R Under development (unstable) (2026-01-12 r89300 ucrt) -- "Unsuffered Consequences"
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> # test_zerovar.R
> 
> 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

> data("sleepstudy", package="lme4")
> 
> # Baseline fit:
> m0 <- lmer(Reaction ~ Days +  (Days | Subject), sleepstudy,
+            control=lmerControl(optimizer="bobyqa"))
> ## default optimizer does not converge proporly
> m0
Linear mixed model fit by REML ['lmerModLmerTest']
Formula: Reaction ~ Days + (Days | Subject)
   Data: sleepstudy
REML criterion at convergence: 1743.628
Random effects:
 Groups   Name        Std.Dev. Corr
 Subject  (Intercept) 24.740       
          Days         5.922   0.07
 Residual             25.592       
Number of obs: 180, groups:  Subject, 18
Fixed Effects:
(Intercept)         Days  
     251.41        10.47  
> (an0 <- anova(m0))
Type III Analysis of Variance Table with Satterthwaite's method
     Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days  30031   30031     1    17  45.853 3.264e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # Make a fit with a zero variance estimate:
> n <- nrow(sleepstudy)
> g <- factor(rep(1:2, c(n - 10, 10)))
> m <- lmer(Reaction ~ Days +  (Days | Subject) + (1|g), sleepstudy,
+           control=lmerControl(optimizer="bobyqa"))
boundary (singular) fit: see help('isSingular')
> m
Linear mixed model fit by REML ['lmerModLmerTest']
Formula: Reaction ~ Days + (Days | Subject) + (1 | g)
   Data: sleepstudy
REML criterion at convergence: 1743.628
Random effects:
 Groups   Name        Std.Dev. Corr
 Subject  (Intercept) 24.740       
          Days         5.922   0.07
 g        (Intercept)  0.000       
 Residual             25.592       
Number of obs: 180, groups:  Subject, 18; g, 2
Fixed Effects:
(Intercept)         Days  
     251.41        10.47  
optimizer (bobyqa) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings 
> (an <- anova(m))
Type III Analysis of Variance Table with Satterthwaite's method
     Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days  30031   30031     1    17  45.853 3.264e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # check that fit has a zero variance
> vc <- as.data.frame(VarCorr(m))
> stopifnot(isTRUE(
+   all.equal(0, vc[vc$grp == "g", "sdcor"], tolerance=1e-4)
+ ))
> # The hessian/vcov is actually positive definite:
> stopifnot(isTRUE(
+   all(eigen(m@vcov_varpar, only.values = TRUE)$values > 0)
+ ))
> 
> # Check that ANOVA tables are the same:
> stopifnot(isTRUE(
+   all.equal(an0[, 1:5], an[, 1:5], tolerance=1e-4)
+ ))
> 
> stopifnot(isTRUE( # Equality of summary tables
+   all.equal(coef(summary(m0)), coef(summary(m)), tolerance=1e-4)
+ ))
> stopifnot(isTRUE( # Equality of lme4-anova tables
+   all.equal(anova(m0, ddf="lme4"), anova(m, ddf="lme4"), tolerance=1e-4)
+ ))
> 
> 
> proc.time()
   user  system elapsed 
   2.54    0.20    2.73