0
$\begingroup$

I am working with a dataset where the continuous independent variables are on different scales and I plan on standardizing them before running a binary logistic regression.

However, I am not sure on how to explain the co-efficients from the model after standardizing the variables.

For example, without standardizing my variables I get Exp(B) value of 1.111 for Average Rate of Return (independent variable) and I would explain it as -> For every one percent increase in average rate of return, the odds of being Retirement Ready (dependent variable) is higher by 11%. How do i interpret the model output in a similar format after using standardized variables?

$\endgroup$
  • $\begingroup$ Your problem is that your current explanation is incorrect, so investigate that first. In doing so it's likely you will obtain the answer to your question. $\endgroup$ – whuber Jun 28 '18 at 20:45
  • $\begingroup$ hi @whuber i have recently started learning predictive modeling and was looking for sources that would help me understand how to interpret and explain coefficients in a logistic regression. I found a tutorial online which explained the output like the one above. Apologies if my interpretation is wrong. It would really help me if you can point me to the right source $\endgroup$ – neha Jun 28 '18 at 21:04
  • 2
    $\begingroup$ @whuber: If Average Rate of Return is expressed as a percentage, then a 1-unit increase (i.e., one percent increase) in Average Rate of Return is associated with an 11% increase in the odds of being Retirement Ready. Not quite sure why you believe the interpretation provided in the original question is incorrect? $\endgroup$ – Isabella Ghement Jun 29 '18 at 2:53
  • 1
    $\begingroup$ @Isabella The use of "percentage increase" is ambiguous. If it were understood as an additive increase, then this question becomes trivial (since standardization merely re-expresses the same data in a different unit of measurement), so I thought it had to be understood as a multiplicative increase. $\endgroup$ – whuber Jun 29 '18 at 13:11
  • 1
    $\begingroup$ Great point, @whuber! I edited my answer below to clarify where the increase is additive. 🤗 $\endgroup$ – Isabella Ghement Jun 29 '18 at 14:19
2
$\begingroup$

Let's say Y = Being Retirement Ready, X1 = Average Rate of Return and X2 = (X1 - m1)/s1 is the standardized version of X1, where m1 is the sample mean of X1 and s1 is the sample standard deviation of X1.

Assume we fit the binary logistic regression model:

log(odds of being retirement ready) = beta0 + beta1*X1,

and obtain an estimate b1 of beta1. If exp(b1) = 1.11, say, then we can state the following:

For every 1-unit additive increase in X1 (Average Return Rate), we 
estimate that the odds of being retirement ready increase by a 
multiplicative factor of 1.11 (i.e., an 11% increase).

Next, assume we fit the binary logistic regression model:

log(odds of being retirement ready) = gamma0 + gamma1*X2, 

and obtain an estimate g1 of gamma1. If exp(g1) = 1.12, say, then we can state either of the following:

For every 1-unit additive increase in X2 (Standardized Average Return 
Rate), we estimate that the odds of being retirement ready increase by 
a multiplicative factor of 1.12 (i.e., a 12% increase).

For every s1-units additive increase in X1 (Average Return Rate), we    
estimate that the odds of being retirement ready increase by a 
multiplicative factor of 1.12 (i.e., a 12% increase).

If Average Return Rate is expressed in percentage points, then a 1-unit additive increase means a 1 percent additive increase. You need to calculate the value of s1 to figure out how many units additive increase in X1 you are dealing with (e.g., if s1 = 20%, then you are dealing with a 20 percent increase on the additive scale). You could also say, more generically, something like this:

For every standard deviation additive increase in the value of X1 
(Average Return Rate), we estimate that the odds of being retirement 
ready increase by a multiplicative factor of 1.12 (i.e., a 12% 
increase).
$\endgroup$
  • $\begingroup$ hi @Isabella Ghement thank you for the detailed explanation. This makes sense. So, if the standard deviation for the Average Rate of Return is 20% and I were to explain it in terms of a unit increase, would it be correct to infer that for every 1% additive increase in X1 (Average Return Rate), we estimate that the odds of being retirement ready increase by a multiplicative factor of 1.006 (i.e., a 0.6% increase). $\endgroup$ – neha Jul 2 '18 at 13:38
  • $\begingroup$ What odds ratio did you start out with for your calculation? $\endgroup$ – Isabella Ghement Jul 2 '18 at 13:45
  • $\begingroup$ i was using the percentage value of 12% $\endgroup$ – neha Jul 2 '18 at 13:51
  • $\begingroup$ hi @Isabella Ghement, Rephrasing my question - Given the same outcome - s1 = 20% and exp(g1) = 1.12, What would the multiplicative factor be if I were to explain the result in terms of every 1 unit additive increase in X1 (Average Return Rate) instead of s1-units additive increase? $\endgroup$ – neha Jul 2 '18 at 15:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.