A Grambank typology of omnipredicativity - Supplementary materials

More model comparisons Model Formula ELPD Difference SE Difference (1) S-indexing + phylo + areal GP (main) 0.0 0.0 (2) phylo + areal GP (only controls) -0.5 1.3 (3) S-indexing + phylo + (1 | macroarea) -7.1 6.4 (4) S-indexing + (1 | macrofamily) + areal GP -8.0 -3.0 (5) S-indexing + areal GP -18.3 6.9 (6) S-indexing + (1 | macrofamily) + (1 | macroarea) (hierarchical) -24.0 8.5 (7) S-indexing + phylo -44.5 9.9 (8) S-indexing + (1 | macrofamily) -59.2 11.2 (9) S-indexing + (1 | macroarea) -91.0 13.1 (10) S-indexing (no controls) -377.1 22.8 Table S1. ELPD and SE difference between the main model, the five models discussed in the main text (highlighted here in blue), and four additional models. The cells highlighted in blue indicate the models which were presented and compared in the main paper. Table S1 above presents the same model comparison results that are present in Table 2 of the main text, with the addition of four more models. These four models involve different combinations of the group-level predictors for areal and genetic effects that are featured in the hierarchical model. The reasoning behind running these additional four models was to cover all possible model configurations given the set of bias controls that I was working with which was based on the bias controls evaluated by Guzmán Naranjo & Becker (2021). However, this approach also offers us some deeper insight into how effective Guzmán Naranjo & Becker’s (2021) areal and genetic controls are in comparison with the more traditional group-level effects. In hindsight, this is also interesting because given the hardware I was working with (an 8-core laptop and a 12-core desktop), the models involving an areal Gaussian Process took extremely long times to run - anywhere from 18-96 hours. First, let’s look at Models (8) and (9) because these models both include S-indexing as a predictor alongside one traditional bias control in the form of a group-level effect. Model (8) includes S-indexing and a group-level effect for macrofamily as a phylogenetic bias control. The ELDP difference of Model (8) is much more than two times the SE difference. Therefore, we can be certain that Model (8) does perform worse than the main model and better-ranked models. Model (9) includes S-indexing and a group-level effect for macroarea as an areal bias control. The ELDP difference of Model (9) is much more than two times the SE difference. Therefore, we can be certain that Model (9) does perform worse than the main model and better-ranked models. Looking solely at these two models, we might be compelled to conclude that predicting copula use in predicate nominals is more strongly influenced by the phylogenetic signal than the areal signal. However, this is the opposite of what we see when we compare Models (5) and (7) which contain S-indexing as a predictor alongside one of Guzmán Naranjo & Becker’s (2021) bias controls. As discussed in the main text, including Guzmán Naranjo & Becker’s (2021) areal GP alongside S-indexing (Model (5)) results in better model performance than only including Guzmán Naranjo & Becker’s (2021) phylogenetic control alongside S-indexing (Model (7)). Looking solely at these two models, we would then be compelled to conclude that predicting copula use in predicate nominals is more strongly influenced by the areal signal than the phylogenetic signal. This is the opposite of the conclusion arrived at from looking at only Models (8) and (9). If both sets of bias controls showed a stronger areal signal than phylogenetic signal, then the conclusion would be clearly supported. This unexpected contrast opens up the possibility of and highlights the importance of further application of different statistical bias controls. With this variation in conclusions drawn from different parts of the data discussed, I will argue for one conclusion over the other. I am inclined to put more trust in the conclusion that copula use in predicate nominals is mediated more strongly by an areal signal than a phylogenetic signal. This is because Guzmán Naranjo & Becker (2021) make a strong case for the superiority of their bias controls over the traditional group-level effects and because I found that my best performing models were the models that included both of Guzmán Naranjo & Becker’s (2021) bias controls. Now, having discussed all of the models consisting of S-indexing and one of the four possible bias controls, let’s look at Models (3) and (4) which consist of S-indexing as a predictor alongside two bias controls - one traditional and one from Guzmán Naranjo & Becker (2021). Model (3) includes the following predictors: S-indexing, Guzmán Naranjo & Becker’s phylogenetic control, and a group-level effect for macroarea as an areal control. The ELDP difference of Model (3) is much less than two times the SE difference. Therefore, we cannot be certain that this model performs any worse than either the main model or the model with only Guzmán Naranjo & Becker’s (2021) areal and phylogenetic controls. This is not what I expected, so I will discuss this further and explain how it fits into my interpretation of the model comparisons. To dig a bit deeper, let’s contrast Model (3) with Model (7). Model (7) includes only S-indexing and Guzmán Naranjo & Becker’s (2021) phylogenetic control, and it performed much worse than Model (3) in comparison to the main model. This confused me upon first glance because I expected that high-performing models would be high-performing due to the inclusion of one or both of Guzmán Naranjo & Becker’s (2021) more effective bias controls. However, Model (7) indicates that Guzmán Naranjo & Becker’s (2021) phylogenetic control alone does not account very well for the model’s ability to predict copula use in predicate nominals. So, my expectation that Model (3)’s high performance was due to Guzmán Naranjo & Becker’s (2021) phylogenetic control cannot be true. Thus, the remaining possible explanation for Model (3)’s high performance lies with the inclusion of the more traditional, less effective group-level effect for macroarea as a control for areal bias. This explanation also relies on the notion that Guzmán Naranjo & Becker’s (2021) bias controls are indeed better than the traditional, group-level effects method. In order for Model (3) to outperform Model (7), the areal signal in the data must be so strong that even a less-effective areal control picks up enough of the areal signal in the data to make a difference in the model comparison results. The fact that Model (3) outperforms Model (9) also emphasizes that the prediction of copula use in predicate nominals is indeed partially dependent on a phylogenetic signal. So, it seems that having Guzmán Naranjo & Becker’s new-and-improved phylogenetic control in combination with any areal control results in better predictive power for this data set. This indicates that given a strong enough trend in the data, even sub-par bias controls can provide reliable answers when compared to the quality of better bias control methods. Of course, this is not to say that better bias controls such as those outlined by Guzmán Naranjo & Becker (2021) are superfluous, but that perhaps sub-par bias controls can have a place in the earlier stages of a quantitative workflow for investigating cross-linguistic trends so that one can avoid having to run and re-run models with a cumbersome run-time. Model (4) includes the following predictors: S-indexing, a group-level effect for macrofamily, and Guzmán Naranjo & Becker’s (2021) areal control. The ELDP difference of Model (4) is more than two times the SE difference. Therefore, we can be certain that this model performs worse than any of the three preceding models. This time, as expected, the high performance of this model can be attributed to the effectiveness of Guzmán Naranjo & Becker’s (2021) new-and-improved areal control. However, given my conclusion that the prediction of copula use in predicate nominals is more dependent on the areal signal than the phylogenetic signal, it is surprising that the inclusion of Guzmán Naranjoy & Becker’s (2021) better areal bias control alongside the group-level effect for macrofamily does not perform as well as Model (3). This brings into question my assertion that the performance of Model (3) is due to such a strong areal signal being present. This could possibly be explained by a large gap in the effectiveness of the group-level effect for macro family and the phylogenetic bias control via covariance matrix outlined by Guzmán Naranjo & Becker (2021) with their control capturing substantially more of the phylogenetic signal than the group-level effect. However, this brings up the question of how do we differentiate between variation in the amount of areal/phylogenetic signal in different datasets and methods which distort the amount of areal/phylogenetic signal in different datasets?