3
$\begingroup$

I ran a multilevel logistic regression, and I rescaled the variables using the scale function. The variables in my data set are centered around the mean and rescaled.

Below are my results:

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: allbuster0 ~ lageutradeshare100 + lagtradeopenP + colonial +  
    lagsitc0100 + lnlaggdpp + lnlaggdpt + duration + lndist +  
    lagtradecontrol0 + nobust0 + nobust0sq + nobust0cb + (1 |  
    YearID) + (1 | partnercode) + (1 | caseid)
   Data: multi.sanctions.bust0a.full@frame
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

     AIC      BIC   logLik deviance df.resid 
  3304.8   3417.3  -1636.4   3272.8     8343 

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-3.380 -0.231 -0.110 -0.058 38.171 

Random effects:
 Groups      Name        Variance Std.Dev.
 caseid      (Intercept) 0.3006   0.5483  
 YearID      (Intercept) 0.1861   0.4314  
 partnercode (Intercept) 0.7699   0.8774  
Number of obs: 8359, groups:  caseid, 93; YearID, 28; partnercode, 25

Fixed effects:
                    Estimate Std. Error z value Pr(>|z|)    
(Intercept)        -4.196786   0.324192 -12.945  < 2e-16 ***
lageutradeshare100 -0.254297   0.142502  -1.785 0.074340 .  
lagtradeopenP       0.607378   0.175615   3.459 0.000543 ***
colonial1           1.356447   0.202574   6.696 2.14e-11 ***
lagsitc0100         0.300612   0.074151   4.054 5.03e-05 ***
lnlaggdpp           0.859417   0.277255   3.100 0.001937 ** 
lnlaggdpt          -0.304214   0.089577  -3.396 0.000683 ***
duration           -0.032064   0.114298  -0.281 0.779074    
lndist             -0.324538   0.077989  -4.161 3.16e-05 ***
lagtradecontrol0    0.009115   0.088184   0.103 0.917678    
nobust0            -1.679246   0.285480  -5.882 4.05e-09 ***
nobust0sq           1.433486   0.726499   1.973 0.048480 *  
nobust0cb          -0.541682   0.545776  -0.992 0.320954    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

My question is: how do I interpret the coefficients when the data is rescaled?

The variable that I am interested in is lageutradeshare100. When it is not rescaled, it is a percentage. Is the 1 unit increase now 1 standard deviation of the variable rather than the variable's original units (in this case, percent)?

$\endgroup$
  • 2
    $\begingroup$ This question is about statistics, not programming, so it belongs on stats.stackexchange. But the short answer is "yes, that's what scaling by the standard deviation does to your interpretation." $\endgroup$ – Gregor Thomas Dec 10 '19 at 3:43
3
$\begingroup$

Is the 1 unit increase now 1 standard deviation of the variable rather than the variable's original units (in this case, percent)?

Short answer, yes, although you can simply reverse the scaling and interpret the coefficients in the usual way.

Longer answer: with untransformed data, a one unit (on the original scale of the variable) change in the variable is associated with a change in the log-odds of whatever the estimated regression coefficient for that variable is.

With a standardised variable (rescaled to have a zero mean and unit variance) one unit of the rescaled variable corresponds to one standard deviation, so a 1 SD change in the rescaled variable is associated with a change in the log-odds of whatever the estimated regression coefficient for that variable is. In order to aid in interpretation, the coefficients can be back-transformed, by multiplying by the original standard deviation and adding the original mean. Then the coefficients can be interpreted in the usual manner.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ So if the log odds for a standardized coefficient is 0.45, the original standard deviation is 1.86, and the original mean is 11, I would multiply 1.86*0.45 and then add the mean? $\endgroup$ – Keith Jan 5 at 3:27
  • 1
    $\begingroup$ Yes indeed, that is correct $\endgroup$ – Robert Long Jan 5 at 9:18

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.