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We develop a unified model embedding different behavioral mechanisms of social interactions and design a statistical model selection test to differentiate between them in empirical applications.

The best phylogenetic model was determined using TOPALi version 2.5 model selection test based on the Akaike information criterion.

A recent study showed that the new causal model selection test (CMST test) outperforms BIC in terms of statistical precision, although it has lower statistical power [ 20].

Vuong's model selection test is a formal parametric hypothesis test devised to quantify the uncertainty associated with a model selection criterion, comparing two models based on their (penalized) likelihood scores.

Vuong's model selection test is based on the latter criterion and the null and alternative hypotheses are defined as H 0 : E 0 [ L R 12 ] = 0,   H 1 : E 0 [ L R 12 ] > 0,   H 2 : E 0 [ L R 12 ] < 0, (2)where LR12 = log f1 − log f2.

For each locus retained in the genetic model for a given trait, their LCMS (Likelihood-based Causality Model Selection) test evaluates genes for causality by comparing three of the five single anchor models (models 1, 2, and 3) shown in our Figure 2(a) for smallest AIC.

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Table 4 Estimated models for model selection tests Variable Tobit Probit Truncated regression Heckman Coef.

However, this contradicts the logic of model selection tests.

Model selection tests were performed as described [ 1, 2].

Therefore the model selection tests work appropriately with the artificial data.

The model selection tests prefer common ancestry for this artificial data set.

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