lme4

I am working with an r code procedure for a ARFIMA mutilevel model that
estimates a
linear mixed model fit by REMLP['lmermod']. I have now been asked to
compare the model's results with alternatives that include ARFIMA-LDV.
The only output diagnostics that the code provides in addition to
parameter estimates is shown below :

???? " REML criterion at convergence: 1694929 Scaled residuals:
???? Min 1Q Median 3Q Max -3.4407 -0.7361 0.0482 0.7791 2.9853

???? Random effects: Groups Name Variance Std.Dev.? time
???? (Intercept) 42.5 6.519 Residual 1229.0 35.057 Number of
???? obs: 170217, groups: time, 363"

I understand that REML is most directly about estimatingvariance
components, but is it meaningful to consider it
?as a measure of fit in comparing nested models. Here the alternatives
are LDV and an MLM that is not fractionally differenced.

Given the difference in estimation methodology, I do not think it is
feasible to compare 'lmermod' with alternatives in OLS.Do any comparable
model variants for comparison in the estimation procedure of lme4 come
to mind ?

Would be grateful for any observations that you could provide.

Steven