Extending models

Guiding model building

Given a base model and a proposed elaboration of that model, does the elaboration reveal new aspects of the relationship between the response and explanatory variables?

• Inputs from the model:
  • $v_r$ and $n$
  • $v_m^{base}$ and $v_m^{elab}$,
  • degrees of flexibility $^\circ\!{\cal F}^{base}$ and $^\circ\!{\cal F}^{elab}$

• Output:

  $$\Delta \mbox{F} = \frac{n - (^\circ\!{\cal F}^{elab} + 1)}{^\circ\!{\cal F}^{elab} - ^\circ\!{\cal F}^{base}} \cdot \frac{v_m^{elab} - v_m^{base}}{v_r - v_m^{elab}}$$

• Interpretation: Is $\Delta$F $\gtrapprox 4$? Then a relationship is discernible.¹

  • Notes:
    • The special case of a model with $^\circ{\cal F} = 0$ is called the Null Model and corresponds to the claim that there is no relationship between the explanatory variables and the response variable. In this special case, $\mbox{F} = \Delta \mbox{F}$.
    • $\Delta \mbox{F} \neq \mbox{F}^{elab} - \mbox{F}^{base}$

Example

An exercise comparing two models

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