The table shows the p-value of Lagrange multiplier and Likelihood-ratio test
for the null hypothesis of linearity against the alternative of logistic (m=1) or exponent (m = 2) PSTR specification.
The null hypothesis of no overdispersion, [alpha] : [H.sub.o] ([alpha] = 0), can be determined via a Likelihood-ratio test
Also, the likelihood-ratio test
(LR test), which is performed upon heteroscedasticity in the panel data, indicates the presence of heteroscedasticity, and the Wooldridge test, which checks for autocorrelation, supports the presence of autocorrelation in the panel data (Table 3, Hall-Roeger model, Eq.
The REML solution is obtained at the maximum of the restricted likelihood at which point a likelihood-ratio test
statistic (LRT) of the form -2 ln([L.sub.0]/[L.sub.1]) can be constructed to test hypotheses concerning [v.sup.2].
(c) Likelihood-ratio test
comparing a model with adjustment covariates only to models with adjustment covariates and quartiles of NT-proBNP or BNP.
A likelihood-ratio test
showed that none of the variables could be excluded from the cointegration vector.
1.016 * 1.118 * Dummy: Black-owned EIN Dummy: Hispanic-owned EIN Dummy: Asian/other-owned EIN Number of Observations 1,745 373 Percents of EINs Surviving to 1996 45.6 35.6 Model Chi-Squares Likelihood-Ratio Test
Statistics 81.783 131.125 Score Test Statistics 82.582 107.972 Wald Test Statistics 81.896 86.023 Hazard Ratios White Asian/ Covariate Description Hispanic-Owned Other-Owned 1992 EIN employment 0.947 * 0.999 Dummy: incorporated EIN 0.553 * 0.516 * Dummy: MSA 0.732 0.737 * Dummy: Northeast census region 1.756 0.917 Dummy: South census region 2.131 * 1.391 * Dummy: West census region 1.681 1.499 Dummy: woman-owned EIN 1.416 ** 1.105 1992 percent of pop.
Although other comparison tests are possible for hierarchical models (Quinn and Deriso, 1999), the Neyman Pearson lemma assures that in the situation where it applies, the likelihood-ratio test
is optimal in that it yields the most powerful test for any given choice of significance level, [alpha] (Rice, 1995).
In this study, the number of lags applied in each cointegration test is based on information provided by the Sims likelihood-ratio test
, the Akaike Information Criterion and the Ljung-Box test.
Since the linear model is nested in the nonlinear model, this can be done by an analysis of deviance (a likelihood-ratio test
) of the two models.
After each new set of parameters is added, a likelihood-ratio test
is performed that determines whether the additional parameters significantly improve the fit between the model and the data.
As the two models are obviously non-nested, we follow the likelihood-ratio test
procedure of Vuong .