st: Paradoxical RRR with logit and auto.dta

[Michael Ingre <Michael.Ingre@ipm.ki.se>]

Dear list

Paradoxes do exist, but this one might be attributed to my ignorance. 
Below is an example using the auto.dta that to me at least, is 
difficult to understand. Two -logit- models are fitted and then, 
Relative Risk Ratios (RRR) are calculated using -nlcom- that contrasts 
the probability at different levels of the independent variable. In the 
first model, the greater the contrast the greater the significance. 
However, in the second model, the opposite apply.

If anyone could explain this apparent paradox for me, or point me to my 
mistakes, I would be very happy.

Thanks,

Michael

Paradoxical code below (output omitted):

sysuse auto

logit foreign mpg

// Contrast probability of mpg=1 with mpg=10
nlcom (exp(1   * _b[mpg] + _cons) / (1+ exp(1   * _b[mpg] + _cons))) /  
///
      (exp(10  * _b[mpg] + _cons) / (1+ exp(10  * _b[mpg] + _cons)))    
//

// Contrast probability of mpg=1 with mpg=100
nlcom (exp(1   * _b[mpg] + _cons) / (1+ exp(1   * _b[mpg] + _cons))) /  
///
      (exp(100 * _b[mpg] + _cons) / (1+ exp(100 * _b[mpg] + _cons)))    
//

// Paradoxical model
logit foreign length

// Contrast probability of length=1 with length=10
nlcom (exp(1   * _b[length] + _cons) / (1+ exp(1   * _b[length] + 
_cons))) /  ///
      (exp(10  * _b[length] + _cons) / (1+ exp(10  * _b[length] + 
_cons)))     //

// Contrast probability of length=1 with length=100
nlcom (exp(1   * _b[length] + _cons) / (1+ exp(1   * _b[length] + 
_cons))) / ///
      (exp(100 * _b[length] + _cons) / (1+ exp(100 * _b[length] + 
_cons)))    //






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