IL LCR Manova
IL Political Extremism
Amir Freund
2025-08-23
wave_var <- "Wave"
wave_order <- c("First", "Second", "Third", "Fourth", "Fifth", "Sixth")
community_var <- "pe_left_center_right"
community_title <- "Political Orientation"
community_order <- c("left", "center", "right") # Set "center" as the reference level since it is the 'neutral' level.
dimension_vars <- c("Ideology" = "pe_ideology", "Violence" = "pe_violence","Intolerance" = "pe_intolerance")
demographic_vars <- c("gender", "age_group") # , "education"
respondent_id_var <- "respondent_id"
var_labels = c("event_occurred" = "Event Main Effect",
"pe_left_center_right" = "Political Orientation",
"gender" = "Gender",
"age_group" = "Age Group",
"event_occurred:pe_left_center_right" = "Event × Political Orientation"
)
event_var <- "event_occurred"
event_names = c("Inland Terror", "Bennet Gov. Fall", "Judicial Reform", "Gallant Dismissal", "Oct. 7th War")
# Read the data from indices_table.txt
df <- as.data.frame(readRDS("Israel Survey/data/il_pe.RDS"))
# Calculate the Political Extremism Gauge Indices
indices_result <- af_gauge_indices(df, pop_var1 = wave_var, comm_var1 = community_var)
df <- indices_result$df1 Pairwise Analysis
m1 <- af_manova_model(data = df, wave_pair = c("First", "Second"), is_panel = FALSE,
extremism_vars = dimension_vars, wave_var = wave_var,
group_var = community_var, control_vars = demographic_vars,
id_var = respondent_id_var, event_var = event_var)
m2 <- af_manova_model(data = df, wave_pair = c("Second", "Third"), is_panel = FALSE,
extremism_vars = dimension_vars, wave_var = wave_var,
group_var = community_var, control_vars = demographic_vars,
id_var = respondent_id_var, event_var = event_var)
m3 <- af_manova_model(data = df, wave_pair = c("Third", "Fourth"), is_panel = TRUE,
extremism_vars = dimension_vars, wave_var = wave_var,
group_var = community_var, control_vars = demographic_vars,
id_var = respondent_id_var, event_var = event_var)
m4 <- af_manova_model(data = df, wave_pair = c("Fourth", "Fifth"), is_panel = FALSE,
extremism_vars = dimension_vars, wave_var = wave_var,
group_var = community_var, control_vars = demographic_vars,
id_var = respondent_id_var, event_var = event_var)
m5 <- af_manova_model(data = df, wave_pair = c("Fifth", "Sixth"), is_panel = FALSE,
extremism_vars = dimension_vars, wave_var = wave_var,
group_var = community_var, control_vars = demographic_vars,
id_var = respondent_id_var, event_var = event_var)
r1 <- af_manova_results(m1, group_legend_title = community_title, plot_title = event_names[1])
r2 <- af_manova_results(m2, group_legend_title = community_title, plot_title = event_names[2])
r3 <- af_manova_results(m3, group_legend_title = community_title, plot_title = event_names[3])
r4 <- af_manova_results(m4, group_legend_title = community_title, plot_title = event_names[4])
r5 <- af_manova_results(m5, group_legend_title = community_title, plot_title = event_names[5])
model_results_list <- list(r1, r2, r3, r4, r5)
names(model_results_list) <- event_namesThe study examines how various types of destabilizing events differently affect people with different political affiliations (left-wing, center-wing, right-wing), thereby increasing or decreasing their level of political extremism dimensions.
The hypotheses we test are:
- H1: Various dimensions of political extremism do not respond uniformly to socio-political events.
- H2: The effect of different destabilizing events will be moderated by political orientation.
We use Multivariate Analysis of Variance (MANOVA) analysis on each consecutive pair of Political Extremism Survey waves. A destabilizing event occurred between the two waves of each pair. The target of the analysis is to determine whether the event influenced the three dimensions of political extremism and whether this effect was moderated by the political orientation of the survey respondents. The third and forth waves were panel survey waves. We thus analyze them using Repeated measures MANOVA.
The response variables are the three dimensions of political extremism: Cognitive (Ideology) dimension: pe_ideology, Behavioral (Violence) dimension: pe_violence, and Social (Intolerance) dimension: pe_intolerance. The events are flagged by the event_occurred variable, set to 0 for the first wave and 1 for the second wave. Political orientation is identified by the pe_left_center_right variable. Gender (gender) and age group (age_group) are control variables.
The MANOVA analysis tests whether the political orientation groups differ on the combination of the three political extremism dimensions (our three dependent variables) simultaneously. Instead of testing each extremism dimension separately, it asks: “Do the groups differ when we consider all three dimensions together?”
We selected MANOVA Pillai’s Trace (scale 0 to 1, higher values = stronger multivariate effect.) as the main the test statistic for the analysis since it is the most robust MANOVA test statistic to violations of assumptions (especially unequal covariance matrices) and since it is the most conservative (less likely to find false positives).
The detailed results section in the supplemntary appendix provides the results for all four Manova test statistics: Pillai Trace, Wilks’ Lambda, Hotelling-Lawley, and Roy’s Greatest Root.
1.1 Results
manova_table_c <- af_manova_summary_table(model_list = model_results_list,
variable_labels = var_labels,
panel_model_ids = c("Judicial Reform"),
show_intercept = FALSE,
test_statistics = c("Pillai"),
title = "MANOVA Results Across Destabilizing Events",
subtitle = "Multivariate Tests of Event Effects on Political Extremism Dimensions")
manova_table_c| MANOVA Results Across Destabilizing Events | |||||
| Multivariate Tests of Event Effects on Political Extremism Dimensions | |||||
| Variable | Inland Terror | Bennet Gov. Fall | Judicial Reform § | Gallant Dismissal | Oct. 7th War |
|---|---|---|---|---|---|
| Event Main Effect | 0.011*** | 0.003† | 0.002 | 0.002 | 0.001 |
| Political Orientation | 0.098*** | 0.175*** | 0.105*** | 0.080*** | 0.083*** |
| Gender | 0.035*** | 0.046*** | 0.063*** | 0.056*** | 0.045*** |
| Age Group | 0.031*** | 0.042*** | 0.067*** | 0.040*** | 0.030*** |
| Event × Political Orientation | 0.007*** | 0.006* | 0.006 | 0.004 | 0.005† |
| Test statistic: Pillai's Trace. *** p < .001; ** p < .01; * p < .05; † p < .10. § Panel analysis (same respondents across waves). Panel model columns highlighted in blue | |||||
1.2 Interpretation
The multivariate analysis of variance revealed differential patterns of political extremism responses across the five destabilizing events examined. For Inland Terror, the MANOVA demonstrated significant multivariate effects for the event occurrence (Pillai’s trace = 0.011, p < 0.001), political orientation (Pillai’s trace = 0.098, p < 0.001), and their interaction (Pillai’s trace = 0.007, p < 0.001), indicating that this security threat influenced the combination of extremism dimensions differently across political groups. The Bennett Government Fall showed a marginally significant main event effect (Pillai’s trace = 0.003, p = 0.051) but maintained significant political orientation effects (Pillai’s trace = 0.175, p < 0.001) and a significant interaction (Pillai’s trace = 0.006, p = 0.028), suggesting politically differentiated responses to this governmental transition. The Judicial Reform, occurring between panel waves with the same respondents, exhibited non-significant main event effects (Pillai’s trace = 0.002, p = 0.488) and interaction effects (Pillai’s trace = 0.006, p = 0.201), though political orientation remained highly significant (Pillai’s trace = 0.105, p < 0.001), indicating that this constitutional crisis may have had more subtle or delayed impacts on extremism dimensions. The Gallant Dismissal similarly showed non-significant event effects (Pillai’s trace = 0.002, p = 0.241) and interactions (Pillai’s trace = 0.004, p = 0.218), while maintaining strong political orientation effects (Pillai’s trace = 0.080, p < 0.001). Finally, the October 7th War displayed non-significant main event effects (Pillai’s trace = 0.001, p = 0.418) but a marginally significant interaction (Pillai’s trace = 0.005, p = 0.057), alongside robust political orientation effects (Pillai’s trace = 0.083, p < 0.001).
1.3 Discussion
The findings provide mixed support for our first two hypotheses regarding the differential nature of political extremism responses to destabilizing events. Hypothesis 1, positing that various dimensions of political extremism do not respond uniformly to socio-political events, receives partial support, as evidenced by the significant multivariate effects observed for Inland Terror and the marginally significant effects for Bennett Government Fall, indicating that at least some events produce differentiated responses across the ideology, violence, and intolerance dimensions. However, the non-significant main effects for Judicial Reform, Gallant Dismissal, and October 7th War suggest that not all destabilizing events generate uniform multivariate impacts on extremism dimensions. Hypothesis 2, predicting that political orientation moderates the effect of destabilizing events, receives stronger empirical support, with significant interaction effects observed for Inland Terror and Bennett Government Fall, and marginally significant interactions for October 7th War, demonstrating that citizens’ political affiliations systematically condition their extremism responses to external shocks.
These results advance our understanding of how various types of destabilizing events differentially affect citizens with different political affiliations, revealing that the relationship between external threats and political extremism is contingent upon both the nature of the destabilizing event and the political identity of the affected population.
1.4 Results Plot
plot_list <- list (r1$profile_plot, r2$profile_plot, r3$profile_plot, r4$profile_plot, r5$profile_plot)
title <- "Events Impact on Extremism Dimensions by Political Orientation"
subtitle <- "Pairwise multivariate ANOVA (MANOVA) analysis"
note <- "models 1,2,4,5 include cross-sectional survey waves, model 3 includes panel survey waves."
y_title <- "Mean Scores"
combined_plot <- af_combine_manova_plots(
plot_list = plot_list, main_title = title, subtitle = subtitle, note = note, y_axis_title = y_title)
print(combined_plot)
1.5 Robustness (For SI)
1.5.1 Inland Terror
rob1 <- af_test_manova_prerequisites(
data = df %>% filter(df$Wave %in% c("First", "Second")),
dependent_vars = c("pe_ideology", "pe_violence", "pe_intolerance"),
grouping_var = community_var
)
# Print overall summary
cat(rob1$overall_assessment$summary)The MANOVA prerequisites assessment examined 6 key assumptions across 3215 observations with 3 dependent variables and 3 groups. Multivariate normality was violated (Shapiro-Wilk W = 0.6664 , p = 0 ), This is a common finding with large datasets. However, because your sample size is large (n > 200), MANOVA is considered robust to this violation due to the Central Limit Theorem. Covariance matrix homogeneity was violated (Box’s M χ² = 296.14 , p = 0 ), which is adequately addressed by using Pillai’s trace as the test statistic. Linear relationships showed some concerns (correlations range: 0.026 to 0.239 ) that warrant careful interpretation of results. Multicollinearity levels were acceptable (correlation matrix determinant = 9.28e-01 ). Multivariate outliers were within acceptable limits (2.8% of cases exceed critical value). Sample size was adequate for robust analysis (minimum group size = 488 , recommended minimum total N = 19 ).
MANOVA analysis may proceed with appropriate caution regarding assumption violations. The use of robust test statistics like Pillai’s trace is recommended.
# # Print individual detailed reports
# cat(rob1$sample_size$detailed_report)
# cat(rob1$multivariate_normality$detailed_report)
# cat(rob1$covariance_homogeneity$detailed_report)
# cat(rob1$linearity$detailed_report)
# cat(rob1$multicollinearity$detailed_report)
# cat(rob1$outliers$detailed_report)1.5.2 Bennet Gov. Fall
rob2 <- af_test_manova_prerequisites(
data = df %>% filter(df$Wave %in% c("Second", "Third")),
dependent_vars = c("pe_ideology", "pe_violence", "pe_intolerance"),
grouping_var = community_var
)
# Print overall summary
cat(rob2$overall_assessment$summary)The MANOVA prerequisites assessment examined 6 key assumptions across 2493 observations with 3 dependent variables and 3 groups. Multivariate normality was violated (Shapiro-Wilk W = 0.8283 , p = 0 ), This is a common finding with large datasets. However, because your sample size is large (n > 200), MANOVA is considered robust to this violation due to the Central Limit Theorem. Covariance matrix homogeneity was violated (Box’s M χ² = 327.99 , p = 0 ), which is adequately addressed by using Pillai’s trace as the test statistic. Linear relationships showed some concerns (correlations range: 0.073 to 0.238 ) that warrant careful interpretation of results. Multicollinearity levels were acceptable (correlation matrix determinant = 9.24e-01 ). Multivariate outliers were within acceptable limits (2.4% of cases exceed critical value). Sample size was adequate for robust analysis (minimum group size = 351 , recommended minimum total N = 19 ).
MANOVA analysis may proceed with appropriate caution regarding assumption violations. The use of robust test statistics like Pillai’s trace is recommended.
# # Print individual detailed reports
# cat(rob2$sample_size$detailed_report)
# cat(rob2$multivariate_normality$detailed_report)
# cat(rob2$covariance_homogeneity$detailed_report)
# cat(rob2$linearity$detailed_report)
# cat(rob2$multicollinearity$detailed_report)
# cat(rob2$outliers$detailed_report)1.5.3 Judicial Reform
df3 <- df %>% filter(df$Wave %in% c("Third", "Fourth"))
# Find respondents who appear in both waves
wave1_ids <- df3 %>% filter(Wave=="Third") %>% pull(respondent_id)
wave2_ids <- df3 %>% filter(Wave=="Fourth") %>% pull(respondent_id)
common_ids <- intersect(wave1_ids, wave2_ids)
df3 <- df3 %>% filter(respondent_id %in% common_ids)
rob3 <- af_test_repeated_measures_manova_prerequisites(
data = df3,
dependent_vars = c("pe_ideology", "pe_violence", "pe_intolerance"),
wave_var = "Wave", grouping_var = community_var, subject_id_var = "respondent_id"
)
# Print overall summary
cat(rob3$overall_assessment$summary)The Repeated Measures MANOVA prerequisites assessment examined 3 key assumptions across 1342 observations from 671 subjects. The data structure is appropriate for a repeated measures design, confirming independence between subjects. Multivariate normality was violated in at least one group, though Repeated Measures MANOVA maintains robustness with an adequate number of subjects. Sphericity was not assessed as it requires three or more waves.
The Repeated Measures MANOVA analysis may proceed with appropriate caution regarding assumption violations. The use of corrections for sphericity is recommended if applicable.
# # Print individual detailed reports
# cat(rob3$sample_size$detailed_report)
# cat(rob3$multivariate_normality$detailed_report)
# cat(rob3$covariance_homogeneity$detailed_report)
# cat(rob3$linearity$detailed_report)
# cat(rob3$multicollinearity$detailed_report)
# cat(rob3$outliers$detailed_report)1.5.4 Gallant Dismissal
rob4 <- af_test_manova_prerequisites(
data = df %>% filter(df$Wave %in% c("Fourth", "Fifth")),
dependent_vars = c("pe_ideology", "pe_violence", "pe_intolerance"),
grouping_var = community_var
)
# Print overall summary
cat(rob4$overall_assessment$summary)The MANOVA prerequisites assessment examined 6 key assumptions across 2221 observations with 3 dependent variables and 3 groups. Multivariate normality was violated (Shapiro-Wilk W = 0.8409 , p = 0 ), This is a common finding with large datasets. However, because your sample size is large (n > 200), MANOVA is considered robust to this violation due to the Central Limit Theorem. Covariance matrix homogeneity was violated (Box’s M χ² = 120.94 , p = 0 ), which is adequately addressed by using Pillai’s trace as the test statistic. Linear relationships showed some concerns (correlations range: 0.081 to 0.135 ) that warrant careful interpretation of results. Multicollinearity levels were acceptable (correlation matrix determinant = 9.67e-01 ). Multivariate outliers were within acceptable limits (2.8% of cases exceed critical value). Sample size was adequate for robust analysis (minimum group size = 267 , recommended minimum total N = 19 ).
MANOVA analysis may proceed with appropriate caution regarding assumption violations. The use of robust test statistics like Pillai’s trace is recommended.
# # Print individual detailed reports
# cat(rob4$sample_size$detailed_report)
# cat(rob4$multivariate_normality$detailed_report)
# cat(rob4$covariance_homogeneity$detailed_report)
# cat(rob4$linearity$detailed_report)
# cat(rob4$multicollinearity$detailed_report)
# cat(rob4$outliers$detailed_report)1.5.5 Oct. 7th War
rob5 <- af_test_manova_prerequisites(
data = df %>% filter(df$Wave %in% c("Fifth", "Sixth")),
dependent_vars = c("pe_ideology", "pe_violence", "pe_intolerance"),
grouping_var = community_var
)
# Print overall summary
cat(rob5$overall_assessment$summary)The MANOVA prerequisites assessment examined 6 key assumptions across 2638 observations with 3 dependent variables and 3 groups. Multivariate normality was violated (Shapiro-Wilk W = 0.846 , p = 0 ), This is a common finding with large datasets. However, because your sample size is large (n > 200), MANOVA is considered robust to this violation due to the Central Limit Theorem. Covariance matrix homogeneity was violated (Box’s M χ² = 128.99 , p = 0 ), which is adequately addressed by using Pillai’s trace as the test statistic. Linear relationships showed some concerns (correlations range: 0.084 to 0.122 ) that warrant careful interpretation of results. Multicollinearity levels were acceptable (correlation matrix determinant = 9.71e-01 ). Multivariate outliers were within acceptable limits (2.5% of cases exceed critical value). Sample size was adequate for robust analysis (minimum group size = 302 , recommended minimum total N = 19 ).
MANOVA analysis may proceed with appropriate caution regarding assumption violations. The use of robust test statistics like Pillai’s trace is recommended.
# # Print individual detailed reports
# cat(rob5$sample_size$detailed_report)
# cat(rob5$multivariate_normality$detailed_report)
# cat(rob5$covariance_homogeneity$detailed_report)
# cat(rob5$linearity$detailed_report)
# cat(rob5$multicollinearity$detailed_report)
# cat(rob5$outliers$detailed_report)1.6 Detailed results (For SI)
1.6.1 Full Results table
manova_table_f <- af_manova_summary_table(model_list = model_results_list,
variable_labels = var_labels,
panel_model_ids = c("Judicial Reform"),
show_intercept = FALSE,
test_statistics = c("Pillai", "Wilks", "Hotelling", "Roy"),
title = "Full MANOVA Results Across Destabilizing Events",
subtitle = "Multivariate Tests of Event Effects on Political Extremism Dimensions")
manova_table_f| Full MANOVA Results Across Destabilizing Events | ||||||||||||||||||||
| Multivariate Tests of Event Effects on Political Extremism Dimensions | ||||||||||||||||||||
| Variable | Inland Terror | Bennet Gov. Fall | Judicial Reform § | Gallant Dismissal | Oct. 7th War | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pillai | Wilks | Hotelling | Roy | Pillai | Wilks | Hotelling | Roy | Pillai | Wilks | Hotelling | Roy | Pillai | Wilks | Hotelling | Roy | Pillai | Wilks | Hotelling | Roy | |
| Event Main Effect | 0.011*** | 0.989*** | 0.011*** | 0.011*** | 0.003† | 0.997† | 0.003† | 0.003† | 0.002 | 0.998 | 0.002 | 0.002 | 0.002 | 0.998 | 0.002 | 0.002 | 0.001 | 0.999 | 0.001 | 0.001 |
| Political Orientation | 0.098*** | 0.904*** | 0.105*** | 0.087*** | 0.175*** | 0.829*** | 0.202*** | 0.178*** | 0.105*** | 0.896*** | 0.115*** | 0.108*** | 0.080*** | 0.920*** | 0.086*** | 0.079*** | 0.083*** | 0.918*** | 0.089*** | 0.084*** |
| Gender | 0.035*** | 0.965*** | 0.037*** | 0.037*** | 0.046*** | 0.954*** | 0.048*** | 0.048*** | 0.063*** | 0.937*** | 0.067*** | 0.067*** | 0.056*** | 0.944*** | 0.059*** | 0.059*** | 0.045*** | 0.955*** | 0.047*** | 0.047*** |
| Age Group | 0.031*** | 0.969*** | 0.032*** | 0.029*** | 0.042*** | 0.958*** | 0.043*** | 0.033*** | 0.067*** | 0.934*** | 0.070*** | 0.051*** | 0.040*** | 0.961*** | 0.041*** | 0.033*** | 0.030*** | 0.970*** | 0.031*** | 0.028*** |
| Event × Political Orientation | 0.007*** | 0.993*** | 0.007*** | 0.007*** | 0.006* | 0.994* | 0.006* | 0.004* | 0.006 | 0.994 | 0.006 | 0.006* | 0.004 | 0.996 | 0.004 | 0.004* | 0.005† | 0.995† | 0.005† | 0.004* |
| Test statistics: Pillai's Trace, Wilks's Trace, Hotelling-Lawley's Trace, Roy's Trace. *** p < .001; ** p < .01; * p < .05; † p < .10. § Panel analysis (same respondents across waves). Panel model columns highlighted in blue | ||||||||||||||||||||
1.6.2 Inland Terror
Type III MANOVA Tests:
Sum of squares and products for error:
pe_ideology pe_violence pe_intolerance
pe_ideology 10981.3193 -696.3135 144.3300
pe_violence -696.3135 2907.8640 959.1213
pe_intolerance 144.3300 959.1213 6414.8861
------------------------------------------
Term: (Intercept)
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 7555.819 3314.650 7542.454
pe_violence 3314.650 1454.098 3308.787
pe_intolerance 7542.454 3308.787 7529.113
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.6853927 2325.983 3 3203 < 2.22e-16 ***
Wilks 1 0.3146073 2325.983 3 3203 < 2.22e-16 ***
Hotelling-Lawley 1 2.1785662 2325.983 3 3203 < 2.22e-16 ***
Roy 1 2.1785662 2325.983 3 3203 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 80.74783 -31.163465 -23.938914
pe_violence -31.16347 12.027093 9.238881
pe_intolerance -23.93891 9.238881 7.097053
Multivariate Tests: event_occurred
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0107042 11.5522 3 3203 1.572e-07 ***
Wilks 1 0.9892958 11.5522 3 3203 1.572e-07 ***
Hotelling-Lawley 1 0.0108200 11.5522 3 3203 1.572e-07 ***
Roy 1 0.0108200 11.5522 3 3203 1.572e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 252.83967 -18.909131 -139.8934
pe_violence -18.90913 5.361815 52.0852
pe_intolerance -139.89337 52.085200 516.2625
Multivariate Tests: pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0978791 54.95704 6 6408 < 2.22e-16 ***
Wilks 2 0.9035655 55.53018 6 6406 < 2.22e-16 ***
Hotelling-Lawley 2 0.1051279 56.10326 6 6404 < 2.22e-16 ***
Roy 2 0.0866842 92.57874 3 3204 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: gender
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 255.8700441 78.9899000 -0.759273691
pe_violence 78.9899000 24.3850519 -0.234396149
pe_intolerance -0.7592737 -0.2343961 0.002253083
Multivariate Tests: gender
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0352332 38.9911 3 3203 < 2.22e-16 ***
Wilks 1 0.9647668 38.9911 3 3203 < 2.22e-16 ***
Hotelling-Lawley 1 0.0365199 38.9911 3 3203 < 2.22e-16 ***
Roy 1 0.0365199 38.9911 3 3203 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: age_group
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 50.87196 -23.75719 37.14001
pe_violence -23.75719 28.39269 -47.78936
pe_intolerance 37.14001 -47.78936 81.48543
Multivariate Tests: age_group
Df test stat approx F num Df den Df Pr(>F)
Pillai 3 0.0314536 11.31967 9 9615.000 < 2.22e-16 ***
Wilks 3 0.9686313 11.41743 9 7795.411 < 2.22e-16 ***
Hotelling-Lawley 3 0.0322968 11.48930 9 9605.000 < 2.22e-16 ***
Roy 3 0.0293085 31.31124 3 3205.000 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred:pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 35.61209 -13.931134 -26.33292
pe_violence -13.93113 5.486435 10.00659
pe_intolerance -26.33292 10.006587 21.83676
Multivariate Tests: event_occurred:pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0073738 3.952186 6 6408 0.00059880 ***
Wilks 2 0.9926284 3.957075 6 6406 0.00059145 ***
Hotelling-Lawley 2 0.0074240 3.961959 6 6404 0.00058419 ***
Roy 2 0.0071046 7.587759 3 3204 4.6942e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
1.6.3 Bennet Gov. Fall
Type III MANOVA Tests:
Sum of squares and products for error:
pe_ideology pe_violence pe_intolerance
pe_ideology 6867.35866 -524.5048 20.87414
pe_violence -524.50482 2386.0624 741.03880
pe_intolerance 20.87414 741.0388 5125.00075
------------------------------------------
Term: (Intercept)
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 5158.019 2781.156 5852.324
pe_violence 2781.156 1499.573 3155.518
pe_intolerance 5852.324 3155.518 6640.086
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.7150793 2075.562 3 2481 < 2.22e-16 ***
Wilks 1 0.2849207 2075.562 3 2481 < 2.22e-16 ***
Hotelling-Lawley 1 2.5097480 2075.562 3 2481 < 2.22e-16 ***
Roy 1 2.5097480 2075.562 3 2481 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 2.390096 2.265898 5.270528
pe_violence 2.265898 2.148155 4.996654
pe_intolerance 5.270528 4.996654 11.622323
Multivariate Tests: event_occurred
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0031309 2.597418 3 2481 0.050748 .
Wilks 1 0.9968691 2.597418 3 2481 0.050748 .
Hotelling-Lawley 1 0.0031408 2.597418 3 2481 0.050748 .
Roy 1 0.0031408 2.597418 3 2481 0.050748 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 329.48267 -67.05813 -331.6678
pe_violence -67.05813 28.52099 149.6096
pe_intolerance -331.66784 149.60957 787.1407
Multivariate Tests: pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.1747714 79.21980 6 4964 < 2.22e-16 ***
Wilks 2 0.8287895 81.41308 6 4962 < 2.22e-16 ***
Hotelling-Lawley 2 0.2022823 83.61002 6 4960 < 2.22e-16 ***
Roy 2 0.1781666 147.40317 3 2482 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: gender
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 208.39212 68.23992 -31.521768
pe_violence 68.23992 22.34579 -10.322094
pe_intolerance -31.52177 -10.32209 4.768039
Multivariate Tests: gender
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0460056 39.88137 3 2481 < 2.22e-16 ***
Wilks 1 0.9539944 39.88137 3 2481 < 2.22e-16 ***
Hotelling-Lawley 1 0.0482241 39.88137 3 2481 < 2.22e-16 ***
Roy 1 0.0482241 39.88137 3 2481 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: age_group
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 95.63705 -25.12365 46.20348
pe_violence -25.12365 31.62212 -40.89030
pe_intolerance 46.20348 -40.89030 57.62548
Multivariate Tests: age_group
Df test stat approx F num Df den Df Pr(>F)
Pillai 3 0.0419780 11.74563 9 7449.000 < 2.22e-16 ***
Wilks 3 0.9583368 11.83472 9 6038.253 < 2.22e-16 ***
Hotelling-Lawley 3 0.0431460 11.88751 9 7439.000 < 2.22e-16 ***
Roy 3 0.0333643 27.61455 3 2483.000 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred:pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 18.6344266 -0.6357863 7.806405
pe_violence -0.6357863 0.7568399 2.692659
pe_intolerance 7.8064052 2.6926588 15.180429
Multivariate Tests: event_occurred:pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0057064 2.367308 6 4964 0.027592 *
Wilks 2 0.9943001 2.367041 6 4962 0.027609 *
Hotelling-Lawley 2 0.0057261 2.366772 6 4960 0.027625 *
Roy 2 0.0041530 3.435914 3 2482 0.016267 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
1.6.4 Judicial Reform
Type III MANOVA Tests:
Sum of squares and products for error:
pe_ideology pe_violence pe_intolerance
pe_ideology 3653.53584 -263.4479 -12.16402
pe_violence -263.44787 1132.1982 299.64894
pe_intolerance -12.16402 299.6489 2974.11061
------------------------------------------
Term: (Intercept)
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 2308.418 1200.5620 2650.462
pe_violence 1200.562 624.3884 1378.452
pe_intolerance 2650.462 1378.4524 3043.188
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.682026 950.9107 3 1330 < 2.22e-16 ***
Wilks 1 0.317974 950.9107 3 1330 < 2.22e-16 ***
Hotelling-Lawley 1 2.144911 950.9107 3 1330 < 2.22e-16 ***
Roy 1 2.144911 950.9107 3 1330 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 0.01397858 -0.1694271 -0.04529566
pe_violence -0.16942711 2.0535379 0.54900512
pe_intolerance -0.04529566 0.5490051 0.14677432
Multivariate Tests: event_occurred
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0018233 0.8098173 3 1330 0.48842
Wilks 1 0.9981767 0.8098173 3 1330 0.48842
Hotelling-Lawley 1 0.0018267 0.8098173 3 1330 0.48842
Roy 1 0.0018267 0.8098173 3 1330 0.48842
------------------------------------------
Term: pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 154.0407 -33.99090 -158.57989
pe_violence -33.9909 10.07508 46.57252
pe_intolerance -158.5799 46.57252 215.33734
Multivariate Tests: pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.1046494 24.49650 6 2662 < 2.22e-16 ***
Wilks 2 0.8960533 25.00905 6 2660 < 2.22e-16 ***
Hotelling-Lawley 2 0.1152208 25.52140 6 2658 < 2.22e-16 ***
Roy 2 0.1079561 47.89651 3 1331 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: gender
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 152.76377 54.727708 24.470573
pe_violence 54.72771 19.606233 8.766597
pe_intolerance 24.47057 8.766597 3.919836
Multivariate Tests: gender
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0631004 29.85861 3 1330 < 2.22e-16 ***
Wilks 1 0.9368996 29.85861 3 1330 < 2.22e-16 ***
Hotelling-Lawley 1 0.0673502 29.85861 3 1330 < 2.22e-16 ***
Roy 1 0.0673502 29.85861 3 1330 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: age_group
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 109.12662 -33.14113 29.34509
pe_violence -33.14113 37.90901 -20.08097
pe_intolerance 29.34509 -20.08097 16.74445
Multivariate Tests: age_group
Df test stat approx F num Df den Df Pr(>F)
Pillai 3 0.0673814 10.20158 9 3996.000 1.0968e-15 ***
Wilks 3 0.9335516 10.30644 9 3237.021 7.9428e-16 ***
Hotelling-Lawley 3 0.0701798 10.36062 9 3986.000 5.7450e-16 ***
Roy 3 0.0510979 22.68748 3 1332.000 2.5101e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred:pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 0.63911481 -0.08173498 0.1043172
pe_violence -0.08173498 6.59379216 -0.7907546
pe_intolerance 0.10431721 -0.79075456 0.1088301
Multivariate Tests: event_occurred:pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0063987 1.424005 6 2662 0.201355
Wilks 2 0.9936024 1.424976 6 2660 0.200985
Hotelling-Lawley 2 0.0064377 1.425943 6 2658 0.200617
Roy 2 0.0062575 2.776245 3 1331 0.040095 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
1.6.5 Gallant Dismissal
Type III MANOVA Tests:
Sum of squares and products for error:
pe_ideology pe_violence pe_intolerance
pe_ideology 6721.3933 -447.1900 -147.6616
pe_violence -447.1900 1958.5432 478.3327
pe_intolerance -147.6616 478.3327 5054.3931
------------------------------------------
Term: (Intercept)
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 2947.947 1463.9190 3389.280
pe_violence 1463.919 726.9665 1683.080
pe_intolerance 3389.280 1683.0803 3896.684
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.6097896 1150.683 3 2209 < 2.22e-16 ***
Wilks 1 0.3902104 1150.683 3 2209 < 2.22e-16 ***
Hotelling-Lawley 1 1.5627199 1150.683 3 2209 < 2.22e-16 ***
Roy 1 1.5627199 1150.683 3 2209 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 9.477481 2.2029277 -1.1054014
pe_violence 2.202928 0.5120444 -0.2569374
pe_intolerance -1.105401 -0.2569374 0.1289280
Multivariate Tests: event_occurred
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0018994 1.401218 3 2209 0.2406
Wilks 1 0.9981006 1.401218 3 2209 0.2406
Hotelling-Lawley 1 0.0019030 1.401218 3 2209 0.2406
Roy 1 0.0019030 1.401218 3 2209 0.2406
------------------------------------------
Term: pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 230.53549 -15.386354 -207.255724
pe_violence -15.38635 2.506649 3.717557
pe_intolerance -207.25572 3.717557 255.470549
Multivariate Tests: pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0801917 30.77106 6 4420 < 2.22e-16 ***
Wilks 2 0.9203320 31.20875 6 4418 < 2.22e-16 ***
Hotelling-Lawley 2 0.0859954 31.64629 6 4416 < 2.22e-16 ***
Roy 2 0.0787716 58.02839 3 2210 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: gender
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 208.458219 92.256367 5.9826152
pe_violence 92.256367 40.829463 2.6476977
pe_intolerance 5.982615 2.647698 0.1716972
Multivariate Tests: gender
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0559363 43.62817 3 2209 < 2.22e-16 ***
Wilks 1 0.9440637 43.62817 3 2209 < 2.22e-16 ***
Hotelling-Lawley 1 0.0592506 43.62817 3 2209 < 2.22e-16 ***
Roy 1 0.0592506 43.62817 3 2209 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: age_group
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 82.37454 -31.09623 44.26317
pe_violence -31.09623 31.64215 -35.71754
pe_intolerance 44.26317 -35.71754 49.55744
Multivariate Tests: age_group
Df test stat approx F num Df den Df Pr(>F)
Pillai 3 0.0396330 9.866846 9 6633.000 3.6370e-15 ***
Wilks 3 0.9606080 9.946311 9 5376.276 2.7849e-15 ***
Hotelling-Lawley 3 0.0407568 9.997483 9 6623.000 2.1294e-15 ***
Roy 3 0.0334432 24.647674 3 2211.000 1.0997e-15 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred:pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 18.380618 -4.278467 -8.537851
pe_violence -4.278467 1.130429 1.784352
pe_intolerance -8.537851 1.784352 4.272206
Multivariate Tests: event_occurred:pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0037405 1.380331 6 4420 0.218437
Wilks 2 0.9962600 1.380801 6 4418 0.218245
Hotelling-Lawley 2 0.0037534 1.381270 6 4416 0.218054
Roy 2 0.0036024 2.653741 3 2210 0.047084 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
1.6.6 Oct. 7th War
Type III MANOVA Tests:
Sum of squares and products for error:
pe_ideology pe_violence pe_intolerance
pe_ideology 8357.2436 -541.8413 -261.9729
pe_violence -541.8413 2401.0483 575.1074
pe_intolerance -261.9729 575.1074 6144.8528
------------------------------------------
Term: (Intercept)
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 5459.225 2712.203 6027.581
pe_violence 2712.203 1347.452 2994.569
pe_intolerance 6027.581 2994.569 6655.108
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.6965669 2009.432 3 2626 < 2.22e-16 ***
Wilks 1 0.3034331 2009.432 3 2626 < 2.22e-16 ***
Hotelling-Lawley 1 2.2956196 2009.432 3 2626 < 2.22e-16 ***
Roy 1 2.2956196 2009.432 3 2626 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 0.01331587 -0.01323362 -0.2962955
pe_violence -0.01323362 0.01315187 0.2944654
pe_intolerance -0.29629553 0.29446535 6.5929646
Multivariate Tests: event_occurred
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0010786 0.9451729 3 2626 0.41785
Wilks 1 0.9989214 0.9451729 3 2626 0.41785
Hotelling-Lawley 1 0.0010798 0.9451729 3 2626 0.41785
Roy 1 0.0010798 0.9451729 3 2626 0.41785
------------------------------------------
Term: pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 197.988429 1.3765715 -234.984413
pe_violence 1.376572 0.5315731 -9.383015
pe_intolerance -234.984413 -9.3830145 393.932021
Multivariate Tests: pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0829274 37.87898 6 5254 < 2.22e-16 ***
Wilks 2 0.9175072 38.50364 6 5252 < 2.22e-16 ***
Hotelling-Lawley 2 0.0894360 39.12826 6 5250 < 2.22e-16 ***
Roy 2 0.0837825 73.36550 3 2627 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: gender
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 175.55221 90.800794 -15.415967
pe_violence 90.80079 46.964854 -7.973594
pe_intolerance -15.41597 -7.973594 1.353740
Multivariate Tests: gender
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0451116 41.35318 3 2626 < 2.22e-16 ***
Wilks 1 0.9548884 41.35318 3 2626 < 2.22e-16 ***
Hotelling-Lawley 1 0.0472428 41.35318 3 2626 < 2.22e-16 ***
Roy 1 0.0472428 41.35318 3 2626 < 2.22e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: age_group
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 98.32895 -42.90311 52.51452
pe_violence -42.90311 24.15415 -32.16636
pe_intolerance 52.51452 -32.16636 47.34359
Multivariate Tests: age_group
Df test stat approx F num Df den Df Pr(>F)
Pillai 3 0.0300046 8.849857 9 7884.000 2.2418e-13 ***
Wilks 3 0.9700720 8.921462 9 6391.145 1.7415e-13 ***
Hotelling-Lawley 3 0.0307725 8.974162 9 7874.000 1.3510e-13 ***
Roy 3 0.0279726 24.503987 3 2628.000 1.2340e-15 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------
Term: event_occurred:pe_left_center_right
Sum of squares and products for the hypothesis:
pe_ideology pe_violence pe_intolerance
pe_ideology 5.073683 5.856826 2.295252
pe_violence 5.856826 7.440281 4.314510
pe_intolerance 2.295252 4.314510 5.118435
Multivariate Tests: event_occurred:pe_left_center_right
Df test stat approx F num Df den Df Pr(>F)
Pillai 2 0.0046517 2.041398 6 5254 0.056849 .
Wilks 2 0.9953504 2.042114 6 5252 0.056761 .
Hotelling-Lawley 2 0.0046693 2.042828 6 5250 0.056673 .
Roy 2 0.0041835 3.663331 3 2627 0.011894 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1