mod1 = lmer(data=data, ln_duration ~ treatment + (1 | id/date/size) +
(1 | visitor), na.action=na.exclude)

Linear mixed model fit by REML
t-tests use  Satterthwaite approximations to degrees of freedom ['lmerMod']
Formula: ln_duration ~ treatment + (1 | id/date/size) +
(1 | visitor)
 Data: data

REML criterion at convergence: 248

Scaled residuals:
  Min      1Q  Median      3Q     Max
-2.7323 -0.4963 -0.0206  0.5600  3.8502

Random effects:
 Groups                             Name        Variance Std.Dev.
 display_size:(date:id)             (Intercept) 0.00000  0.0000
 date:id                            (Intercept) 0.00000  0.0000
 visitor                            (Intercept) 0.03574  0.1891
 id                                 (Intercept) 0.01164  0.1079
 Residual                                       0.20001  0.4472
Number of obs: 170, groups:
size:(date:id), 130; date:id, 128; visitor, 118; id, 58

Fixed effects:
                      Estimate Std. Error       df t value Pr(>|t|)
(Intercept)               -0.17012    0.06334 41.63000  -2.686 0.010348 *
       treatmenttreatment  0.31172    0.08135 40.27000   3.832 0.000436 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr)
    trtmnt -0.729