electromagnetism - Why does electrical impedance have as many parameters as it has?

The impedance of a circuit is written:

$$ Z(R,L,C,f) = R + j ( 2 \pi f L - \frac{1}{2 \pi f C} ). $$

What is the line of thinking that frequency, resistance, capacitance, and inductance are the only parameters? From a physical perspective, why is the definition of impedance parameterized exclusively by these four variables? This model can be verified with experiments, but what goes to show that I couldn't make another circuit element that affects the inductance without changing any of those four properties?