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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.

## 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

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
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
Empirical BIC 0.90
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
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.