Understanding the statistical properties of the percent model affinity index can improve biomonitoring related decision making

The percent model affinity (PMA) index is used to measure the similarity of two probability profiles representing, for example, an ideal profile (i.e. reference condition) and a monitored profile (i.e. possibly impacted condition). The goal of this work is to study the effects of sample size, evenness, true value of the index and number of classes on the statistical properties of the estimator of the PMA index. We derive and extend previous formulas of the expectation and variance of the estimator for estimated monitored profile and fixed reference profile. Using the obtained extension, we find that the estimator is asymptotically unbiased, converging faster when the profiles differ. When both profiles are estimated, we calculate the expectation using transformation rules for expectation and in addition derive the formula for the estimator's variance. Since the computation of the probabilities in the variance formula is slow, we study the behavior of the variance with simulation experiments and assess whether it could be approximated with the variance for the fixed reference profile. Finally, we provide a set of recommendations for the users of the PMA index to avoid the most common caveats of the index.