R Under development (unstable) (2026-01-12 r89300 ucrt) -- "Unsuffered Consequences"
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> library(lmerTest)
Loading required package: lme4
Loading required package: Matrix

Attaching package: 'lmerTest'

The following object is masked from 'package:lme4':

    lmer

The following object is masked from 'package:stats':

    step

> 
> # Read in data set
> load(system.file("testdata","potdata.RData", package="lmerTest"))
> 
> # Mixed model
> lmerout <- lmer(biomass ~ CO2*nutrients + (1|chamber),data=potdata)
> summary(lmerout)
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: biomass ~ CO2 * nutrients + (1 | chamber)
   Data: potdata

REML criterion at convergence: 49.2

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.4159 -0.5588  0.0000  0.5588  1.4159 

Random effects:
 Groups   Name        Variance Std.Dev.
 chamber  (Intercept) 0.2437   0.4936  
 Residual             1.5797   1.2568  
Number of obs: 24, groups:  chamber, 4

Fixed effects:
                  Estimate Std. Error      df t value Pr(>|t|)    
(Intercept)        12.8500     0.9548 11.0163  13.458 3.49e-08 ***
CO2675              2.0000     1.3503 11.0163   1.481 0.166595    
nutrients2          7.3500     1.2568 10.0000   5.848 0.000162 ***
nutrients3         10.4500     1.2568 10.0000   8.314 8.39e-06 ***
nutrients4         18.6500     1.2568 10.0000  14.839 3.88e-08 ***
nutrients5         25.0500     1.2568 10.0000  19.931 2.22e-09 ***
nutrients6         29.0000     1.2568 10.0000  23.074 5.28e-10 ***
CO2675:nutrients2  -0.5000     1.7775 10.0000  -0.281 0.784214    
CO2675:nutrients3   1.9000     1.7775 10.0000   1.069 0.310218    
CO2675:nutrients4   3.4500     1.7775 10.0000   1.941 0.080949 .  
CO2675:nutrients5   5.9000     1.7775 10.0000   3.319 0.007756 ** 
CO2675:nutrients6   5.2500     1.7775 10.0000   2.954 0.014444 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) CO2675 ntrnt2 ntrnt3 ntrnt4 ntrnt5 ntrnt6 CO2675:2 CO2675:3
CO2675      -0.707                                                            
nutrients2  -0.658  0.465                                                     
nutrients3  -0.658  0.465  0.500                                              
nutrients4  -0.658  0.465  0.500  0.500                                       
nutrients5  -0.658  0.465  0.500  0.500  0.500                                
nutrients6  -0.658  0.465  0.500  0.500  0.500  0.500                         
CO2675:ntr2  0.465 -0.658 -0.707 -0.354 -0.354 -0.354 -0.354                  
CO2675:ntr3  0.465 -0.658 -0.354 -0.707 -0.354 -0.354 -0.354  0.500           
CO2675:ntr4  0.465 -0.658 -0.354 -0.354 -0.707 -0.354 -0.354  0.500    0.500  
CO2675:ntr5  0.465 -0.658 -0.354 -0.354 -0.354 -0.707 -0.354  0.500    0.500  
CO2675:ntr6  0.465 -0.658 -0.354 -0.354 -0.354 -0.354 -0.707  0.500    0.500  
            CO2675:4 CO2675:5
CO2675                       
nutrients2                   
nutrients3                   
nutrients4                   
nutrients5                   
nutrients6                   
CO2675:ntr2                  
CO2675:ntr3                  
CO2675:ntr4                  
CO2675:ntr5  0.500           
CO2675:ntr6  0.500    0.500  
> 
> an.sat <- anova(lmerout)
> anova(lmerout, ddf="lme4")
Analysis of Variance Table
              npar  Sum Sq Mean Sq  F value
CO2              1   67.86   67.86  42.9589
nutrients        5 3050.44  610.09 386.2129
CO2:nutrients    5   35.47    7.09   4.4906
> TOL <- 1e-5
> stopifnot(isTRUE(all.equal(
+   an.sat[,"DenDF"], c(2, 10, 10), tolerance=TOL
+ )))
> 
> stopifnot(isTRUE(
+   all.equal(an.sat[,"Pr(>F)"], c(0.0224955602, 1e-11, 0.020905569), tolerance=TOL)
+ ))
> 
> # if(require(pbkrtest))
> #   an.kr <- anova(lmerout, ddf="Kenward-Roger")
> #
> # TOL <- 1e-7
> # stopifnot(all.equal(an.kr[,"Pr(>F)"], c(0.0224955602, 1e-11, 0.020905569) ,
> #                     tol=TOL),
> #           all.equal(an.kr[,"DenDF"],
> #                     c(2, 10, 10) , tol=TOL),
> #           TRUE)
> 
> proc.time()
   user  system elapsed 
   1.95    0.28    2.23