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Data Analysis and Visualization

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Task 01: Visualizing Average concern for threats



* Demographic factor analysis in Appendix

Task 02: Reliability Analysis for the Desire for Cultural Tightness Scale

Dimensionality Check - EFA

Summary of EFA Fit Indices
1–3 Factor Models Compared
Number of Factors Variance Explained RMSEA TLI RMSR BIC
1 0.3970 0.0668 0.9426 0.0349 829
2 0.4394 0.0364 0.9830 0.0166 65
3 0.4562 0.0238 0.9927 0.0083 −38

Dimensionality Check - CFA

Summary of Confirmatory Factor Analysis (CFA) Fit Indices
Comparison of 2-Factor and 3-Factor Models
Model Chi-Square Degrees of Freedom P-Value CFI TLI RMSEA SRMR AIC BIC
2-Factor 570.9872 26 0 0.9776 0.9690 0.0491 0.0242 275,819 275,953
3-Factor 441.5970 24 0 0.9828 0.9743 0.0448 0.0208 275,694 275,842

Reliability Check

Internal Consistency of the Scale
Overall and Subscale Reliability Estimates
Scale Cronbach's Alpha McDonald's Omega
Overall 0.8521 0.8680
Factor 1 0.7455 0.7467
Factor 2 0.6254 0.6325
Factor 3 0.7398 0.7413
Note: Alpha is calculated by assuming unidimensionality for both overall and subscale acores.

Task 02 Written Summary

Model fit: Due to a low BIC in 1-factor analysis from EFA, a multi-factor analysis for the desire for cultural tightness scale is preferred. A 2-factor model is statistically good enough, but according to the theoretical construct of cultural tightness-looseness from MJ Gelfand et al., 2011, a 3-factor analysis could work better for potential subscale analysis. According to Table 1 from Jackson et al., 2019, the items could possibly be grouped into 3 factors - 1) Group-level compliance with rules/norms (CT_5, CT_6); 2) Group-level tolerance of deviant behavior (Law: CT_2, CT_9; Norm: CT_3); 3) The strength of social norms perceived by the participant (CT_1, CT_4, CT_7, CT_8)

Reliability: 3-factor scale demonstrated strong internal consistency with an omega Total of 0.87, indicating that 87% of the total score variance is reliable. Alpha ≈ 0.74 in subscale 1 and subscale 3 allows us to combine items in these two subscales into one single index confidently. Alpha and omega of subscale 2 is around 0.63, but this might also because the number of items is small. According to the theoretical construct and high overall omega, we could keep the items and believe they are measuring the same psychological construct. So we would be able to combine all the 9 items into an overall index score.

Task 03: Table for correlation between desire for cultural tightness and level of concern for threats

[1] “Item-Total Correlations for score from g loadings” CT_1 CT_2 CT_3 CT_4 CT_5 CT_6 CT_7 CT_8 0.5789483 0.5660922 0.5961276 0.6681864 0.7511014 0.7429981 0.7544633 0.6798462 CT_9 0.7395206 [1] “Item-Total Correlations for downweighted score” CT_1 CT_2 CT_3 CT_4 CT_5 CT_6 CT_7 CT_8 0.5968026 0.5617257 0.5938260 0.6876986 0.7239488 0.7192619 0.7658788 0.6938076 CT_9 0.7363707

Correlation Table
Threat Desire for Cultural Tightness (1) Desire for Cultural Tightness (2)
Crime Surge 0.1996 *** 0.1982 ***
Refugee Influx 0.1785 *** 0.179 ***
Illegal Immigration 0.1712 *** 0.1726 ***
Increase in National Debt 0.1658 *** 0.1648 ***
Pollution 0.1132 *** 0.1141 ***
A Surge of COVID-19 Cases 0.1079 *** 0.1082 ***
Famine 0.0993 *** 0.1012 ***
Natural Disaster 0.0939 *** 0.095 ***
Discrimination 0.0801 *** 0.0776 ***
Attack by A Terrorist Group 0.0503 *** 0.0522 ***
Note: The desire for cultural tightness is measured by the scale adapted from Table 1 in Jackson et al., 2019. Desire for Cultural Tightness (1) is based on a composite index computed by weighting item responses according to their general factor (g) loadings, reflecting each item's overall contribution. Desire for Cultural Tightness (2) employs an index score in which items with lower prominence in the general factor structure are downweighted, thereby emphasizing those items that are more central to the construct.
The stars represent statistical significance based on p-values: * * for p-value ≤ 0.05, * ** for p-value ≤ 0.01, * *** for p-value ≤ 0.001.

Task 04: Regression summary on concern about COVID-19 concern and desire of cultural tightness

Regression Summary
Fixed Effects Random Effects
* p < 0.05, ** p < 0.01, *** p < 0.001
SocietalThreat_8 0.055*** 0.056***
(0.014) (0.009)
Age 0.008*** 0.008***
(0.001) (0.001)
Religion -0.009 -0.010
(0.017) (0.009)
Income 0.022 0.022
(0.012) (0.013)
Education -0.081 -0.081**
(0.046) (0.027)
(Intercept) 4.044***
(0.102)
SD (Intercept Country) 0.488
SD (Observations) 0.994
Num.Obs. 8593 8593
R2 0.217
R2 Adj. 0.213
R2 Marg. 0.017
R2 Cond. 0.208
R2 Within 0.016
R2 Within Adj. 0.015
AIC 24326.1 24483.5
BIC 24636.7 24539.9
ICC 0.2
RMSE 0.99 0.99
Std.Errors by: Country
FE: Country X 
        Fixed_Effects Random_Effects

Coefficient 0.0550 0.0559 Std_Error 0.0144 0.0093 t_value 3.8081 5.9957 p_value 0.0005 NA Overall R2 0.2168 0.2082

$Country Algeria Argentina Australia Belgium Benin 3.964609 3.505093 5.296955 4.184057 4.273050 3.475036 Brazil Canada China Columbia Egypt Ethiopia 4.866572 4.172007 3.851447 4.879225 3.011489 3.562384 France Germany Greece India Indonesia Ireland 4.316422 4.307215 4.079762 3.937327 4.012316 4.115265 Israel Japan Kenya Malaysia Mexico Morocco 4.080549 3.857745 3.816147 3.702140 4.632898 3.610201 Nigeria Philippines Portugal Russia Saudi Arabia Singapore 3.925906 3.944967 4.132745 3.927019 2.803868 3.274306 South Africa South Korea Spain Switzerland Taiwan Tunisia 4.757167 4.501636 4.452723 4.011961 4.421288 3.876655 UAE UK USA 3.896122 4.234566 4.021655

attr(,“class”) [1] “fixest.fixef” “list”
attr(,“exponential”) [1] FALSE [1] “Difference in R-squared (with vs. without SocietalThreat_8): 0.00318410530909186” [1] “Difference in R-squared (with vs. without Religion): 9.91828161897024e-05” [1] “Difference in R-squared (with vs. without Country): 0.111099206646451” [1] “Difference in R-squared (with vs. without Country and Religion): 0.184375255475813” [1] “Difference in R-squared (with vs. without Age): 0.00760846383456992” [1] “Difference in R-squared (with vs. without Income): -0.00104305324601905” [1] “Difference in R-squared (with vs. without Education): 0.000843773437440021”

Task 04 [Written Summary]

Treating country as a categorical variable, the fixed and random effects regression models produce similar results.

A fixed effect model that controlled for age, income, education, religion, and absorbed effects of country indicated that the effect of concern about a rise of COVID-19 cases on the composite scale score for desire of cultural tightness was significantly positive, b = 0.055, SE = 0.014, t ≈ 3.81, p < .001. Similarly, a random effects model yielded nearly identical results, b = 0.056, SE = 0.009, t ≈ 5.999, p < .001, suggesting that higher concern about a rise of COVID-19 cases robustly predict increased desire of cultural tightness.

However, country contributes the most to the variation in the desire for cultural tightness. Taking the fixed effect model for example, the inclusion of SocietalThreat_8 only explains an additional 0.318% of the variance in CT_weighted, while country explains a significant portion of the variance (11.11%). So it would be important to check within-country association between COVID-19 concern and desire for cultural tightness.

Task 05: Association between COVID-19 concern and desire for cultural tightness within country

Appendix: Demographic Factor Analysis for Task 01

In addition to the overall pattern in Task 01, the analysis by demographic factor here eyeballs the mean concern level across different groups. Country (and religion) show more variance than other groupings. Age also plays a role, but might be more about experience, growth and change in mindset, which are intertwined with country and religion. Income explains more for the concern level of threats like polution, famine and refugee influx, but doesn’t cause too much variance in factors like COVID.