Compare and contrast:

  1. \frac{\mathit{exp}(\beta_0 + \beta_1 x_1 + \beta_2 x_2)}{1 + \mathit{exp}(\beta_0 + \beta_1 x_1 + \beta_2 x_2)}
  2. \mathit{logit}^{-1}(\beta_0 + \beta_1 x_1 + \beta_2 x_2), where \mathit{logit}^{-1}(x) is defined as \frac{\mathit{exp}(x)}{1 + \mathit{exp}(x)}

Variants of version 1 are often found in psychology journals.  Rather than separating out reusable defintions, e.g., here of the logit function, many psychologists for some reason find it necessary to plug all bits of a formula in together at once to make a monster formula.

Here’s another example; two definitions of correlation:

  1. \frac{n\sum x_iy_i-\sum x_i\sum y_i}  {\sqrt{n\sum x_i^2-(\sum x_i)^2}~\sqrt{n\sum y_i^2-(\sum y_i)^2}}
  2. \mathit{cov}(X,Y) \over \sigma_X \sigma_Y

(Okay, I cheated a bit with the second and left out definitions of covariance and SD.)

So the question: which do you find easier to understand?


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