Ofek - vigilantism survey

Data preparation

  • Item Q6_4 was reversed.

  • Item Q12_3 was reversed.

  • Following the recommendations of … we removed subjects who hurried through the questionnaire, completing it in less than a third of the average completion time of the entire sample (that is, less than 53 seconds).

  • We remain with \(N = 468\) observations.

Survey data

Confirmatory Factor Analysis (CFA)

  • First, we assessed the reliability of the measurement model for the latent variables using confirmatory factor analysis.

  • The table below details the reliability measures for the latent variables.

  • pj, trust, and efficacy show good \(\alpha\) values.

  • vig is acceptable, just over the common threshold of 0.75.

measure pj trust eff vig
alpha 0.9445 0.9277 0.8562 0.7734
omega 0.9446 0.9276 0.8559 0.7898
omega2 0.9446 0.9276 0.8559 0.7898
omega3 0.9446 0.9275 0.8555 0.7908
avevar 0.7089 0.8103 0.6645 0.5656

Measurement invariance

  • Measurement invariance of past victims and non-victims was assessed by fitting a multigroup SEM model.

  • There were 303 non-victims and 121 victims.

  • The model fitted the data well, CFI = .967, TLI = .956, RMSEA = .059.

  • All item loadings were significant in both groups.

  • We conclude that measurement invariance holds; the grouping variable will be treated as a manifest variable (directly observed, without error).

  • Surprisingly in both groups, higher police efficacy was associated with MORE self-vigilantism.

  • The output below details all the estimates for this model.

0 1
Estimate Std. Err. z p Estimate Std. Err. z p
Factor Loadings
pj
q5.1 1.00+ 1.00+
q5.2 0.94 0.04 25.48 .000 1.01 0.09 11.34 .000
q5.3 0.98 0.04 24.23 .000 1.03 0.11 9.78 .000
q5.4 0.98 0.05 21.37 .000 1.06 0.10 10.98 .000
q5.5 0.91 0.04 21.65 .000 1.04 0.10 10.02 .000
q5.6 1.00 0.03 29.85 .000 1.03 0.09 11.17 .000
q5.7 0.95 0.04 25.47 .000 1.12 0.10 11.49 .000
dj
q8.1 1.00+ 1.00+
trust
q7.1 1.00+ 1.00+
q7.2 1.00 0.03 30.45 .000 1.01 0.06 16.26 .000
q7.3 0.98 0.04 22.63 .000 1.02 0.05 18.94 .000
eff
q6.1 1.00+ 1.00+
q6.2 1.06 0.06 18.15 .000 1.01 0.09 10.84 .000
q6.3 1.07 0.06 17.77 .000 0.89 0.10 9.15 .000
vig
q9.1 1.00+ 1.00+
q9.2 1.32 0.11 11.72 .000 1.52 0.49 3.12 .002
q9.3 0.85 0.10 8.53 .000 0.79 0.14 5.54 .000
Regression Slopes
vig
pj -0.32 0.14 -2.33 .020 -0.32 0.14 -2.33 .020
dj 0.01 0.08 0.17 .868 0.01 0.08 0.17 .868
trust -0.22 0.12 -1.88 .060 -0.22 0.12 -1.88 .060
eff 0.52 0.18 2.89 .004 0.52 0.18 2.89 .004
Intercepts
q5.1 2.24 0.06 36.73 .000 2.02 0.10 19.72 .000
q5.2 2.37 0.06 41.84 .000 1.94 0.09 21.77 .000
q5.3 2.48 0.06 43.27 .000 2.13 0.09 23.53 .000
q5.4 2.84 0.06 47.38 .000 2.58 0.10 26.65 .000
q5.5 2.43 0.06 42.27 .000 2.07 0.10 20.87 .000
q5.6 2.34 0.06 40.19 .000 2.06 0.10 21.41 .000
q5.7 2.40 0.06 43.32 .000 2.13 0.09 22.65 .000
q8.1 2.54 0.06 46.00 .000 2.19 0.10 22.28 .000
q7.1 2.72 0.06 44.69 .000 2.28 0.09 23.98 .000
q7.2 2.75 0.06 44.60 .000 2.40 0.10 23.49 .000
q7.3 2.61 0.06 42.22 .000 2.19 0.10 23.05 .000
q6.1 2.45 0.06 44.38 .000 2.06 0.10 21.41 .000
q6.2 2.40 0.06 41.18 .000 2.23 0.10 22.47 .000
q6.3 2.55 0.06 44.04 .000 2.25 0.09 23.84 .000
q9.1 2.24 0.07 33.09 .000 2.25 0.11 20.83 .000
q9.2 1.98 0.06 31.16 .000 2.02 0.10 20.10 .000
q9.3 1.62 0.06 29.48 .000 1.67 0.09 18.53 .000
Residual Variances
q5.1 0.38 0.04 10.39 .000 0.59 0.12 5.08 .000
q5.2 0.31 0.04 7.34 .000 0.27 0.06 4.80 .000
q5.3 0.28 0.03 8.41 .000 0.27 0.04 6.23 .000
q5.4 0.37 0.04 9.61 .000 0.38 0.06 6.77 .000
q5.5 0.39 0.04 9.65 .000 0.48 0.09 5.11 .000
q5.6 0.27 0.03 8.83 .000 0.41 0.07 6.26 .000
q5.7 0.24 0.03 8.89 .000 0.21 0.04 5.22 .000
q8.1 0.00+ 0.00+
q7.1 0.20 0.04 4.64 .000 0.20 0.04 4.80 .000
q7.2 0.23 0.04 6.30 .000 0.37 0.12 3.03 .002
q7.3 0.29 0.05 5.49 .000 0.17 0.04 3.85 .000
q6.1 0.35 0.04 9.91 .000 0.35 0.10 3.57 .000
q6.2 0.39 0.05 8.44 .000 0.39 0.12 3.16 .002
q6.3 0.37 0.05 7.39 .000 0.46 0.09 5.35 .000
q9.1 0.89 0.11 8.21 .000 0.93 0.21 4.42 .000
q9.2 0.21 0.09 2.43 .015 0.11 0.29 0.37 .711
q9.3 0.54 0.07 7.52 .000 0.72 0.14 5.08 .000
Latent Intercepts
pj 0.00+ 0.00+
dj 0.00+ 0.00+
trust 0.00+ 0.00+
eff 0.00+ 0.00+
vig 0.00+ 0.00+
Latent Variances
pj 0.87 0.07 11.74 .000 0.71 0.14 5.03 .000
dj 1.02 0.07 15.02 .000 1.22 0.13 9.53 .000
trust 1.04 0.08 12.65 .000 0.94 0.11 8.61 .000
eff 0.66 0.07 9.41 .000 0.84 0.13 6.57 .000
vig 0.61 0.10 6.14 .000 0.45 0.24 1.87 .061
Latent Covariances
pj w/dj 0.79 0.06 12.14 .000 0.67 0.11 6.31 .000
pj w/trust 0.80 0.06 12.34 .000 0.68 0.10 7.10 .000
pj w/eff 0.68 0.06 10.92 .000 0.68 0.10 6.52 .000
dj w/trust 0.87 0.07 12.89 .000 0.87 0.11 8.16 .000
dj w/eff 0.69 0.06 10.97 .000 0.79 0.12 6.81 .000
trust w/eff 0.67 0.06 10.44 .000 0.77 0.10 7.33 .000
Fit Indices
χ2 454.45
CFI 0.96
TLI 0.96
RMSEA 0.07
Scaled χ2 376.35(224) .000
+Fixed parameter


SEM fitting

  • As the measurement invariance assumption is plausible, we proceed to fitting a SEM model to the entire dataset.
lavaan 0.6.15 ended normally after 66 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        44

                                                  Used       Total
  Number of observations                           461         538

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               283.767     224.155
  Degrees of freedom                               126         126
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  1.266
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              6678.620    4901.647
  Degrees of freedom                               153         153
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.363

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.976       0.979
  Tucker-Lewis Index (TLI)                       0.971       0.975
                                                                  
  Robust Comparative Fit Index (CFI)                         0.981
  Robust Tucker-Lewis Index (TLI)                            0.977

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8597.650   -8597.650
  Scaling correction factor                                  1.378
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -8455.767   -8455.767
  Scaling correction factor                                  1.295
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                               17283.301   17283.301
  Bayesian (BIC)                             17465.170   17465.170
  Sample-size adjusted Bayesian (SABIC)      17325.527   17325.527

Root Mean Square Error of Approximation:

  RMSEA                                          0.052       0.041
  90 Percent confidence interval - lower         0.044       0.033
  90 Percent confidence interval - upper         0.060       0.049
  P-value H_0: RMSEA <= 0.050                    0.323       0.972
  P-value H_0: RMSEA >= 0.080                    0.000       0.000
                                                                  
  Robust RMSEA                                               0.046
  90 Percent confidence interval - lower                     0.036
  90 Percent confidence interval - upper                     0.056
  P-value H_0: Robust RMSEA <= 0.050                         0.726
  P-value H_0: Robust RMSEA >= 0.080                         0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.047       0.047

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  pj =~                                               
    q5_1              1.000                           
    q5_2              0.974    0.036   27.073    0.000
    q5_3              1.001    0.041   24.562    0.000
    q5_4              1.002    0.043   23.269    0.000
    q5_5              0.951    0.040   23.527    0.000
    q5_6              1.014    0.035   29.385    0.000
    q5_7              0.996    0.037   27.075    0.000
  dj =~                                               
    q8_1              1.000                           
  trust =~                                            
    q7_1              1.000                           
    q7_2              0.996    0.029   34.655    0.000
    q7_3              0.985    0.034   28.973    0.000
  eff =~                                              
    q6_1              1.000                           
    q6_2              1.023    0.048   21.286    0.000
    q6_3              1.009    0.050   20.300    0.000
  vig =~                                              
    q9_1              1.000                           
    q9_2              1.342    0.104   12.924    0.000
    q9_3              0.837    0.082   10.163    0.000

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  vig ~                                               
    pj        (h2)   -0.306    0.147   -2.076    0.038
    dj        (h4)   -0.004    0.076   -0.049    0.961
    trust     (h1)   -0.207    0.107   -1.943    0.052
    eff       (h3)    0.501    0.178    2.817    0.005
    q1        (h5)    0.001    0.087    0.012    0.990

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  pj ~~                                               
    dj                0.772    0.056   13.726    0.000
    trust             0.788    0.054   14.587    0.000
    eff               0.700    0.053   13.103    0.000
  dj ~~                                               
    trust             0.899    0.057   15.762    0.000
    eff               0.742    0.056   13.318    0.000
  trust ~~                                            
    eff               0.730    0.055   13.277    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .q5_1              0.442    0.044   10.142    0.000
   .q5_2              0.302    0.035    8.689    0.000
   .q5_3              0.276    0.027   10.260    0.000
   .q5_4              0.372    0.032   11.804    0.000
   .q5_5              0.413    0.039   10.640    0.000
   .q5_6              0.307    0.029   10.746    0.000
   .q5_7              0.239    0.023   10.492    0.000
   .q8_1              0.000                           
   .q7_1              0.202    0.033    6.037    0.000
   .q7_2              0.266    0.042    6.286    0.000
   .q7_3              0.260    0.040    6.446    0.000
   .q6_1              0.356    0.038    9.331    0.000
   .q6_2              0.396    0.049    8.155    0.000
   .q6_3              0.391    0.044    8.981    0.000
   .q9_1              0.890    0.093    9.576    0.000
   .q9_2              0.207    0.078    2.652    0.008
   .q9_3              0.583    0.062    9.410    0.000
    pj                0.832    0.069   12.141    0.000
    dj                1.102    0.060   18.406    0.000
    trust             1.049    0.067   15.657    0.000
    eff               0.738    0.063   11.724    0.000
   .vig               0.582    0.085    6.866    0.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)
    TRUST            -0.207    0.107   -1.943    0.052
    PJ               -0.306    0.147   -2.076    0.038
    EFFICACY          0.501    0.178    2.817    0.005
    DJ               -0.004    0.076   -0.049    0.961
    Victim            0.001    0.087    0.012    0.990
Model
Estimate Std. Err. z p
Regression Slopes
vig
pj -0.17 0.10 -1.81 .071
dj 0.02 0.07 0.29 .770
trust -0.15 0.08 -2.04 .041
eff 0.26 0.07 3.55 .000
q1 0.00 0.10 0.04 .967
Residual Variances
vig 0.85 0.06 14.91 .000
pj 0.86+
dj 1.10+
trust 1.11+
eff 0.88+
q1 0.20+
Residual Covariances
pj w/dj 0.76+
pj w/trust 0.77+
pj w/eff 0.70+
pj w/q1 -0.06+
dj w/trust 0.89+
dj w/eff 0.75+
dj w/q1 -0.07+
trust w/eff 0.73+
trust w/q1 -0.08+
eff w/q1 -0.06+
Fit Indices
χ2 0.00(0)
CFI 1.00
TLI 1.00
RMSEA 0.00
+Fixed parameter


                 npar                  fmin                 chisq 
                6.000                 0.000                 0.000 
                   df                pvalue        baseline.chisq 
                0.000                    NA                15.419 
          baseline.df       baseline.pvalue                   cfi 
                5.000                 0.009                 1.000 
                  tli                  nnfi                   rfi 
                1.000                 1.000                 1.000 
                  nfi                  pnfi                   ifi 
                1.000                 0.000                 1.000 
                  rni                  logl     unrestricted.logl 
                1.000              -623.190              -623.190 
                  aic                   bic                ntotal 
             1258.381              1283.233               465.000 
                 bic2                 rmsea        rmsea.ci.lower 
             1264.190                 0.000                 0.000 
       rmsea.ci.upper        rmsea.ci.level          rmsea.pvalue 
                0.000                 0.900                    NA 
       rmsea.close.h0 rmsea.notclose.pvalue     rmsea.notclose.h0 
                0.050                    NA                 0.080 
                  rmr            rmr_nomean                  srmr 
                0.000                 0.000                 0.000 
         srmr_bentler   srmr_bentler_nomean                  crmr 
                0.000                 0.000                 0.000 
          crmr_nomean            srmr_mplus     srmr_mplus_nomean 
                0.000                 0.000                 0.000 
                cn_05                 cn_01                   gfi 
                   NA                    NA                 1.000 
                 agfi                  pgfi                   mfi 
                1.000                 0.000                 1.000 
                 ecvi 
                0.026 
Model
Estimate Std. Err. z p
Regression Slopes
vig
pj -0.31 0.15 -2.08 .038
dj -0.00 0.08 -0.05 .961
trust -0.21 0.11 -1.94 .052
eff 0.50 0.18 2.82 .005
q1 0.00 0.09 0.01 .990
Fit Indices
χ2 283.77
CFI 0.98
TLI 0.97
RMSEA 0.05
Scaled χ2 224.16(126) .000
+Fixed parameter


  [1]  2  2  4  2  4  4  4  3  4  4  4  2  3  3  4  3  3  1  2  4  3  4  2  1  2
 [26]  3  1  1  1  4  2  2  1  3  1  2  1  5  1  3  1  2  3  3  1  1  2  4  2  5
 [51]  3  3  1  3  3  4  3  4  3  4  3  4  1  4  3  1  4  2  2  4  1  4  4 NA  1
 [76]  3  1  2  2  3  3  1  4  4  3  1  4  4  4  3  3  3  3  3  3  3  1  2  3  2
[101]  4  1  4  4  4  3  2  1  4  5  3  4  4  5  3  2  1  4  3  4  3  4  3  4  4
[126]  1  4  4  2  2  4  4  2  3  5  1  2  2  4  4  1  4  2  2  4  1  5  2  1  1
[151]  2  1  3  3  3  1  2  2  2  2  1  1  3  4  4  2  3  4  1  2  1  4  4  4  1
[176]  4  3  4  3  1  3  1  5  4 NA  1  1  4  1  4  1  2  1  1  4  2  5  4  1  3
[201]  4  2  1  1  1  4  4  1  2  4  2  4  2  1  4  4  5  4  3  3  3  3  1  5  4
[226]  1  1  2  1  4  3  2  3  4  5  2  4  3  4  2  3  4  1  3  1  1  4  2  4  5
[251]  4  1  2  4  1  4  4  2  1  4  3  2  3  4  1  2  2  2  1  1  4  2  2  5  1
[276]  1  3  1  1  2  3  1  1  1  2  3  4  4  2  1  1  4  4  2  3  3  5  1  2  3
[301]  2  1  2  3  3  3  3  1  1  1  3  1  2  3  4  4  3  4  2  4  1  3  1  5  3
[326]  4  3  1  3  2 NA  4  2  5  3  2 NA  4  2  4  2  3  4  2  3  3  4  4  1  3
[351]  4  2  4  4  3  1  1  5  4  2  1  5  3  1  3  4  4  4  1  1  3  3  4  1  1
[376]  1  3  4  4  4  3  3  4  3  1  3  1  3  3  4  4  2  4  3  2  4  3  3  5  1
[401]  3  1 NA  3  1  4  4  5 NA  2  4  2 NA  1  1  2  3  1  1  3  3  5  4  1  3
[426]  3  2  4  4  3  2  3  3  4  3  4  1  3  4  1  4  1  1  1  4  2  1 NA  1  5
[451]  1  1  3  4  1  1  2  2  4  2  4  2  2  1  4  3  2  2  5  3  4  1  5 NA  3
[476]  2  2  3  1  3 NA NA NA NA NA NA  3  2  4  2  3 NA  2  2  4  1  2  4  4  3
[501]  3  2  2 NA NA  4 NA NA NA NA  4  4  4  4 NA  4 NA NA  4  3  3  4  4 NA NA
[526] NA NA NA  5 NA NA NA NA  3 NA NA  3 NA NA NA NA  3  2 NA  1  4  5 NA  4 NA
[551] NA

Extra models

lavaan 0.6.15 ended normally after 47 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        31

                                                  Used       Total
  Number of observations                           439         538

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               523.683     403.307
  Degrees of freedom                                74          74
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  1.298
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              4468.699    3164.864
  Degrees of freedom                                91          91
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.412

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.897       0.893
  Tucker-Lewis Index (TLI)                       0.874       0.868
                                                                  
  Robust Comparative Fit Index (CFI)                         0.901
  Robust Tucker-Lewis Index (TLI)                            0.879

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8096.075   -8096.075
  Scaling correction factor                                  1.261
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -7834.234   -7834.234
  Scaling correction factor                                  1.287
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                               16254.150   16254.150
  Bayesian (BIC)                             16380.769   16380.769
  Sample-size adjusted Bayesian (SABIC)      16282.391   16282.391

Root Mean Square Error of Approximation:

  RMSEA                                          0.118       0.101
  90 Percent confidence interval - lower         0.108       0.092
  90 Percent confidence interval - upper         0.127       0.109
  P-value H_0: RMSEA <= 0.050                    0.000       0.000
  P-value H_0: RMSEA >= 0.080                    1.000       1.000
                                                                  
  Robust RMSEA                                               0.115
  90 Percent confidence interval - lower                     0.104
  90 Percent confidence interval - upper                     0.126
  P-value H_0: Robust RMSEA <= 0.050                         0.000
  P-value H_0: Robust RMSEA >= 0.080                         1.000

Standardized Root Mean Square Residual:

  SRMR                                           0.062       0.062

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  pj =~                                               
    q11_1             1.000                           
    q11_2             1.034    0.065   15.904    0.000
    q11_3             1.284    0.077   16.624    0.000
    q11_4             1.287    0.077   16.720    0.000
    q11_5             1.209    0.080   15.086    0.000
    q11_6             1.425    0.091   15.685    0.000
    q11_7             1.447    0.092   15.750    0.000
  sa =~                                               
    q12_1             1.000                           
    q12_2             1.073    0.046   23.433    0.000
    q12_3             0.152    0.078    1.941    0.052
  vig =~                                              
    q15_1             1.000                           
    q15_2             1.043    0.064   16.248    0.000
    q15_3             0.979    0.081   12.104    0.000
    q15_4             1.365    0.091   14.937    0.000

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  vig ~                                               
    pj               -0.293    0.184   -1.590    0.112
    sa                0.175    0.159    1.098    0.272

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  pj ~~                                               
    sa                0.721    0.064   11.281    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .q11_1             0.874    0.076   11.523    0.000
   .q11_2             0.498    0.046   10.919    0.000
   .q11_3             0.391    0.051    7.715    0.000
   .q11_4             0.309    0.041    7.505    0.000
   .q11_5             0.475    0.050    9.533    0.000
   .q11_6             0.438    0.060    7.345    0.000
   .q11_7             0.482    0.060    7.993    0.000
   .q12_1             0.423    0.048    8.754    0.000
   .q12_2             0.337    0.071    4.752    0.000
   .q12_3             1.777    0.081   22.056    0.000
   .q15_1             0.735    0.077    9.524    0.000
   .q15_2             0.910    0.088   10.320    0.000
   .q15_3             0.658    0.076    8.685    0.000
   .q15_4             0.214    0.058    3.722    0.000
    pj                0.674    0.083    8.144    0.000
    sa                0.967    0.080   12.054    0.000
   .vig               0.770    0.098    7.884    0.000
          pj        sa
pj 1.0000000 0.6744761
sa 0.6744761 1.0000000