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.