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Fits many linear mixed effects models for analysis of gaussian data with random effects, with parallelisation and optimisation for speed. It is suitable for longitudinal analysis of high dimensional data. Wald type 2 Chi-squared test is used to calculate p-values.


  id = NULL,
  offset = NULL,
  test.stat = c("Wald", "F", "LRT"),
  reduced = NULL,
  modelData = NULL,
  designMatrix = NULL,
  control = lmerControl(),
  cores = 1,
  removeSingles = FALSE,
  verbose = TRUE,
  returnList = FALSE,
  progress = FALSE,



the model formula. This must be of the form "~ ..." where the structure is assumed to be "gene ~ ...". The formula must include a random effects term. See formula structure for random effects in lme4::lmer()


data matrix with genes in rows and samples in columns


a dataframe of sample information with variables in columns and samples in rows


Optional. Used to specify the column in metadata which contains the sample IDs to be used in repeated samples for random effects. If not specified, the function defaults to using the variable after the "|" in the random effects term in the formula.


Vector containing model offsets (default = NULL). If provided the lmer() offset is set to offset. See lme4::lmer()


Character value specifying test statistic. Current options are "Wald" for type 2 Wald Chi square test using code derived and modified from car::Anova to improve speed for matrix tests. Or "F" for conditional F tests using Saiterthwaite's method of approximated Df. This uses lmerTest::lmer and is somewhat slower.


Optional reduced model formula. If this is chosen, a likelihood ratio test is used to calculate p-values instead of the default Wald type 2 Chi-squared test.


Optional dataframe. Default is generated by call to expand.grid using levels of variables in the formula. Used to calculate model predictions (estimated means & 95% CI) for plotting via modelPlot. It can therefore be used to add/remove points in modelPlot.


Optional custom design matrix generated by call to model.matrix using modelData and FEformula. Used to calculate model predictions for plotting.


the lmer optimizer control (default = lmerControl()). See lme4::lmerControl().


number of cores to use for parallelisation. Default = 1.


whether to remove individuals with no repeated measures (default = FALSE)


Logical whether to display messaging (default = TRUE)


Logical whether to return results as a list or lmmSeq object (default = FALSE). Helpful for debugging.


Logical whether to display a progress bar


Other parameters passed to lmerTest::lmer(). Only available if test.stat = "F".


Returns an S4 class lmmSeq object with results for gene-wise linear mixed models; or a list of results if returnList is TRUE, which is useful for debugging. If all genes return errors from lmer, then an error message is shown and a character vector containing error messages for all genes is returned.


By default, p-values for each model term are computed using Wald type 2 Chi-squared test as per car::Anova(). The underlying code for this has been optimised for speed. However, if a reduced model formula is specified by setting reduced, then a likelihood ratio test (LRT) is performed instead using anova. This will double computation time since two LMM have to be fitted for each gene. For LRT, models being compared are optimised by maximum likelihood and not REML (REML=FALSE).

Two key methods are used to speed up computation above and beyond simple parallelisation. The first is to speed up lme4::lmer() by calling lme4::lFormula() once at the start and then updating the lFormula output with new data. The 2nd speed up is through optimised code for repeated type 2 Wald Chi-squared tests (original code was derived from car::Anova). For example, elements such as the hypothesis matrices are generated only once to reduce unnecessarily repetitive computation, and the generation of p-values from Chi-squared values is vectorised and performed at the end. F-tests using the lmerTest package have not been optimised and are therefore slower.

Parallelisation is performed using parallel::mclapply on unix/mac and parallel::parLapply on windows. Progress bars use pbmcapply::pbmclapply on unix/mac and pbapply::pblapply on windows.

The id argument is usually optional. By default the id column in the metadata is determined as the term after the bar in the random effects term of the model. Note that id is not passed to lmer. It is only really used to remove singletons from the maindata matrix and metadata dataframe. The id is also stored in the output from lmmSeq and used by plotting function modelPlot(). However, due to its flexible nature, in theory lmmSeq should allow for more than one random effect term, although this has not been tested formally. In this case, it is probably prudent to specify a value for id.


logtpm <- log2(tpm +1)
lmmtest <- lmmSeq(~ Timepoint * EULAR_6m + (1 | PATID),
                     maindata = logtpm[1:2, ],
                     metadata = metadata,
                     verbose = FALSE)
#>  [1] "info"      "formula"   "stats"     "predict"   "reduced"   "maindata" 
#>  [7] "metadata"  "modelData" "optInfo"   "errors"    "vars"      "class"