGE             3.294      0.072     45.658      0.000
##     ORGALLY            1.071      0.260      4.125      0.000
## 
##  Variances
##     LDRDIVAD           1.503      0.142     10.583      0.000
##     PDB                0.947      0.089     10.583      0.000
##     POLID              3.510      0.332     10.583      0.000
## 
##  Residual Variances
##     AWARE              0.869      0.082     10.583      0.000
##     MANAGE             0.942      0.089     10.583      0.000
##     ORGALLY            0.899      0.085     10.583      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.138E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
## PLOT INFORMATION
## 
## The following plots are available:
## 
##   Loop plots
## 
##      Beginning Time:  11:42:55
##         Ending Time:  11:42:56
##        Elapsed Time:  00:00:01
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2024 Muthen & Muthen

Hypothesis 5a: Moderated Mediation (Bias-Awareness Efficacy and Organizational Ally Work)

res <- readModels("Mplus Syntax/Study1_Moderated Mediation (OrgAlly).out")

# Extract coefficients
a_int <- res$parameters$unstandardized$est[3]  # Effect of XW on M (a-path)
b_est <- res$parameters$unstandardized$est[10]  # Effect of M on Y (b-path)

# Extract standard errors
a_int_se <- res$parameters$unstandardized$se[3]
b_se <- res$parameters$unstandardized$se[10]

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_int, mu.y = b_est, se.x = a_int_se, se.y = b_se,
               rho = 0, alpha = .10, sims = 10000, method = "parametric")
## 
## --- Index of Moderated Mediation ---
## Estimate: 0.014938
## Standard error: 0.019507
## Monte Carlo 90% CI: [ -0.01479185 , 0.04886504 ]

Hypothesis 5b: Moderated Mediation (Intergroup-Management Efficacy and Organizational Ally Work)

# Extract coefficients
a_int <- res$parameters$unstandardized$est[6]  # Effect of XW on M (a-path)
b_est <- res$parameters$unstandardized$est[11]  # Effect of M on Y (b-path)

# Extract standard errors
a_int_se <- res$parameters$unstandardized$se[6]
b_se <- res$parameters$unstandardized$se[11]

# Compute Monte Carlo confidence interval
mc_ci <- medci(mu.x = a_int, mu.y = b_est, se.x = a_int_se, se.y = b_se,
               rho = 0, alpha = .01, sims = 10000, method = "parametric")
## 
## --- Index of Moderated Mediation ---
## Estimate: 0.07697
## Standard error: 0.02913344
## Monte Carlo 99% CI: [ 0.01663242 , 0.1660568 ]
# Conditional Indirect Effect for High and Low Pro-Diversity Attitudes
# Set moderator values (e.g., ±1 SD)
PDB_low <- -0.98  # 1 SD below mean
PDB_high <- 0.98  # 1 SD above mean

# Extract coefficient and standard error for leader diversity advocacy
a_main <- res$parameters$unstandardized$est[5]  # Effect of X on M (a-path)         
a_main_se <- res$parameters$unstandardized$se[5]

# Compute conditional a-paths
a_low  <- a_main + a_int * PDB_low
a_high <- a_main + a_int * PDB_high

# Compute SEs of conditional a-paths
a_low_se  <- sqrt(a_main_se^2 + (PDB_low^2 * a_int_se^2))
a_high_se <- sqrt(a_main_se^2 + (PDB_high^2 * a_int_se^2))

# Compute Monte Carlo CI for indirect effect at low PDB
mc_ci_low <- medci(mu.x = a_low, mu.y = b_est,
                   se.x = a_low_se, se.y = b_se,
                   rho = 0, alpha = 0.10, sims = 10000, method = "parametric")

# Compute Monte Carlo CI for indirect effect at high PDB
mc_ci_high <- medci(mu.x = a_high, mu.y = b_est,
                    se.x = a_high_se, se.y = b_se,
                    rho = 0, alpha = 0.01, sims = 10000, method = "parametric")
## 
## --- Conditional Indirect Effects ---
## At LOW PDB (-1 SD):
## Indirect effect estimate: 0.05345
## Standard error (LOW PDB): 0.03357
## Monte Carlo 90% CI: [ 0.004 , 0.113 ]
## At HIGH PDB (+1 SD):
## Indirect effect estimate: 0.204
## Standard error (HIGH PDB): 0.05987
## Monte Carlo 99% CI: [ 0.067 , 0.377 ]

View Johnson-Neyman Plots for Conditional Indirect Effects

Figure 3: Conditional Indirect Effect on Organizational Ally Work via Intergroup-Management Self-Efficacy

Supplementary Analysis: Cross-Over (non-hypothesized) Efficacy

Intergroup-Management Efficacy and Relational Ally Work

med_out <- readLines("Mplus Syntax/Study1_Intergroup.Management.Efficacy_RelAlly.out")
cat(paste(med_out, collapse = "\n"))
## Mplus VERSION 8.11 (Mac)
## MUTHEN & MUTHEN
## 09/04/2025   2:19 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Study 1
##   DATA: FILE = "Study1.dat";
##   VARIABLE:
##     NAMES = Male White Ideology LdrDivAd PDB Aware Regulate Manage OrgAlly RelAlly;
##   MISSING = ALL (999);
## 
##   USEVARIABLES LdrDivAd PDB Aware Manage RelAlly
##           PolID;
## 
##   DEFINE:
##   ! Political Ideology centered at the scale midpoint (= 4)
##   PolID = Ideology - 4;
## 
##   ! Grand-mean center Leader Diversity Advocacy and Pro-Diversity Attitudes
##   CENTER LdrDivAd PDB (GRANDMEAN);
## 
##   ANALYSIS:
##     ESTIMATOR = ML;
## 
##   MODEL:
##     Aware    ON PDB LdrDivAd;
##     Manage ON PDB LdrDivAd;
## 
##     RelAlly  ON PolID PDB LdrDivAd Aware Manage;
## 
## 
##     ! Covariances among predictors
##     PDB WITH LdrDivAd PolID;
##     LdrDivAd WITH PolID;
##     Aware WITH Manage;
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Study 1
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                         224
## 
## Number of dependent variables                                    3
## Number of independent variables                                  3
## Number of continuous latent variables                            0
## 
## Observed dependent variables
## 
##   Continuous
##    AWARE       MANAGE      RELALLY
## 
## Observed independent variables
##    LDRDIVAD    PDB         POLID
## 
## Variables with special functions
## 
##   Centering (GRANDMEAN)
##    LDRDIVAD    PDB
## 
## 
## Estimator                                                       ML
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Study1.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns             1
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               AWARE         MANAGE        RELALLY       LDRDIVAD      PDB
##               ________      ________      ________      ________      ________
##  AWARE          1.000
##  MANAGE         1.000         1.000
##  RELALLY        1.000         1.000         1.000
##  LDRDIVAD       1.000         1.000         1.000         1.000
##  PDB            1.000         1.000         1.000         1.000         1.000
##  POLID          1.000         1.000         1.000         1.000         1.000
## 
## 
##            Covariance Coverage
##               POLID
##               ________
##  POLID          1.000
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      AWARE                 3.690      -0.610       1.000    1.79%       2.667      3.667      4.000
##              224.000       1.164      -0.498       5.000   20.09%       4.000      4.667
##      MANAGE                3.409      -0.422       1.000    4.02%       2.200      3.200      3.600
##              224.000       1.439      -0.893       5.000   13.84%       4.000      4.600
##      RELALLY               3.548      -0.668       1.250    3.12%       2.875      3.375      3.750
##              224.000       0.890      -0.233       5.000    0.45%       3.875      4.500
##      LDRDIVAD              0.000      -0.436      -2.269   12.05%      -1.019     -0.269     -0.019
##              224.000       1.503      -0.730       1.731   12.05%       0.481      0.981
##      PDB                   0.000      -1.748      -3.318    1.34%      -0.568      0.182      0.432
##              224.000       0.947       2.453       0.682   45.98%       0.682      0.682
##      POLID                -0.688       0.488      -3.000   19.20%      -2.000     -2.000     -1.000
##              224.000       3.509      -0.878       3.000    8.04%       0.000      1.000
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       25
## 
## Loglikelihood
## 
##           H0 Value                       -1845.223
##           H1 Value                       -1844.359
## 
## Information Criteria
## 
##           Akaike (AIC)                    3740.446
##           Bayesian (BIC)                  3825.737
##           Sample-Size Adjusted BIC        3746.508
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                              1.728
##           Degrees of Freedom                     2
##           P-Value                           0.4214
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.000
##           90 Percent C.I.                    0.000  0.127
##           Probability RMSEA <= .05           0.596
## 
## CFI/TLI
## 
##           CFI                                1.000
##           TLI                                1.000
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                            458.376
##           Degrees of Freedom                    12
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.016
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  AWARE    ON
##     PDB                0.335      0.073      4.559      0.000
##     LDRDIVAD           0.212      0.058      3.635      0.000
## 
##  MANAGE   ON
##     PDB                0.281      0.077      3.661      0.000
##     LDRDIVAD           0.404      0.061      6.623      0.000
## 
##  RELALLY  ON
##     POLID             -0.007      0.027     -0.265      0.791
##     PDB                0.354      0.060      5.915      0.000
##     LDRDIVAD           0.193      0.045      4.296      0.000
##     AWARE              0.135      0.065      2.061      0.039
##     MANAGE             0.110      0.063      1.757      0.079
## 
##  PDB      WITH
##     LDRDIVAD           0.536      0.087      6.131      0.000
##     POLID             -0.870      0.135     -6.444      0.000
## 
##  LDRDIVAD WITH
##     POLID             -0.149      0.154     -0.968      0.333
## 
##  AWARE    WITH
##     MANAGE             0.680      0.078      8.679      0.000
## 
##  Means
##     LDRDIVAD           0.000      0.082      0.000      1.000
##     PDB                0.000      0.065      0.000      1.000
##     POLID             -0.688      0.125     -5.493      0.000
## 
##  Intercepts
##     AWARE              3.690      0.064     57.767      0.000
##     MANAGE             3.409      0.067     51.076      0.000
##     RELALLY            2.671      0.180     14.853      0.000
## 
##  Variances
##     LDRDIVAD           1.503      0.142     10.583      0.000
##     PDB                0.947      0.089     10.583      0.000
##     POLID              3.510      0.332     10.583      0.000
## 
##  Residual Variances
##     AWARE              0.914      0.086     10.583      0.000
##     MANAGE             0.998      0.094     10.583      0.000
##     RELALLY            0.431      0.041     10.583      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.130E-02
##        (ratio of smallest to largest eigenvalue)
## 
## 
##      Beginning Time:  14:19:52
##         Ending Time:  14:19:52
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2024 Muthen & Muthen

Self-Regulation Efficacy and Organizational Ally Work

med_out <- readLines("Mplus Syntax/Study1_Self.Regulation.Efficacy_OrgAlly.out")
cat(paste(med_out, collapse = "\n"))
## Mplus VERSION 8.11 (Mac)
## MUTHEN & MUTHEN
## 09/04/2025   2:17 PM
## 
## INPUT INSTRUCTIONS
## 
##   TITLE: Study 1
##   DATA: FILE = "Study1.dat";
##   VARIABLE:
##     NAMES = Male White Ideology LdrDivAd PDB Aware Regulate Manage OrgAlly RelAlly;
##   MISSING = ALL (999);
## 
##   USEVARIABLES LdrDivAd PDB Aware Regulate OrgAlly
##           PolID;
## 
##   DEFINE:
##   ! Political Ideology centered at the scale midpoint (= 4)
##   PolID = Ideology - 4;
## 
##   ! Grand-mean center Leader Diversity Advocacy and Pro-Diversity Attitudes
##   CENTER LdrDivAd PDB (GRANDMEAN);
## 
##   ANALYSIS:
##     ESTIMATOR = ML;
## 
##   MODEL:
##     Aware    ON PDB LdrDivAd;
##     Regulate ON PDB LdrDivAd;
## 
##     OrgAlly  ON PolID PDB LdrDivAd Aware Regulate;
## 
## 
##     ! Covariances among predictors
##     PDB WITH LdrDivAd PolID;
##     LdrDivAd WITH PolID;
##     Aware WITH Regulate;
## 
## 
## 
## INPUT READING TERMINATED NORMALLY
## 
## 
## 
## Study 1
## 
## SUMMARY OF ANALYSIS
## 
## Number of groups                                                 1
## Number of observations                                         224
## 
## Number of dependent variables                                    3
## Number of independent variables                                  3
## Number of continuous latent variables                            0
## 
## Observed dependent variables
## 
##   Continuous
##    AWARE       REGULATE    ORGALLY
## 
## Observed independent variables
##    LDRDIVAD    PDB         POLID
## 
## Variables with special functions
## 
##   Centering (GRANDMEAN)
##    LDRDIVAD    PDB
## 
## 
## Estimator                                                       ML
## Information matrix                                        OBSERVED
## Maximum number of iterations                                  1000
## Convergence criterion                                    0.500D-04
## Maximum number of steepest descent iterations                   20
## Maximum number of iterations for H1                           2000
## Convergence criterion for H1                             0.100D-03
## 
## Input data file(s)
##   Study1.dat
## 
## Input data format  FREE
## 
## 
## SUMMARY OF DATA
## 
##      Number of missing data patterns             1
## 
## 
## COVARIANCE COVERAGE OF DATA
## 
## Minimum covariance coverage value   0.100
## 
## 
##      PROPORTION OF DATA PRESENT
## 
## 
##            Covariance Coverage
##               AWARE         REGULATE      ORGALLY       LDRDIVAD      PDB
##               ________      ________      ________      ________      ________
##  AWARE          1.000
##  REGULATE       1.000         1.000
##  ORGALLY        1.000         1.000         1.000
##  LDRDIVAD       1.000         1.000         1.000         1.000
##  PDB            1.000         1.000         1.000         1.000         1.000
##  POLID          1.000         1.000         1.000         1.000         1.000
## 
## 
##            Covariance Coverage
##               POLID
##               ________
##  POLID          1.000
## 
## 
## 
## UNIVARIATE SAMPLE STATISTICS
## 
## 
##      UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
## 
##          Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
##         Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median
## 
##      AWARE                 3.690      -0.610       1.000    1.79%       2.667      3.667      4.000
##              224.000       1.164      -0.498       5.000   20.09%       4.000      4.667
##      REGULATE              4.278      -1.277       1.400    0.45%       3.800      4.200      4.400
##              224.000       0.591       1.382       5.000   29.91%       4.600      5.000
##      ORGALLY               2.558       0.306       1.000   21.43%       1.000      2.000      2.556
##              224.000       1.627      -1.041       5.000    6.70%       3.000      3.778
##      LDRDIVAD              0.000      -0.436      -2.269   12.05%      -1.019     -0.269     -0.019
##              224.000       1.503      -0.730       1.731   12.05%       0.481      0.981
##      PDB                   0.000      -1.748      -3.318    1.34%      -0.568      0.182      0.432
##              224.000       0.947       2.453       0.682   45.98%       0.682      0.682
##      POLID                -0.688       0.488      -3.000   19.20%      -2.000     -2.000     -1.000
##              224.000       3.509      -0.878       3.000    8.04%       0.000      1.000
## 
## 
## THE MODEL ESTIMATION TERMINATED NORMALLY
## 
## 
## 
## MODEL FIT INFORMATION
## 
## Number of Free Parameters                       25
## 
## Loglikelihood
## 
##           H0 Value                       -1903.837
##           H1 Value                       -1902.772
## 
## Information Criteria
## 
##           Akaike (AIC)                    3857.673
##           Bayesian (BIC)                  3942.965
##           Sample-Size Adjusted BIC        3863.736
##             (n* = (n + 2) / 24)
## 
## Chi-Square Test of Model Fit
## 
##           Value                              2.129
##           Degrees of Freedom                     2
##           P-Value                           0.3450
## 
## RMSEA (Root Mean Square Error Of Approximation)
## 
##           Estimate                           0.017
##           90 Percent C.I.                    0.000  0.135
##           Probability RMSEA <= .05           0.525
## 
## CFI/TLI
## 
##           CFI                                1.000
##           TLI                                0.997
## 
## Chi-Square Test of Model Fit for the Baseline Model
## 
##           Value                            277.388
##           Degrees of Freedom                    12
##           P-Value                           0.0000
## 
## SRMR (Standardized Root Mean Square Residual)
## 
##           Value                              0.014
## 
## 
## 
## MODEL RESULTS
## 
##                                                     Two-Tailed
##                     Estimate       S.E.  Est./S.E.    P-Value
## 
##  AWARE    ON
##     PDB                0.335      0.073      4.559      0.000
##     LDRDIVAD           0.212      0.058      3.636      0.000
## 
##  REGULATE ON
##     PDB                0.240      0.054      4.435      0.000
##     LDRDIVAD           0.099      0.043      2.300      0.021
## 
##  ORGALLY  ON
##     POLID              0.026      0.040      0.637      0.524
##     PDB                0.202      0.090      2.250      0.024
##     LDRDIVAD           0.410      0.062      6.558      0.000
##     AWARE              0.414      0.078      5.292      0.000
##     REGULATE          -0.198      0.106     -1.872      0.061
## 
##  PDB      WITH
##     LDRDIVAD           0.536      0.087      6.131      0.000
##     POLID             -0.869      0.135     -6.444      0.000
## 
##  LDRDIVAD WITH
##     POLID             -0.149      0.154     -0.968      0.333
## 
##  AWARE    WITH
##     REGULATE           0.329      0.050      6.561      0.000
## 
##  Means
##     LDRDIVAD           0.000      0.082      0.000      1.000
##     PDB                0.000      0.065      0.000      1.000
##     POLID             -0.688      0.125     -5.493      0.000
## 
##  Intercepts
##     AWARE              3.690      0.064     57.767      0.000
##     REGULATE           4.278      0.047     90.881      0.000
##     ORGALLY            1.894      0.406      4.662      0.000
## 
##  Variances
##     LDRDIVAD           1.503      0.142     10.583      0.000
##     PDB                0.947      0.089     10.583      0.000
##     POLID              3.510      0.332     10.583      0.000
## 
##  Residual Variances
##     AWARE              0.914      0.086     10.583      0.000
##     REGULATE           0.496      0.047     10.583      0.000
##     ORGALLY            0.947      0.090     10.583      0.000
## 
## 
## QUALITY OF NUMERICAL RESULTS
## 
##      Condition Number for the Information Matrix              0.703E-03
##        (ratio of smallest to largest eigenvalue)
## 
## 
##      Beginning Time:  14:17:47
##         Ending Time:  14:17:47
##        Elapsed Time:  00:00:00
## 
## 
## 
## MUTHEN & MUTHEN
## 3463 Stoner Ave.
## Los Angeles, CA  90066
## 
## Tel: (310) 391-9971
## Fax: (310) 391-8971
## Web: www.StatModel.com
## Support: Support@StatModel.com
## 
## Copyright (c) 1998-2024 Muthen & Muthen

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