Alternative approaches for econometric modeling of panel data using mixture distributions

Journal of Statistical Distributions and Applications

Table 2 Likelihood ratio tests comparing the two-component models

	\(\mathcal {M}_{1}\) vs \(\mathcal {M}_{2}\)	\(\mathcal {M}_{2}\) vs \(\mathcal {M}_{3}\)	\(\mathcal {M}_{1}\) vs \(\mathcal {M}_{5}\)	\(\mathcal {M}_{2}\) vs \(\mathcal {M}_{6}\)	\(\mathcal {M}_{5}\) vs \(\mathcal {M}_{6}\)
Likelihood ratio	1833.337	19.504	1890.253	767.080	710.163
Degrees of freedom	7.000	2.000	9.000	2.000	7.000
pvalue	0.000	0.000	0.000	0.000	0.000

Notes: These are regular likelihood ratio tests. The likelihood ratio is 2*(L ₂−L ₁) where L ₂ is the log-likelihood of the bigger model and L ₁, the log-likelihood of the smaller model. Under the null hypothesis that the smaller model is true, this statistic has a χ ²(k ₂−k ₁) distribution where k ₂ is the number of parameters from the bigger model and k ₁, the number of parameters from the smaller model