# Interpeting multilevel logistic regression

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)?

• 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." Dec 10, 2019 at 3:43