glmer(Response~Handedness+Color+(1|Subject)+(1|Item)+(1|NumResponses),data=r1,family="binomial")

AIC  BIC logLik deviance
1733 1755 -828.9     1702
Random effects:
Groups     Name        Variance Std.Dev.
Subject         (Intercept) 2.1680   1.47243
NumResponses (Intercept) 0.0000   0.00000
Item    (Intercept) 0.4183   0.64676
Number of obs: 1708, groups: Subject, 560; NumResponses, 48; Item, 48

Fixed effects:
          Estimate Std. Error z value Pr(>|z|)
          (Intercept)               1.2097     0.2310   5.238 1.63e-07 ***
ColorGreen  -0.2254     0.3271  -0.689    0.491
ColorRed  -1.2007     0.2285  -5.254 1.49e-07 ***
HandednessLeft          1.2248     0.2189   5.595 2.20e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1