Extending models

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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

Continue to Causality

Recall that I’m using discernible as a replacement for significant, as proposed by Jeff Witmer.↩