Thresholds form a continuum from linear to dichotomous transformations.

Evidence

There is really an underlying continuum here as well, which might be called “degree of thresholdness.” Linear transforms have no threshold. S-curve relationships have varying degrees of thresholdness depending on how sharp the S-curve is. Dichotomous transformations are the extreme threshold where there is a vertical threshold leap. For example, typically poverty measures are linear from zero until the threshold (poverty line) and then flat above that. Headcount measures of poverty use the extreme dichotomization threshold transformation. — Gary Goertz, Social Science Concepts and Measurement, 120

Categorization

• DEFINE: Introduces ‘degree of thresholdness’ as a continuous property, with the poverty line as the extreme dichotomous case.
• XREF: Connects to poverty measurement debates (headcount vs. depth) and to the general question of where a continuous variable gets a hard cutoff.