Ofek - vigilantism
Data preparation
Item
Q6_4was reversed.Item
Q12_3was 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
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
- The previous encounter with the police was treated as a manifest variable.
- Including it as a latent variable results in a non-positive-definite covariance matrix.
lavaan 0.6.15 ended normally after 69 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 49
Used Total
Number of observations 461 538
Model Test User Model:
Standard Scaled
Test Statistic 277.628 217.037
Degrees of freedom 122 122
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.279
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 6677.835 4874.889
Degrees of freedom 153 153
P-value 0.000 0.000
Scaling correction factor 1.370
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.976 0.980
Tucker-Lewis Index (TLI) 0.970 0.975
Robust Comparative Fit Index (CFI) 0.981
Robust Tucker-Lewis Index (TLI) 0.976
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9306.387 -9306.387
Scaling correction factor 1.398
for the MLR correction
Loglikelihood unrestricted model (H1) -9167.573 -9167.573
Scaling correction factor 1.313
for the MLR correction
Akaike (AIC) 18710.774 18710.774
Bayesian (BIC) 18913.310 18913.310
Sample-size adjusted Bayesian (SABIC) 18757.798 18757.798
Root Mean Square Error of Approximation:
RMSEA 0.053 0.041
90 Percent confidence interval - lower 0.044 0.033
90 Percent confidence interval - upper 0.061 0.049
P-value H_0: RMSEA <= 0.050 0.291 0.970
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 0.708
P-value H_0: Robust RMSEA >= 0.080 0.000
Standardized Root Mean Square Residual:
SRMR 0.027 0.027
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 0.973 0.036 26.900 0.000
q5_3 1.000 0.041 24.472 0.000
q5_4 1.002 0.043 23.297 0.000
q5_5 0.951 0.040 23.549 0.000
q5_6 1.014 0.034 29.420 0.000
q5_7 0.996 0.037 27.089 0.000
dj =~
q8_1 1.000
previous =~
int 1.000
trust =~
q7_1 1.000
q7_2 0.994 0.029 34.253 0.000
q7_3 0.984 0.034 28.778 0.000
eff =~
q6_1 1.000
q6_2 1.023 0.048 21.230 0.000
q6_3 1.009 0.050 20.287 0.000
vig =~
q9_1 1.000
q9_2 1.342 0.104 12.916 0.000
q9_3 0.837 0.082 10.157 0.000
Regressions:
Estimate Std.Err z-value P(>|z|)
vig ~
pj (h2) -0.300 0.148 -2.031 0.042
dj (h4) -0.002 0.076 -0.029 0.977
trust (h1) -0.211 0.107 -1.966 0.049
eff (h3) 0.499 0.178 2.803 0.005
previous -0.023 0.028 -0.820 0.412
Covariances:
Estimate Std.Err z-value P(>|z|)
pj ~~
dj 0.772 0.056 13.743 0.000
previous 0.093 0.054 1.736 0.082
trust 0.789 0.054 14.606 0.000
eff 0.700 0.053 13.120 0.000
dj ~~
previous 0.080 0.061 1.322 0.186
trust 0.899 0.057 15.776 0.000
eff 0.742 0.056 13.320 0.000
previous ~~
trust 0.049 0.059 0.829 0.407
eff 0.063 0.053 1.191 0.234
trust ~~
eff 0.731 0.055 13.290 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.q5_1 0.441 0.043 10.194 0.000
.q5_2 0.303 0.035 8.671 0.000
.q5_3 0.276 0.027 10.240 0.000
.q5_4 0.372 0.032 11.767 0.000
.q5_5 0.413 0.039 10.667 0.000
.q5_6 0.307 0.029 10.755 0.000
.q5_7 0.238 0.023 10.456 0.000
.q8_1 0.000
.int 0.000
.q7_1 0.200 0.033 5.988 0.000
.q7_2 0.268 0.043 6.225 0.000
.q7_3 0.260 0.040 6.453 0.000
.q6_1 0.356 0.038 9.319 0.000
.q6_2 0.396 0.049 8.137 0.000
.q6_3 0.391 0.044 8.957 0.000
.q9_1 0.890 0.093 9.578 0.000
.q9_2 0.207 0.078 2.640 0.008
.q9_3 0.583 0.062 9.381 0.000
pj 0.833 0.069 12.151 0.000
dj 1.102 0.060 18.406 0.000
previous 1.282 0.154 8.347 0.000
trust 1.051 0.067 15.654 0.000
eff 0.738 0.063 11.727 0.000
.vig 0.581 0.085 6.873 0.000
Defined Parameters:
Estimate Std.Err z-value P(>|z|)
TRUST -0.211 0.107 -1.966 0.049
PJ -0.300 0.148 -2.031 0.042
EFFICACY 0.499 0.178 2.803 0.005
DJ -0.002 0.076 -0.029 0.977Hypothesis testing:
PJ reduces vigilantism, p = .026.
Efficacy INCREASES vigilantism, p = .008.
DJ, victim, and previous exp are not associated with vigilantism.
Trust is significant (p = .035), and is negatively correlated with vigilantism.
| Model | ||||
| Estimate | Std. Err. | z | p | |
| Constructed | ||||
| TRUST | -0.21 | 0.11 | -1.97 | .049 |
| PJ | -0.30 | 0.15 | -2.03 | .042 |
| EFFICACY | 0.50 | 0.18 | 2.80 | .005 |
| DJ | -0.00 | 0.08 | -0.03 | .977 |
| Fit Indices | ||||
| χ2 | 277.63 | |||
| CFI | 0.98 | |||
| TLI | 0.97 | |||
| RMSEA | 0.05 | |||
| Scaled χ2 | 217.04(122) | .000 | ||
| +Fixed parameter | ||||
Plot of Structural model only:
Same plot, but with manifest variables:
Experiment data
We fitted a parsimonious model to the experimental data (see illustration below).
The data are assumed to come from a 2 * 2 between subject design.
- The control subjects are omitted in this analysis.
- If you have ideas how to model them, please let me know…
In this analysis we use \(N = 358\) observations.
CFA
- As seen by the following CFA output, the data support our measurement model for vigilantism before and after the experimental manipulation.
| measure | vig_post | vig_pre |
|---|---|---|
| alpha | 0.8491 | 0.7687 |
| omega | 0.8535 | 0.7875 |
| omega2 | 0.8535 | 0.7875 |
| omega3 | 0.8555 | 0.799 |
| avevar | 0.5956 | 0.5578 |
| Model | ||||
| Estimate | Std. Err. | z | p | |
| Factor Loadings | ||||
| vig_post | ||||
| q15.1 | 1.00+ | |||
| q15.2 | 1.05 | 0.07 | 15.56 | .000 |
| q15.3 | 0.94 | 0.09 | 9.95 | .000 |
| q15.4 | 1.24 | 0.10 | 12.76 | .000 |
| vig_pre | ||||
| q9.1 | 1.00+ | |||
| q9.2 | 1.26 | 0.10 | 12.42 | .000 |
| q9.3 | 0.90 | 0.10 | 8.90 | .000 |
| Residual Variances | ||||
| q15.1 | 0.68 | 0.09 | 7.73 | .000 |
| q15.2 | 0.86 | 0.10 | 8.68 | .000 |
| q15.3 | 0.68 | 0.10 | 7.12 | .000 |
| q15.4 | 0.38 | 0.09 | 4.17 | .000 |
| q9.1 | 0.85 | 0.10 | 8.32 | .000 |
| q9.2 | 0.28 | 0.09 | 3.23 | .001 |
| q9.3 | 0.58 | 0.07 | 8.28 | .000 |
| Latent Variances | ||||
| vig.post | 0.85 | 0.11 | 7.55 | .000 |
| vig.pre | 0.64 | 0.10 | 6.40 | .000 |
| Latent Covariances | ||||
| vig.post w/vig.pre | 0.35 | 0.07 | 5.23 | .000 |
| Fit Indices | ||||
| χ2 | 61.64 | |||
| CFI | 0.95 | |||
| TLI | 0.92 | |||
| RMSEA | 0.10 | |||
| Scaled χ2 | 56.24(13) | .000 | ||
| +Fixed parameter | ||||
SEM
- The model fit the data well (see fit measures below).
Hypothesis testing:
The high PJ treatment is associated with a significant (p = .024) reduction self-vigilantismץ
The high avaןlability condition is not statistically significant, (z = -.68, p = .494).
Vigilantism reported before the experiment is significantly positively associated with the vigilantism after p < .001.