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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?

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  • $\begingroup$ 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, 2018 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, 2018 at 21:04
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    $\begingroup$ @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, 2018 at 2:53
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    $\begingroup$ @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, 2018 at 13:11
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    $\begingroup$ Great point, @whuber! I edited my answer below to clarify where the increase is additive. 🤗 $\endgroup$
    – Isabella Ghement
    Jun 29, 2018 at 14:19

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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).
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  • $\begingroup$ 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, 2018 at 13:38
  • $\begingroup$ What odds ratio did you start out with for your calculation? $\endgroup$
    – Isabella Ghement
    Jul 2, 2018 at 13:45
  • $\begingroup$ i was using the percentage value of 12% $\endgroup$
    – neha
    Jul 2, 2018 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, 2018 at 15:30

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