# Individual slopes for cross-level random slope model

my question relates to this post: Extracting slopes for cases from a mixed effects model (lme4)

with Sven Hohenstein's great explanation. My question is: how do I extract/interpret individual coefs if I have an additional 2nd level predictor? My random slope model with cross-level-interaction:

Scaled residuals:
Min      1Q  Median      3Q     Max
-5.3837 -0.4603 -0.0878  0.3895  5.1209

Random effects:
Groups   Name        Variance Std.Dev. Corr
CODE     (Intercept) 0.28950  0.5381
MZP.log     0.04025  0.2006   -0.38
Residual             0.09409  0.3067
Number of obs: 13866, groups:  CODE, 3917

Fixed effects:
Estimate Std. Error         df t value Pr(>|t|)
(Intercept)           9.925e-01  9.822e-03  3.936e+03 101.055  < 2e-16 ***
MZP.log              -1.771e-01  5.634e-03  4.615e+03 -31.432  < 2e-16 ***
ABS002P1.cgm          5.658e-03  5.767e-04  3.884e+03   9.811  < 2e-16 ***
MZP.log:ABS002P1.cgm  1.192e-03  3.235e-04  3.709e+03   3.686 0.000231 ***

Correlation of Fixed Effects:
(Intr) MZP.lg ABS002
MZP.log     -0.510
ABS002P1.cg -0.009  0.041
MZP.:ABS002  0.045 -0.223 -0.502


I get individual coefs using coef(RS.L2)\$CODE which gives:

                          (Intercept)    MZP.log   ABS002P1.cgm  MZP.log:ABS002P1.cgm
==AM0MDMx0CM4ETM0ITZmV2a   1.4243088 -0.1719496549   0.00565832          0.001192448
==AM0UDMx0SO5cDM4EDajVma   1.9458975 -0.0529674147   0.00565832          0.001192448
==AM1cDMx0SN1ATM1ITdnlGZ   0.8161014 -0.1141229315   0.00565832          0.001192448
==AM1ITM0AzV               0.4187989 -0.0886104357   0.00565832          0.001192448
==AM2ADMx0iN5kDMxEjcmVGa   1.1081334 -0.2264506549   0.00565832          0.001192448
==AM2gDMzAjR               0.8997179 -0.2053793890   0.00565832          0.001192448
==AM2IDM0AjQ               0.6851151 -0.2432147380   0.00565832          0.001192448
==AM2kDMwMDajxWZ           0.9268792 -0.0418086190   0.00565832          0.001192448
==AM2UDM3ATYtVGb           0.8382071 -0.1377587548   0.00565832          0.001192448
...


what I don't understand: are the first two columns (Intercept and MZP.Log) a combination of fixed and random effects? I assume yes, but to what part in the final equation

Yti = Beta00 + Beta10 * MZP.Log-ti + Beta01 * ABS002P1.cgm-i + Beta11 * MZP.Log-ti * ABS002P1.cgm-i + r1-i * MZP.Log-ti + r0-i + e-ti

do they refer? Would (Intercept) = Beta00 + r0-i and MZP.Log = Beta10 + r1-i? My aim is to illustrate an individual equation for a specific person (CODE).

I am deeply grateful for any help!

## 1 Answer

The thing you are missing here is the output of ranef(RS.L2).

This should give you 2 columns of numbers that are the individual random effects for each level of CODE for the intercept and MZP.log

For example, for the first level of CODE (==AM0MDMx0CM4ETM0ITZmV2a) the random effect for the intercept should be be 1.4243088 - 9.925e-01 = 0.4318088

That is the individual intercept for a particular level of CODE is equal to the global intercept plus the random effect for that level of CODE. Likewise for MZP.log

• Thank you! That's what I was thinking but wasn't sure. – 1k2a3l4m Aug 21 '20 at 10:49