[R] lmer model building--include random effects?

[Ista Zahn]

Hello,
This is a follow up question to my previous one http://tolstoy.newcastle.edu.au/R/e4/help/08/02/3600.html

I am attempting to model relationship satisfaction (MAT) scores  
(measurements at 5 time points), using participant (spouseID) and  
couple id (ID) as grouping variables, and time (years) and conflict  
(MCI.c) as predictors. I have been instructed to include random  
effects for the slopes of both predictors as well as the intercepts,  
and then to drop non-significant random effects from the model. The  
instructor and the rest of the class is using HLM 6.0, which gives p- 
values for random effects, and the procedure is simply to run a model,  
note which random effects are not significant, and drop them from the  
model. I was hoping I could to something analogous by using the anova  
function to compare models with and without a particular random  
effect, but I get dramatically different results than those obtained  
with HLM 6.0.

For example, I wanted to determine if I should include a random effect  
for the variable "MCI.c" (at the couple level), so I created two  
models, one with and one without, and compared them:

 > m.3 <- lmer(MAT ~ 1 + years + MCI.c + (1 + years | spouseID) + (1 +  
years + MCI.c | ID), data=Data, method = "ML")
 > m.1 <- lmer(MAT ~ 1 + years + MCI.c  + (1 + years + MCI.c |  
spouseID) + (1 + years + MCI.c | ID), data=Data, method = "ML")
 > anova(m.1, m.3)
Data: Data
Models:
m.3: MAT ~ 1 + years + MCI.c + (1 + years | spouseID) + (1 + years +
m.1:     MCI.c | ID)
m.3: MAT ~ 1 + years + MCI.c + (1 + years + MCI.c | spouseID) + (1 +
m.1:     years + MCI.c | ID)
     Df     AIC     BIC  logLik  Chisq Chi Df Pr(>Chisq)
m.3 12  5777.8  5832.7 -2876.9
m.1 15  5780.9  5849.5 -2875.4 2.9428      3     0.4005

The corresponding output from HLM 6.0 reads

  Random Effect           Standard      Variance     df    Chi- 
square   P-value
                          Deviation     Component
   
------------------------------------------------------------------------------
  INTRCPT1,       R0      6.80961      46.37075      60      
112.80914    0.000
     YEARS slope, R1      1.49329       2.22991      60       
59.38729    >.500
       MCI slope, R2      5.45608      29.76881      60       
90.57615    0.007
   
------------------------------------------------------------------------------

To me, this seems to indicate that HLM 6.0 is suggesting that the  
random effect should be included in the model, while R is suggesting  
that it need not be. This is not (quite) a "why do I get different  
results with X" post, but rather an "I'm worried that I might be doing  
something wrong" post. Does what I've done look reasonable? Is there a  
better way to go about it?

Thank you very much for reading this, and for any advice.
-Ista