Log10LL

Log10LL is not a universally standardized statistical term, but a notation sometimes used in statistics and data analysis to denote a base-10 logarithmic quantity related to a likelihood-like value. Because “LL” often stands for a log-likelihood in many texts and software, log10LL can refer to different things depending on context. The most common interpretations are described below.

Interpretation A: log10 of a likelihood value (log10(L))

In this usage, log10LL = log10(L), where L is a likelihood or likelihood-like quantity. This is useful for working with very small likelihood values or for presenting results on a more interpretable scale. Since L can exceed 1 for certain models or densities, log10(L) may be positive, zero, or negative. Differences between log10(L) values reflect changes in model fit, and because log10 is a monotone transformation, the order of models by likelihood is preserved if using log10(L) instead of L. The relation to the natural log is log10(L) = ln(L) / ln(10).

Interpretation B: log10 of a log-likelihood (log-likelihood LL)

In other contexts, log10LL can denote log10(LL), where LL is the log-likelihood value (the natural log of the likelihood). Since LL is typically nonpositive for many models, log10(LL) is often undefined when LL ≤ 0, making this interpretation less common and potentially problematic. If used, it requires careful handling of the domain of LL.

Practical notes

Because log-likelihood comparisons are standardly based on LL values themselves or their natural logarithm, log10LL is less common and can lead to confusion if the underlying quantity is not clearly defined. When used, it is important to state precisely what LL or L represents and to be aware of domain issues.

See also: log-likelihood, likelihood, base-10 logarithm, numerical stability.