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I would like to share some of my thoughts when trying to improve the model fitting time of a linear mixed effects model in R using the lme4 package.
Dataset Size: The dataset consists, approximately, of 400.000 rows and 32 columns. Unfortunately, no information can be shared about the nature of the data.
Assumptions and Checks: It is assumed that the response variable comes from a Normal distribution. Prior to the model fitting process, variables were tested for collinearity and multicollinearity using correlation tables and the alias function provided in R.
Continuous variables were scaled in order to help convergence.
Model Structure: The model equation contains 31 fixed effects (including intercept) and 30 random effects (intercept is not included). Random effects are randomized for a specific factor variable that has 2700 levels. The covariance structure is Variance Components as it is assumed that there is independency between random effects.
Model equation example:
lmer(Response ~ 1 + Var1 + Var2 + ... + Var30 + (Var1-1| Group) + (Var2-1| Group) + ... + (Var30-1| Group), data=data, REML=TRUE)
Model was fitted successfully, however, it took about 3,1 hours to provide results. The same model in SAS took a few seconds. There is available literature on the web on how to reduce time by using the non-linear optimization algorithm nloptwrap and turnining off the time consuming derivative calculation that is performed after the optmization is finished calc.derivs = FALSE:
https://cran.r-project.org/web/packages/lme4/vignettes/lmerperf.html
Time was reduced by 78%.
Question: Is there any other alternative way to reduce the model fitting time by defining the lmer parameter inputs accordingly? There is so much difference between R and SAS in terms of model fitting time.
Any suggestion is appreciated.
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Mixed-model formulas. Like most model-fitting functions in R, lmer takes as its first two arguments a formula spec- ifying the model and the data with which to evaluate the formula. This second argument, data, is optional but recommended and is usually the name of an R data frame.
The lmer() function is for linear mixed models and the glmer() function is for generalized mixed models.
The second option tells glmer to fit using the "nloptwrap" optimizer (there are several other optimizers available, too), which tends to be faster than the default optimization method. The impact can be rather startling. With the default options the above model takes about 3 hours to fit.
lme4 automatically constructs the random effects model matrix (Z) as a sparse matrix. At present it does not allow an option for a sparse fixed-effects model matrix (X), which is useful if the fixed-effect model includes factors with many levels.
lmer() determines the parameter estimates by optimizing the profiled log-likehood or profiled REML criterion with respect to the parameters in the covariance matrix of the random effects. In your example there will be 31 such parameters, corresponding to the standard deviations of the random effects from each of the 31 terms. Constrained optimizations of that size take time.
It is possible that SAS PROC MIXED has specific optimization methods or has more sophisticated ways of determining starting estimates. SAS being a closed-source system means we won't know what they do.
By the way, you can write the random effects as (1+Var1+Var2+...+Var30||Group)
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We have implemented random intercepts regression assuming compound symmetry in the R package Rfast. The command is rint.reg. It is 30+ times faster than the corresponding lme4 function. I do not know if this helps, but just in case.
https://cran.r-project.org/web/packages/Rfast/index.html
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