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Department of Medical Biochemistry, Semmelweis University, and Neurochemical Group of the Hungarian Academy of Sciences, Budapest, Hungary
Correspondence: Address reprint requests to László Csanády, Dept. of Medical Biochemistry, Semmelweis University, 1444 Budapest, Pf. 262, Hungary. Tel.: 36-1-266-2755, Ext. 4023; E-mail: csanady{at}puskin.sote.hu.
The distributions of log-likelihood ratios (
LL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (
, full model;
R, submodel) were studied both theoretically and using simulated data. When
is true,
LL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When
R is true and corresponds to a distinct point in full parameter space,
LL is
-distributed (2
LL is
-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components,
R corresponds to an infinite set of points in parameter space. The distribution of
LL is a mixture of two components, one identically zero, the other approximated by a
-distribution. This empirical distribution of
LL, assuming
R, allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize
, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and
LL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of
LL when
or
R is true.
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