Fast Linear Mixed Model with 1 Random Effect

Fit a linear mixed-effects model with 1 random effect with REML or maximum likelihood using the very fast algorithm and implementation

Usage

fastlmm(
  formula,
  data,
  REML = FALSE,
  delta = NULL,
  weights = NULL,
  delta.range = c(-10, 10),
  tol = 1e-06,
  nthreads = 6,
  lambda = 0
)

Arguments

formula: a two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars (|) separating expressions for design matrices from grouping factors.
data: an optional data frame containing the variables named in
REML: logical scalar - Should the estimates be chosen to optimize the REML criterion vs ML?
delta: if NULL estimate delta, if value is given use this fixed value
weights: an optional vector of prior weights with a value for each sample. When the response has multiple columns, a vector of weight can be reused for each respose, or a matrix the same dimension as the responses matrix can weight each response separately.
delta.range: min and max values (in log space), of the search space for delta to fit the random effect
tol: convergence criterion for the 1D search of the delta space
nthreads: number of threads
lambda: ridge shrinkage parameter

Details

Hoffman (2013), Lippert, et al. (2011)

References

Hoffman, G. E. (2013). Correcting for population structure and kinship using the linear mixed model: theory and extensions. PloS one, 8(10), e75707. doi:10.1371/journal.pone.0075707

Lippert, C., Listgarten, J., Liu, Y., Kadie, C. M., Davidson, R. I., & Heckerman, D. (2011). FaST linear mixed models for genome-wide association studies. Nature methods, 8(10), 833-835. doi:10.1038/nmeth.1681

Examples

library(lme4)

fit <- fastlmm(Reaction ~ Days + (1 | Subject), sleepstudy)

fit
#> 
#> Call:
#> fastlmm(formula = Reaction ~ Days + (1 | Subject), data = sleepstudy)
#> 
#> Coefficients:
#> (Intercept)         Days  
#>      251.41        10.47  
#> 

summary(fit)
#> Linear mixed model fit by ML ['fastlmm']
#>  Formula: Reaction ~ Days + (1 | Subject)
#> 
#> Coefficients:
#>             Estimate Std. Error    df t value Pr(>|t|)    
#> (Intercept) 251.4051     9.5062  24.5   26.45   <2e-16 ***
#> Days         10.4673     0.8017 162.0   13.06   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual df: 162.2 
#> 
#> Variance components:
#>   sigSq_g: 1297
#>   sigSq_e: 954.5
#>   delta:   0.736

# results are identical for lmer(...,REML=FALSE)
fit2 <- lmer(Reaction ~ Days + (1 | Subject), sleepstudy, REML = FALSE)
coef(summary(fit2))
#>              Estimate Std. Error  t value
#> (Intercept) 251.40510  9.5061852 26.44648
#> Days         10.46729  0.8017354 13.05579