# 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 )
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 ***
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." – Gregor Thomas Dec 10 '19 at 3:43