Meade and Lautenschlager (2004) provided a detailed comparison of the

likelihood-ratio test within IRT and MACS1 that included a simulation study that examined the Type I error rate and power of both methods.

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.

c)

Likelihood-ratio test comparing a model with adjustment covariates only to models with adjustment covariates and quartiles of NT-proBNP or BNP.

6 Model Chi-Squares

Likelihood-Ratio Test Statistics 81.

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).

To investigate the properties of the

likelihood-ratio test of convexity, we will compare it to the results of a log-log unit slope test applied to synthetic data (with various degrees of contamination of measurement error).

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 [31].

A

likelihood-ratio test of identical substitution rates can also be performed in which a prior distribution of node times and topologies is assumed (Rannala and Yang 1996).

5%) slightly exceeded the power of the

likelihood-ratio test of {[k.