How does the monotonic relationship in Figure 6B relate to baseline activation by reward/punishment?
The Pearson coefficient measures the distribution of the points around the linear trend, while the Spearman coefficient measures the monotonicity of the mapping, that is, how well an arbitrary monotonic function describes the relationship between two sets of data.
The remaining question was how LY30 causes non-monotonic effects on cFLIP.
The figures demonstrate that the effect of minimum wages on an immigrant's choice of state is not a monotonic function of how long the immigrant has resided in the U.S. The main results in Table 4 indicate that the most significant coefficients are those for immigrants who are relatively new and mobile, but who also have had time to adjust.
These scatter-plots demonstrate how the rank transformation turns these monotonic relations into linear relations.
However, we show that the use of preference logic grammars allow construction of a much more powerful and declarative commercial standardizer, and discuss in detail how the use of the non-monotonic construct of preferences leads to improved commercial software.
No matter how faithful the model, no guarantee of piecemeal monotonic improvement of a nonlinear model's behavior with respect to the target system can be made (of course, if one waits for long enough times piecemeal confirmation strategies will also fail for linear systems).
However, because it is not clear how best to estimate the maximum slope from monotonic clines, we estimated cline widths by fitting parametric sigmoid clines using Analyse 1.3 [ 66].
It is not clear how best to apply this metric to PAVA monotonic clines, so widths were estimated by fitting sigmoid or stepped models using the Analyse program [ 60].
Moreover, the utility functions adhered to basic assumptions about how utility functions should behave; specifically, they were positive monotonic, nonsaturating within our reward range and quasicontinuous due to the fine-grained fractile CE assessment.
