Correct interpretation of Lmer output

#1
I have produced the following model

lmer(TotalPayoff~PgvnD*Type+Type*Asym+PgvnD*Asym+Game*Type+Game*PgvnD+Game*Asym+(1|Subject)+(1|Pairing),REML=FALSE,data=table1)->m1

PgvnD=A percentage (numeric) Asym= a factor 0 or 1 Type=a factor 1 or 2 Game= a factor 1 or 2

from this model the terms Type,Game and PgvnD:Asym were shown to be significant by removal from the model. PgvnD and Asym on there own were not significant but were left in the model because the interaction between them was. The summary of this model is as follows;

m7 Linear mixed model fit by maximum likelihood Formula: TotalPayoff ~ Type + PgvnD * Asym + Game + (1 | Subject) + (1 | Pairing) Data: table1 AIC BIC logLik deviance REMLdev 1014 1038 -497.8 995.6 964.4 Random effects: Groups Name Variance Std.Dev. Subject (Intercept) 0.000 0.0000 Pairing (Intercept) 716.101 26.7601 Residual 89.364 9.4533 Number of obs: 113, groups: Subject, 73; Pairing, 61

Fixed effects: Estimate Std. Error t value (Intercept) 81.727 6.332 12.907 Type2 7.926 2.852 2.779 PgvnD -8.466 7.554 -1.121 Asym1 -12.167 7.583 -1.604 Game2 15.374 7.147 2.151 PgvnD:Asym1 26.618 9.710 2.741

Correlation of Fixed Effects: (Intr) Type2 PgvnD Asym1 Game2 Type2 -0.188
PgvnD -0.218 -0.038
Asym1 -0.620 0.081 0.189
Game2 -0.483 0.009 -0.010 -0.015
PgvnD:Asym1 0.233 -0.267 -0.766 -0.328 -0.011

Am I interpreting these results correctly?

TotalPayoff is higher when Type=1 than in Type=2, it is also higher when game=2 than when game=1. Also TotalPayoff increases significantly with PgvnD if Asym=1 but not if ASym=0 (indicated by significant interaction term but non-significant single terms).

Also I notice that the Subject random effect has SD and variance of 0. Can this then be removed from the model. What doe this really mean??

Thanks, Jonathan