Contrast Tests in 1D

Compute the test of a one-dimensional (vector) contrast in a linear mixed model fitted with lmer from package lmerTest. The contrast should specify a linear function of the mean-value parameters, beta. The Satterthwaite or Kenward-Roger method is used to compute the (denominator) df for the t-test.

# S3 method for class 'lmerModLmerTest'
contest1D(
  model,
  L,
  rhs = 0,
  ddf = c("Satterthwaite", "Kenward-Roger"),
  confint = FALSE,
  level = 0.95,
  ...
)

# S3 method for class 'lmerMod'
contest1D(
  model,
  L,
  rhs = 0,
  ddf = c("Satterthwaite", "Kenward-Roger"),
  confint = FALSE,
  level = 0.95,
  ...
)

Arguments

model

a model object fitted with lmer from package lmerTest, i.e., an object of class lmerModLmerTest.

L

a numeric (contrast) vector of the same length as fixef(model).

rhs

right-hand-side of the statistical test, i.e. the hypothesized value (a numeric scalar).

ddf

the method for computing the denominator degrees of freedom. ddf="Kenward-Roger" uses Kenward-Roger's method.

confint

include columns for lower and upper confidence limits?

level

confidence level.

...

currently not used.

Value

A data.frame with one row and columns with "Estimate", "Std. Error", "t value", "df", and "Pr(>|t|)" (p-value). If confint = TRUE "lower" and "upper" columns are included before the p-value column.

Details

The t-value and associated p-value is for the hypothesis \(L' \beta = \mathrm{rhs}\) in which rhs may be non-zero and \(\beta\) is fixef(model). The estimated value ("Estimate") is \(L' \beta\) with associated standard error and (optionally) confidence interval.

See also

contest for a flexible and general interface to tests of contrasts among fixed-effect parameters. contestMD is also available as a direct interface for tests of multi degree-of-freedom contrast.

Author

Rune Haubo B. Christensen

Examples

# Fit model using lmer with data from the lme4-package:
data("sleepstudy", package="lme4")
fm <- lmer(Reaction ~ Days + (1 + Days|Subject), sleepstudy)

# Tests and CI of model coefficients are obtained with:
contest1D(fm, c(1, 0), confint=TRUE) # Test for Intercept
#>   Estimate Std. Error       df  t value    lower    upper     Pr(>|t|)
#> 1 251.4051   6.824597 16.99973 36.83809 237.0064 265.8038 1.171558e-17
contest1D(fm, c(0, 1), confint=TRUE) # Test for Days
#>   Estimate Std. Error       df  t value    lower    upper     Pr(>|t|)
#> 1 10.46729    1.54579 16.99998 6.771481 7.205955 13.72862 3.263824e-06

# Tests of coefficients are also part of:
summary(fm)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: Reaction ~ Days + (1 + Days | Subject)
#>    Data: sleepstudy
#> 
#> REML criterion at convergence: 1743.6
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -3.9536 -0.4634  0.0231  0.4634  5.1793 
#> 
#> Random effects:
#>  Groups   Name        Variance Std.Dev. Corr
#>  Subject  (Intercept) 612.10   24.741       
#>           Days         35.07    5.922   0.07
#>  Residual             654.94   25.592       
#> Number of obs: 180, groups:  Subject, 18
#> 
#> Fixed effects:
#>             Estimate Std. Error      df t value Pr(>|t|)    
#> (Intercept)  251.405      6.825  17.000  36.838  < 2e-16 ***
#> Days          10.467      1.546  17.000   6.771 3.26e-06 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Correlation of Fixed Effects:
#>      (Intr)
#> Days -0.138

# Illustrate use of rhs argument:
contest1D(fm, c(0, 1), confint=TRUE, rhs=10) # Test for Days-coef == 10
#>   Estimate Std. Error       df  t value    lower    upper  Pr(>|t|)
#> 1 10.46729    1.54579 16.99998 0.302296 7.205955 13.72862 0.7660937