Hello Jessica,

Think about what exp(B) represents: The expected change in odds of the case belonging to the target category on the DV per unit change in the IV, with all other IVs held constant.

A square root transform for an IV will necessarily compress the scale (unless you're talking about values between 0, 1), so the "unit" has changed on the IV such that it now represents an increasing amount of "units" difference on the original scale, as values go up on either the original or transformed version of the scale.

Example: IV of 9 --> 3 (after transform); IV of 16 --> 4; IV of 25 --> 5. So an original score difference of 16 vs. 25 (9 units on original scale) now is characterized as one unit on the transformed version of the scale. Hence, both B and exp(B) increase.

Good luck with your work.

See these papers

Article Log Odds and the Interpretation of Logit Models

Article Statistics review 14: Logistic regression

Hi David Morse. I think Jessica Lee Oliva said she is using an inverse square root transformation, which I take to mean the reciprocal of the square root. So while your general approach to interpreting things still holds, the specific details need to be tweaked. ;-)

Using Stata:

clear

input byte x

4

9

16

25

36

49

64

end

* Let xt1 = sqrt(x)

generate double xt1 = x^.5

* Let xt2 = 1/sqrt(x), i.e., the INVERSE SQUARE ROOT

generate double xt2 = x^-.5

* Let incx = increment in x from previous row

generate double incx = x - x[_n-1] if _n > 1

* Let incxt1 = increment in xt1 from previous row

generate double incxt1 = xt1 - xt1[_n-1] if _n > 1

* Let incxt2 = increment in xt2 from previous row

generate double incxt2 = xt2 - xt2[_n-1] if _n > 1

list, clean noobs

OUTPUT from the -list- command:

x xt1 xt2 incx incxt1 incxt2

4 2 .5 . . .

9 3 .33333333 5 1 -.16666667

16 4 .25 7 1 -.08333333

25 5 .2 9 1 -.05

36 6 .16666667 11 1 -.03333333

49 7 .14285714 13 1 -.02380952

64 8 .125 15 1 -.01785714

So for David's example, an increase in X from 16 to 25 corresponds to a decrease of 1/20 (-.05) in the inverse square root of X.

HTH.

Good catch, Bruce Weaver !

Might be worth the questioner saying (or showing the code) what they mean by the inverse square root (e.g., x^2, -1* x^.5). I would normally think just x^2 but then why not say squared, so it could be the additive or multiplicative or some other inverse. As to interpretting it, try plotting the results on the original scale (back-transforming depending on what you have done).

Interesting discussion, and that is why I always recommend that predicted response values and CIs are plotted against the original and transformed X variable.

Depends on the units you use. In fact, this is a common situation when you want to use these transformations. For example, if you want to estimate a car price you use mileage and year. But you can also introduce something like mileage/log(years in use). In fact, the purpose of transforming variables is not to get a good interpretation, but to make CLNR assumptions hold true.

As pointed out above, if you want a visual tool, a graph of predicted Y vs X can be used if you need to explain/interpret the model.