Phylogenetic Logistic Regression for Binary Dependent Variables

We develop statistical methods for phylogenetic logistic regression in which the dependent variable is binary (0 or 1) and values are nonindependent among species, with phylogenetically related species tending to have the same value of the dependent variable. The methods are based on an evolutionary model of binary traits in which trait values switch between 0 and 1 as species evolve up a phylogenetic tree. The more frequently the trait values switch (i.e., the higher the rate of evolution), the more rapidly correlations between trait values for phylogenetically related species break down. Therefore, the statistical methods also give a way to estimate the phylogenetic signal of binary traits. More generally, the methods can be applied with continuous- and/or discrete-valued independent variables. Using simulations, we assess the statistical properties of the methods, including bias in the estimates of the logistic regression coefficients and the parameter that estimates the strength of phylogenetic signal in the dependent variable. These analyses show that, as with the case for continuous-valued dependent variables, phylogenetic logistic regression should be used rather than standard logistic regression when there is the possibility of phylogenetic correlations among species. Standard logistic regression does not properly account for the loss of information caused by resemblance of relatives and as a result is likely to give inflated type I error rates, incorrectly identifying regression parameters as statistically significantly different from zero when they are not.