Neas-Seminars

Fox Module 7: Advanced transformations HW


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By NEAS - 12/3/2009 12:38:39 PM

Module 7: Advanced transformations

 

(The attached PDF file has better formatting.)

 

Homework assignment: Logit and probit transformations

 

The logit transformation is tested on the final exam; the probit transformation is not tested. This homework assignment shows their practical equivalence for transforming data.

 

The textbook says that “once their scales are equated, the logit and probit transformations are, for practical purposes, indistinguishable: logit ≈ (ð/√3) × probit.”

 


A.     Explain the logit and probit transformations. A one sentence explanation is sufficient.

B.     Fill in the table below to compare the two transformations.

C.    In what range are the two transformations practically equivalent? In what ranges might the two transformations give different results? (The formula for the logit transformation is in the textbook. Excel gives the probit transformation as the inverse of the CDF of the standard normal distribution.)

 

P

Logit

Probit

P

Logit

Probit

0.001

 

 

0.5

 

 

0.002

 

 

0.6

 

 

0.01

 

 

0.8

 

 

0.02

 

 

0.9

 

 

0.1

 

 

0.98

 

 

0.2

 

 

0.99

 

 

0.4

 

 

0.998

 

 

0.5

 

 

0.999

 

 

 

 

 

 
By FrequentlySevere - 9/10/2010 4:41:14 PM

PLogitProbitprobit * pi/sqrt(3)
0.001-6.91-3.09-5.61
0.002-6.21-2.88-5.22
0.010-4.60-2.33-4.22
0.020-3.89-2.05-3.73
0.100-2.20-1.28-2.32
0.200-1.39-0.84-1.53
0.400-0.41-0.25-0.46
0.5000.000.000.00
0.6000.410.250.46
0.8001.390.841.53
0.9002.201.282.32
0.9803.892.053.73
0.9904.602.334.22
0.9986.212.885.22
0.9996.913.095.61

It's hard to pick a range where they are equal, but I think you can say 'near' p=1/2.

[NEAS: Correct; the two transformations are not exactly the same, but they give the same type of transformation for probabilities near p = 50%. A logit GLM and a probit GLM give nearly the same predictions for probabilities between 25% and 75%. Because of the stochasticity of observed values, we can't choose between the logit and probit GLMS in most analyses. We use the logit GLM because it is simpler.]