generalized mixed linear models, glmmPQL and GLMER give very different results that both do not fit the data well...

Hi,

I have the following type of data: 86 subjects in three independent 
groups (high power vs low power vs control). Each subject solves 8 
reasoning problems of two kinds: conflict problems and noconflict 
problems. I measure accuracy in solving the reasoning problems. To 
summarize: binary response, 1 within subject var (TYPE), 1 between 
subject var (POWER).

I wanted to fit the following model: for problem i, person j:
logodds ( Y_ij ) = b_0j + b_1j TYPE_ij
with b_0j = b_00 + b_01 POWER_j + u_0j
and b_1j = b_10 + b_11 POWER_j

I think it makes sense, but I'm not sure.
Here are the observed cell means:
            conflict       noconflict
control     0.6896552      0.9568966
high        0.6935484      0.9677419
low         0.8846154      0.9903846

GLMER gives me:
Formula: accuracy ~ f_power * f_type + (1 | subject)
  Data: syllogisms
Random effects:
Groups  Name        Variance Std.Dev.
subject (Intercept) 4.9968   2.2353
Number of obs: 688, groups: subject, 86

Fixed effects:
                           Estimate Std. Error z value Pr(>|z|)
(Intercept)                  1.50745    0.50507   2.985  0.00284 **
f_powerhp                    0.13083    0.70719   0.185  0.85323
f_powerlow                   2.04121    0.85308   2.393  0.01672 *
f_typenoconflict             3.28715    0.64673   5.083 3.72e-07 ***
f_powerhp:f_typenoconflict   0.21680    0.93165   0.233  0.81599
f_powerlow:f_typenoconflict -0.01199    1.45807  -0.008  0.99344
---

Strange thing is that when you convert the estimates to probabilities, 
they are quite far off. For control, no conflict (intercept), the 
estimation from glmer is 1.5 -> 81% and for glmmPQL is 1.14 -> 75%, 
whereas the observed is: 68%.

Am I doing something wrong?