A is a
scientific model derived from empirical relationships. It forgoes any attempt to explain its variables interact the way they do, and simply attempts to describe they relate, with the assumption that the relationship
extends, at least within an acceptable error margin, past the measured values. Although not directly derived from
first principles, an
empirical observation-based
model will only be able provide reliable and accurate correspondence to the real world inasmuch as it is
consistent with the underlying fundamental theory behind the
phenomena being described.
Regression analysis is sometimes used to create
statistical models that serve as phenomenological models.
Applicability Phenomenological models have been characterized as being completely independent of theories, though many phenomenological models, while failing to be derivable from a theory, incorporate principles and laws associated with theories. The
liquid drop model of the atomic nucleus, for instance, portrays the nucleus as a liquid drop and describes it as having several properties (surface tension and charge, among others) originating in different theories (
hydrodynamics and
electrodynamics, respectively). Certain paradigmatic features of these theoriesthough usually not the complete theoryare then used to determine both the static and dynamical properties of the nucleus.
Approximations Some empirical relationships are merely approximations, often equivalent to the first few terms of the
Taylor series of an analytical solution describing a phenomenon. Other relationships only hold under certain specific conditions, reducing them to special cases of more general relationship. ==Empiricism and epistemology==