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Introduction
This blog is about world happiness ladder using the world happiness report data sets (Helliwell et. al., 2024). The basic objective is to demonstrate the use of panel data which is quite distinct from cross-sectional or time series data.
Global happiness ladder
Cross-sectional happiness ladder for 2023
Fixed time, it is cross-sectional
Times series vs. panel data visualisation
Each line is a timeseries but together, it is panel data
Mean global happiness lalder
Cross-sectional mean happiness ladder for 2023
Time is fixed, cross-sectional
Times series vs. panel data visualisation
Each line is a timeseires but together, they are panel data
Factor analysis of panel global happiness ladder
Parallel analysis suggests that the number of factors = 4 and the number of components = NA Loadings: MR1 MR2 MR4 MR3 Happiness 0.810 GDP 0.899 Support 0.761 Life_Exp 0.882 Freedom 0.651 Positive 0.775 Corruption -0.831 Negative 0.550 Year 0.487 Generosity 0.440 Regional MR1 MR2 MR4 MR3 SS loadings 3.286 1.687 0.909 0.731 Proportion Var 0.299 0.153 0.083 0.066 Cumulative Var 0.299 0.452 0.535 0.601
| Values | |
|---|---|
| degree of freedom | 17.00 |
| Chi-sq | 132.48 |
| Chi-sq/df | 7.79 |
| Harmonic sample size | 2298.31 |
| Root Mean Square | 0.02 |
| Probability of the empirical chi-sq | 0.00 |
| Adjusted Root Mean Square | 0.04 |
| Empirical BIC | 0.90 |
| Sample size adjusted BIC | 54.91 |
| fit (SSresidual vs SSoriginal values) | 0.90 |
| fit applied to off diagonal elements | 1.00 |
| SD of the residuals | 0.02 |
| Number of factors extracted | 4.00 |
| Number of observations | 2363.00 |
| Value of the minimised function | 0.16 |
| chi-sq based on the objective function | 369.96 |
| p-value of observing the chi-sq | 0.00 |
| chi-sq based on the objective function/df | 6.73 |
| Null model | 5.32 |
| df for null model | 55.00 |
| chi-sq for null model | 12542.24 |
| chi-sq for null model/df | 228.04 |
| Tucker Lewis Index of factoring reliability | 0.91 |
| RMSE Approximation | 0.09 |
| RMSE Approximation-lower | 0.09 |
| RMSE Approximation-upper | 0.10 |
| RMSE Approximation-confidence interval | 0.90 |
| RMSE Approximation-BIC | 237.91 |
| RMSE Approximation-empirical BIC | 291.92 |
| Mean item complexity | 1.58 |
| Kaiser Meyer Olkin Measure of Sampling Adequacy | 0.81 |
| Bartlett Chi | 12542.24 |
| Barlett p-value | 0.00 |
| Barlett df | 55.00 |
| Barlett Chi/df | 228.04 |
lavaan 0.6-18 ended normally after 117 iterations Estimator ML Optimization method NLMINB Number of model parameters 24 Used Total Number of observations 2098 2363 Model Test User Model: Test statistic 2216.113 Degrees of freedom 31 P-value (Chi-square) 0.000 Model Test Baseline Model: Test statistic 10727.135 Degrees of freedom 45 P-value 0.000 User Model versus Baseline Model: Comparative Fit Index (CFI) 0.795 Tucker-Lewis Index (TLI) 0.703 Loglikelihood and Information Criteria: Loglikelihood user model (H0) -15445.704 Loglikelihood unrestricted model (H1) -14337.648 Akaike (AIC) 30939.408 Bayesian (BIC) 31074.978 Sample-size adjusted Bayesian (SABIC) 30998.727 Root Mean Square Error of Approximation: RMSEA 0.183 90 Percent confidence interval - lower 0.177 90 Percent confidence interval - upper 0.190 P-value H_0: RMSEA <= 0.050 0.000 P-value H_0: RMSEA >= 0.080 1.000 Standardized Root Mean Square Residual: SRMR 0.110 Parameter Estimates: Standard errors Standard Information Expected Information saturated (h1) model Structured Latent Variables: Estimate Std.Err z-value P(>|z|) MR1 =~ GDP 1.000 Life_Exp 5.659 0.097 58.044 0.000 Happiness 0.931 0.016 59.736 0.000 Support 0.089 0.002 45.585 0.000 MR2 =~ Positive 1.000 Freedom 1.858 0.076 24.518 0.000 Generosity 0.857 0.058 14.877 0.000 Regional 7.995 1.138 7.026 0.000 MR4 =~ Corruption 1.000 MR3 =~ Year 1.000 Covariances: Estimate Std.Err z-value P(>|z|) MR1 ~~ MR2 0.036 0.002 15.240 0.000 MR4 -0.078 0.005 -16.353 0.000 MR3 0.553 0.121 4.589 0.000 MR2 ~~ MR4 -0.007 0.000 -16.232 0.000 MR3 0.084 0.009 9.636 0.000 MR4 ~~ MR3 -0.086 0.020 -4.320 0.000 Variances: Estimate Std.Err z-value P(>|z|) .GDP 0.197 0.011 17.757 0.000 .Life_Exp 12.638 0.506 24.994 0.000 .Happiness 0.307 0.013 24.065 0.000 .Support 0.006 0.000 28.956 0.000 .Positive 0.007 0.000 26.406 0.000 .Freedom 0.003 0.001 6.186 0.000 .Generosity 0.023 0.001 31.520 0.000 .Regional 10.537 0.327 32.245 0.000 .Corruption 0.000 .Year 0.000 MR1 1.136 0.042 27.217 0.000 MR2 0.005 0.000 14.435 0.000 MR4 0.034 0.001 32.388 0.000 MR3 24.675 0.762 32.388 0.000
| x | |
|---|---|
| npar | 2.400000e+01 |
| fmin | 5.281489e-01 |
| chisq | 2.216113e+03 |
| df | 3.100000e+01 |
| pvalue | 0.000000e+00 |
| baseline.chisq | 1.072713e+04 |
| baseline.df | 4.500000e+01 |
| baseline.pvalue | 0.000000e+00 |
| cfi | 7.954423e-01 |
| tli | 7.030614e-01 |
| nnfi | 7.030614e-01 |
| rfi | 7.001121e-01 |
| nfi | 7.934106e-01 |
| pnfi | 5.465717e-01 |
| ifi | 7.957100e-01 |
| rni | 7.954423e-01 |
| logl | -1.544570e+04 |
| unrestricted.logl | -1.433765e+04 |
| aic | 3.093941e+04 |
| bic | 3.107498e+04 |
| ntotal | 2.098000e+03 |
| bic2 | 3.099873e+04 |
| rmsea | 1.832962e-01 |
| rmsea.ci.lower | 1.768656e-01 |
| rmsea.ci.upper | 1.898093e-01 |
| rmsea.ci.level | 9.000000e-01 |
| rmsea.pvalue | 0.000000e+00 |
| rmsea.close.h0 | 5.000000e-02 |
| rmsea.notclose.pvalue | 1.000000e+00 |
| rmsea.notclose.h0 | 8.000000e-02 |
| rmr | 1.183338e+00 |
| rmr_nomean | 1.183338e+00 |
| srmr | 1.100957e-01 |
| srmr_bentler | 1.100957e-01 |
| srmr_bentler_nomean | 1.100957e-01 |
| crmr | 1.217154e-01 |
| crmr_nomean | 1.217154e-01 |
| srmr_mplus | 1.100957e-01 |
| srmr_mplus_nomean | 1.100957e-01 |
| cn_05 | 4.358775e+01 |
| cn_01 | 5.040973e+01 |
| gfi | 8.167185e-01 |
| agfi | 6.748232e-01 |
| pgfi | 4.603323e-01 |
| mfi | 5.940683e-01 |
| ecvi | 1.079177e+00 |
| MR1 | MR2 | |
|---|---|---|
| alpha | 0.4741262 | 0.0705956 |
| omega | 0.8358631 | 0.0570646 |
| omega2 | 0.8358631 | 0.0570646 |
| omega3 | 0.8354815 | 0.0556176 |
| avevar | 0.7454058 | 0.0295963 |
The inter-connectivity between the latent variables and the various variables used to measure hapiiness.
References
Helliwell, J. F., Layard, R., Sachs, J. D., De Neve, J.-E., Aknin, L. B., & Wang, S. (Eds.). (2024). World Happiness Report 2024. University of Oxford: Wellbeing Research Centre.
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