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> # test_ranova.R
> 
> # Test functionality _before_ attaching lmerTest
> stopifnot(!"lmerTest" %in% .packages()) # ensure that lmerTest is NOT attached
> data("sleepstudy", package="lme4")
> f <- function(form, data) lmerTest::lmer(form, data=data)
> form <- "Reaction ~ Days + (Days|Subject)"
> fm <- f(form, data=sleepstudy)
> lmerTest::ranova(fm)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (Days | Subject)
                         npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      6 -871.81 1755.6                         
Days in (Days | Subject)    4 -893.23 1794.5 42.837  2   4.99e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> lmerTest::rand(fm)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (Days | Subject)
                         npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      6 -871.81 1755.6                         
Days in (Days | Subject)    4 -893.23 1794.5 42.837  2   4.99e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> lmerTest::step(fm)
Backward reduced random-effect table:

                         Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)
<none>                                 6 -871.81 1755.6                     
Days in (Days | Subject)          0    4 -893.23 1794.5 42.837  2   4.99e-10
                            
<none>                      
Days in (Days | Subject) ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days          0  30031   30031     1    17  45.853 3.264e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (Days | Subject)
> 
> 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

> 
> # WRE says "using if(requireNamespace("pkgname")) is preferred, if possible."
> # even in tests:
> assertError <- function(expr, ...)
+   if(requireNamespace("tools")) tools::assertError(expr, ...) else invisible()
> assertWarning <- function(expr, ...)
+   if(requireNamespace("tools")) tools::assertWarning(expr, ...) else invisible()
> 
> TOL <- 1e-4
> #####################################################################
> data("sleepstudy", package="lme4")
> 
> # Test reduction of (Days | Subject) to (1 | Subject):
> fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
> (an <- rand(fm1)) # 2 df test
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (Days | Subject)
                         npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      6 -871.81 1755.6                         
Days in (Days | Subject)    4 -893.23 1794.5 42.837  2   4.99e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> (an <- ranova(fm1)) # 2 df test
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (Days | Subject)
                         npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      6 -871.81 1755.6                         
Days in (Days | Subject)    4 -893.23 1794.5 42.837  2   4.99e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step(fm1)
Backward reduced random-effect table:

                         Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)
<none>                                 6 -871.81 1755.6                     
Days in (Days | Subject)          0    4 -893.23 1794.5 42.837  2   4.99e-10
                            
<none>                      
Days in (Days | Subject) ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days          0  30031   30031     1    17  45.853 3.264e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (Days | Subject)
> stopifnot(
+   nrow(an) == 2L,
+   an[2L, "Df"] == 2L
+ )
> 
> # This test can also be achieved with anova():
> fm2 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy)
> (stp <- step(fm2))
Backward reduced random-effect table:

              Eliminated npar  logLik    AIC   LRT Df Pr(>Chisq)    
<none>                      4 -893.23 1794.5                        
(1 | Subject)          0    3 -946.83 1899.7 107.2  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days          0 162703  162703     1   161   169.4 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (1 | Subject)
> get_model(stp)
Linear mixed model fit by REML ['lmerModLmerTest']
Formula: Reaction ~ Days + (1 | Subject)
   Data: sleepstudy
REML criterion at convergence: 1786.465
Random effects:
 Groups   Name        Std.Dev.
 Subject  (Intercept) 37.12   
 Residual             30.99   
Number of obs: 180, groups:  Subject, 18
Fixed Effects:
(Intercept)         Days  
     251.41        10.47  
> (ana <- anova(fm1, fm2, refit=FALSE))
Data: sleepstudy
Models:
fm2: Reaction ~ Days + (1 | Subject)
fm1: Reaction ~ Days + (Days | Subject)
    npar    AIC    BIC  logLik -2*log(L)  Chisq Df Pr(>Chisq)    
fm2    4 1794.5 1807.2 -893.23    1786.5                         
fm1    6 1755.6 1774.8 -871.81    1743.6 42.837  2   4.99e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> stopifnot(
+   all.equal(an[2L, "LRT"], ana[2L, "Chisq"], tolerance=TOL)
+ )
> 
> # Illustrate complete.test argument:
> # Test removal of (Days | Subject):
> (an <- ranova(fm1, reduce.terms = FALSE)) # 3 df test
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (Days | Subject)
                 npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>              6 -871.81 1755.6                         
(Days | Subject)    3 -946.83 1899.7 150.03  3  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # The likelihood ratio test statistic is in this case:
> fm3 <- lm(Reaction ~ Days, sleepstudy)
> LRT <- 2*c(logLik(fm1, REML=TRUE) - logLik(fm3, REML=TRUE)) # LRT
> stopifnot(
+   nrow(an) == 2L,
+   an[2L, "Df"] == 3L,
+   all.equal(an[2L, "LRT"], LRT, tolerance=TOL)
+ )
> 
> ## _NULL_ model:
> fm <- lmer(Reaction ~ -1 + (1|Subject), sleepstudy)
> step(fm)
Backward reduced random-effect table:

              Eliminated npar   logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      2  -992.84 1989.7                         
(1 | Subject)          0    1 -1284.32 2570.7 582.97  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value Pr(>F)

Model found:
Reaction ~ -1 + (1 | Subject)
> ranova(fm)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ -1 + (1 | Subject)
              npar   logLik    AIC    LRT Df Pr(>Chisq)    
<none>           2  -992.84 1989.7                         
(1 | Subject)    1 -1284.32 2570.7 582.97  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> lm1 <- lm(Reaction ~ 0, data=sleepstudy)
> LRT <- 2*c(logLik(fm, REML=FALSE) - logLik(lm1, REML=FALSE))
> 
> ## Tests of ML-fits agree with anova():
> fm1 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy, REML=FALSE)
> step(fm1)
Backward reduced random-effect table:

              Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      4 -897.04 1802.1                         
(1 | Subject)          0    3 -950.15 1906.3 106.21  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days          0 162703  162703     1   162  170.45 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (1 | Subject)
> lm2 <- lm(Reaction ~ Days, sleepstudy)
> (an1 <- ranova(fm1))
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (1 | Subject)
              npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>           4 -897.04 1802.1                         
(1 | Subject)    3 -950.15 1906.3 106.21  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> (an2 <- anova(fm1, lm2))
Data: sleepstudy
Models:
lm2: Reaction ~ Days
fm1: Reaction ~ Days + (1 | Subject)
    npar    AIC    BIC  logLik -2*log(L)  Chisq Df Pr(>Chisq)    
lm2    3 1906.3 1915.9 -950.15    1900.3                         
fm1    4 1802.1 1814.8 -897.04    1794.1 106.21  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> j <- grep("Chi Df|Df", colnames(an2))
> stopifnot(
+   all.equal(an1[2, "LRT"], an2[2, "Chisq"], tolerance=TOL),
+   all.equal(an1[2, "Df"], an2[2, j[length(j)]], tolerance=TOL),
+   all.equal(an1[1:2, "logLik"], an2[2:1, "logLik"], tolerance=TOL)
+ )
> ## Note that lme4 version <1.1-22 use "Chi Df" while >=1.1-22 use "Df"
> 
> # Expect warnings when old (version < 3.0-0) arguments are used:
> assertWarning(step(fm, reduce.fixed = FALSE, reduce.random = FALSE,
+                    type=3, fixed.calc = FALSE, lsmeans.calc = FALSE,
+                    difflsmeans.calc = TRUE, test.effs = 42, keep.e="save"))
> assertWarning(step(fm, reduce.fixed = FALSE, reduce.random = FALSE,
+                    lsmeans=3))
> 
> 
> check_nrow <- function(obj, expect_nrow) {
+   stopifnot(
+     is.numeric(expect_nrow),
+     nrow(obj) == expect_nrow
+   )
+ }
> 
> # Statistical nonsense, but it works:
> fm1 <- lmer(Reaction ~ Days + (1 | Subject) + (0 + Days|Subject), sleepstudy)
> step(fm1)
Backward reduced random-effect table:

                             Eliminated npar  logLik    AIC    LRT Df
<none>                                     5 -871.83 1753.7          
(1 | Subject)                         0    4 -883.26 1774.5 22.856  1
Days in (0 + Days | Subject)          0    4 -893.23 1794.5 42.796  1
                             Pr(>Chisq)    
<none>                                     
(1 | Subject)                 1.746e-06 ***
Days in (0 + Days | Subject)  6.076e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
Days          0  29442   29442     1 18.156  45.046 2.594e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
> (an <- ranova(fm1))
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
                             npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                          5 -871.83 1753.7                         
(1 | Subject)                   4 -883.26 1774.5 22.856  1  1.746e-06 ***
Days in (0 + Days | Subject)    4 -893.23 1794.5 42.796  1  6.076e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> check_nrow(an, 3)
> ranova(fm1, reduce.terms = FALSE)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
                     npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                  5 -871.83 1753.7                         
(1 | Subject)           4 -883.26 1774.5 22.856  1  1.746e-06 ***
(0 + Days | Subject)    4 -893.23 1794.5 42.796  1  6.076e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # Statistical nonsense, but it works:
> fm1 <- lmer(Reaction ~ Days + (0 + Days|Subject), sleepstudy)
> step(fm1)
Backward reduced random-effect table:

                             Eliminated npar  logLik    AIC   LRT Df Pr(>Chisq)
<none>                                     4 -883.26 1774.5                    
Days in (0 + Days | Subject)          0    4 -893.23 1794.5 19.94  0           

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)    
Days          0  26395   26395     1 21.679  31.347 1.32e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (0 + Days | Subject)
> (an <- ranova(fm1)) # no test of non-nested models
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (0 + Days | Subject)
                             npar  logLik    AIC   LRT Df Pr(>Chisq)
<none>                          4 -883.26 1774.5                    
Days in (0 + Days | Subject)    4 -893.23 1794.5 19.94  0           
> stopifnot(
+   nrow(an) == 2L,
+   an[2L, "Df"] == 0,
+   all(is.na(an[2L, "Pr(>Chisq)"]))
+ )
> fm0 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy)
> step(fm0)
Backward reduced random-effect table:

              Eliminated npar  logLik    AIC   LRT Df Pr(>Chisq)    
<none>                      4 -893.23 1794.5                        
(1 | Subject)          0    3 -946.83 1899.7 107.2  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days          0 162703  162703     1   161   169.4 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (1 | Subject)
> (an2 <- anova(fm1, fm0, refit=FALSE))
Data: sleepstudy
Models:
fm1: Reaction ~ Days + (0 + Days | Subject)
fm0: Reaction ~ Days + (1 | Subject)
    npar    AIC    BIC  logLik -2*log(L) Chisq Df Pr(>Chisq)
fm1    4 1774.5 1787.3 -883.26    1766.5                    
fm0    4 1794.5 1807.2 -893.23    1786.5     0  0           
> stopifnot(
+   (packageVersion("lme4")<="1.1.23" && an2[2L, "Pr(>Chisq)"] == 1) ||
+     is.na(an2[2L, "Pr(>Chisq)"])
+ )
> ranova(fm1, reduce.terms = FALSE)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (0 + Days | Subject)
                     npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                  4 -883.26 1774.5                         
(0 + Days | Subject)    3 -946.83 1899.7 127.14  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> fm1 <- lmer(Reaction ~ Days + (-1 + Days|Subject), sleepstudy)
> step(fm1)
Backward reduced random-effect table:

                              Eliminated npar  logLik    AIC   LRT Df
<none>                                      4 -883.26 1774.5         
Days in (-1 + Days | Subject)          0    4 -893.23 1794.5 19.94  0
                              Pr(>Chisq)
<none>                                  
Days in (-1 + Days | Subject)           

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)    
Days          0  26395   26395     1 21.679  31.347 1.32e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (-1 + Days | Subject)
> (an3 <- ranova(fm1)) # no test of non-nested models
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (-1 + Days | Subject)
                              npar  logLik    AIC   LRT Df Pr(>Chisq)
<none>                           4 -883.26 1774.5                    
Days in (-1 + Days | Subject)    4 -893.23 1794.5 19.94  0           
> stopifnot(
+   all.equal(an, an3, check.attributes=FALSE, tolerance=TOL)
+ )
> 
> # Example where comparison of non-nested models is generated
> fm <- lmer(Reaction ~ poly(Days, 2) + (0 + poly(Days, 2) | Subject), sleepstudy)
boundary (singular) fit: see help('isSingular')
> step(fm)
Backward reduced random-effect table:

                                               Eliminated npar  logLik    AIC
<none>                                                       7 -937.05 1888.1
poly(Days, 2) in (0 + poly(Days, 2) | Subject)          1    5 -884.67 1779.3
(1 | Subject)                                           0    4 -938.16 1884.3
                                                   LRT Df Pr(>Chisq)    
<none>                                                                  
poly(Days, 2) in (0 + poly(Days, 2) | Subject) -104.77  2          1    
(1 | Subject)                                   106.98  1     <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

              Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
poly(Days, 2)          0 163782   81891     2   160  85.329 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ poly(Days, 2) + (1 | Subject)
> an <- ranova(fm)
> stopifnot(
+   nrow(an) == 2L,
+   an[2, "Pr(>Chisq)"] == 1
+ )
> ranova(fm, reduce.terms = FALSE) # test of nested models
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ poly(Days, 2) + (0 + poly(Days, 2) | Subject)
                              npar  logLik    AIC    LRT Df Pr(>Chisq)
<none>                           7 -937.05 1888.1                     
(0 + poly(Days, 2) | Subject)    4 -938.16 1884.3 2.2153  3     0.5289
> 
> # These models are nested, though:
> fm <- lmer(Reaction ~ poly(Days, 2) + (1 + poly(Days, 2) | Subject), sleepstudy)
> step(fm)
Backward reduced random-effect table:

                                               Eliminated npar  logLik    AIC
<none>                                                      10 -856.40 1732.8
poly(Days, 2) in (1 + poly(Days, 2) | Subject)          0    5 -884.67 1779.3
                                                  LRT Df Pr(>Chisq)    
<none>                                                                 
poly(Days, 2) in (1 + poly(Days, 2) | Subject) 56.524  5  6.338e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

              Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
poly(Days, 2)          0  24216   12108     2    17  23.367 1.323e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ poly(Days, 2) + (1 + poly(Days, 2) | Subject)
> ranova(fm)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ poly(Days, 2) + (1 + poly(Days, 2) | Subject)
                                               npar  logLik    AIC    LRT Df
<none>                                           10 -856.40 1732.8          
poly(Days, 2) in (1 + poly(Days, 2) | Subject)    5 -884.67 1779.3 56.524  5
                                               Pr(>Chisq)    
<none>                                                       
poly(Days, 2) in (1 + poly(Days, 2) | Subject)  6.338e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> fm0 <- lmer(Reaction ~ poly(Days, 2) + (1 | Subject), sleepstudy)
> step(fm0)
Backward reduced random-effect table:

              Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      5 -884.67 1779.3                         
(1 | Subject)          0    4 -938.16 1884.3 106.98  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

              Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
poly(Days, 2)          0 163782   81891     2   160  85.329 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ poly(Days, 2) + (1 | Subject)
> anova(fm0, fm, refit=FALSE)
Data: sleepstudy
Models:
fm0: Reaction ~ poly(Days, 2) + (1 | Subject)
fm: Reaction ~ poly(Days, 2) + (1 + poly(Days, 2) | Subject)
    npar    AIC    BIC  logLik -2*log(L)  Chisq Df Pr(>Chisq)    
fm0    5 1779.3 1795.3 -884.67    1769.3                         
fm    10 1732.8 1764.7 -856.40    1712.8 56.524  5  6.338e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> ranova(fm, reduce.terms = FALSE)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ poly(Days, 2) + (1 + poly(Days, 2) | Subject)
                              npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                          10 -856.40 1732.8                         
(1 + poly(Days, 2) | Subject)    4 -938.16 1884.3 163.51  6  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # A model with ||-notation:
> fm1 <- lmer(Reaction ~ Days + (Days||Subject), sleepstudy)
> step(fm1)
Backward reduced random-effect table:

                             Eliminated npar  logLik    AIC    LRT Df
<none>                                     5 -871.83 1753.7          
(1 | Subject)                         0    4 -883.26 1774.5 22.856  1
Days in (0 + Days | Subject)          0    4 -893.23 1794.5 42.796  1
                             Pr(>Chisq)    
<none>                                     
(1 | Subject)                 1.746e-06 ***
Days in (0 + Days | Subject)  6.076e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
Days          0  29442   29442     1 18.156  45.046 2.594e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + ((1 | Subject) + (0 + Days | Subject))
> ranova(fm1)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
                             npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                          5 -871.83 1753.7                         
(1 | Subject)                   4 -883.26 1774.5 22.856  1  1.746e-06 ***
Days in (0 + Days | Subject)    4 -893.23 1794.5 42.796  1  6.076e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # What about models with nested factors?
> fm <- lmer(Coloursaturation ~ TVset*Picture + (1|Assessor:TVset) + (1|Assessor),
+            data=TVbo)
> step(fm)
Backward reduced random-effect table:

                     Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                            15 -280.22 590.44                         
(1 | Assessor)                1   14 -280.27 588.53  0.090  1     0.7643    
(1 | Assessor:TVset)          0   13 -312.24 650.47 63.941  1  1.282e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

              Eliminated Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
TVset:Picture          0   13.8  2.2999     6   159  2.6761 0.01679 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Coloursaturation ~ TVset + Picture + (1 | Assessor:TVset) + TVset:Picture
> (an1 <- ranova(fm))
ANOVA-like table for random-effects: Single term deletions

Model:
Coloursaturation ~ TVset * Picture + (1 | Assessor:TVset) + (1 | Assessor)
                     npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                 15 -280.22 590.44                         
(1 | Assessor:TVset)   14 -302.61 633.22 44.777  1  2.208e-11 ***
(1 | Assessor)         14 -280.27 588.53  0.090  1     0.7643    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> fm <- lmer(Coloursaturation ~ TVset * Picture +
+              (1|Assessor/TVset), data=TVbo)
> step(fm)
Backward reduced random-effect table:

                     Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                            15 -280.22 590.44                         
(1 | Assessor)                1   14 -280.27 588.53  0.090  1     0.7643    
(1 | TVset:Assessor)          0   13 -312.24 650.47 63.941  1  1.282e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

              Eliminated Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
TVset:Picture          0   13.8  2.2999     6   159  2.6761 0.01679 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Coloursaturation ~ TVset + Picture + (1 | TVset:Assessor) + TVset:Picture
> (an2 <- ranova(fm))
ANOVA-like table for random-effects: Single term deletions

Model:
Coloursaturation ~ TVset * Picture + (1 | TVset:Assessor) + (1 | Assessor)
                     npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                 15 -280.22 590.44                         
(1 | TVset:Assessor)   14 -302.61 633.22 44.777  1  2.208e-11 ***
(1 | Assessor)         14 -280.27 588.53  0.090  1     0.7643    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> stopifnot(
+   all.equal(an1, an2, check.attributes=FALSE, tolerance=TOL)
+ )
> 
> #####################################################################
> # Test evaluation within functions, i.e. in other environments etc.
> attach(sleepstudy)
> fm <- lmer(Reaction ~ Days + (Days|Subject))
> step(fm)
Backward reduced random-effect table:

                         Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)
<none>                                 6 -871.81 1755.6                     
Days in (Days | Subject)          0    4 -893.23 1794.5 42.837  2   4.99e-10
                            
<none>                      
Days in (Days | Subject) ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

     Eliminated Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
Days          0  30031   30031     1    17  45.853 3.264e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Reaction ~ Days + (Days | Subject)
> ranova(fm) # OK
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (Days | Subject)
                         npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                      6 -871.81 1755.6                         
Days in (Days | Subject)    4 -893.23 1794.5 42.837  2   4.99e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> detach(sleepstudy)
> 
> # Evaluating in a function works:
> f <- function(form, data) lmer(form, data=data)
> form <- "Informed.liking ~ Product+Information+
+             (1|Consumer) + (1|Product:Consumer) + (1|Information:Consumer)"
> fm <- f(form, data=ham)
> ranova(fm)
boundary (singular) fit: see help('isSingular')
ANOVA-like table for random-effects: Single term deletions

Model:
Informed.liking ~ Product + Information + (1 | Consumer) + (1 | Product:Consumer) + (1 | Information:Consumer)
                           npar  logLik    AIC     LRT Df Pr(>Chisq)    
<none>                        9 -1353.9 2725.8                          
(1 | Consumer)                8 -1355.1 2726.1   2.295  1     0.1298    
(1 | Product:Consumer)        8 -1436.3 2888.6 164.753  1     <2e-16 ***
(1 | Information:Consumer)    8 -1354.5 2725.1   1.255  1     0.2626    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step_res <- step(fm)
boundary (singular) fit: see help('isSingular')
> stopifnot(
+   all(c("Sum Sq", "Mean Sq", "NumDF", "DenDF", "F value", "Pr(>F)") %in%
+         colnames(step_res$fixed))
+ )
> 
> ###########################
> # Evaluation in function without the formula:
> # Reported by Uwe Ligges 2025-01-16.
> f <- function(data) {
+   lmer(Petal.Length ~ Sepal.Length + (1|Species), data=data)
+ }
> 
> res <- f(iris)
> ranova(res) # used to fail - now it works
ANOVA-like table for random-effects: Single term deletions

Model:
Petal.Length ~ Sepal.Length + (1 | Species)
              npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>           4  -34.66  77.32                         
(1 | Species)    3 -193.84 393.68 318.36  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> data <- iris
> ranova(res) # now it works
ANOVA-like table for random-effects: Single term deletions

Model:
Petal.Length ~ Sepal.Length + (1 | Species)
              npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>           4  -34.66  77.32                         
(1 | Species)    3 -193.84 393.68 318.36  1  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> ###########################
> # Evaluation in function without the formula(2):
> # A model with ||-notation:
> f2 <- function(data) {
+   lmer(Reaction ~ Days + (Days||Subject), data)
+ }
> res <- f2(sleepstudy)
> ranova(res)
ANOVA-like table for random-effects: Single term deletions

Model:
Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
                             npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                          5 -871.83 1753.7                         
(1 | Subject)                   4 -883.26 1774.5 22.856  1  1.746e-06 ***
Days in (0 + Days | Subject)    4 -893.23 1794.5 42.796  1  6.076e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> # A model with multiple RE terms:
> f3 <- function(data) {
+   lmer(Coloursaturation ~ TVset*Picture + (1|Assessor:TVset) + (1|Assessor), data)
+ }
> res <- f3(TVbo)
> ranova(res)
ANOVA-like table for random-effects: Single term deletions

Model:
Coloursaturation ~ TVset * Picture + (1 | Assessor:TVset) + (1 | Assessor)
                     npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                 15 -280.22 590.44                         
(1 | Assessor:TVset)   14 -302.61 633.22 44.777  1  2.208e-11 ***
(1 | Assessor)         14 -280.27 588.53  0.090  1     0.7643    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> ###########################
> 
> # Check that step works when form is a character vector
> m <- lmer(form, data=ham)
> step_res <- step(m)
boundary (singular) fit: see help('isSingular')
> (drop1_table <- attr(step_res, "drop1"))
Single term deletions using Satterthwaite's method:

Model:
Informed.liking ~ Product + Information + (1 | Consumer) + (1 | Product:Consumer)
             Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
Product     19.3466  6.4489     3   240  3.8291 0.01048 *
Information  6.5201  6.5201     1   323  3.8714 0.04997 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> stopifnot(
+   all(c("Sum Sq", "Mean Sq", "NumDF", "DenDF", "F value", "Pr(>F)") %in%
+         colnames(drop1_table))
+ )
> # In version < 3.0-1.9002 attr(step_res, "drop1") picked up lme4::drop1.merMod
> # and returned an AIC table after the model had been update'd.
> 
> #####################################################################
> # Model with 2 ranef covarites:
> 
> # Model of the form (x1 + x2 | gr):
> model <- lmer(Preference ~ sens2 + Homesize + (sens1 + sens2 | Consumer)
+               , data=carrots)
boundary (singular) fit: see help('isSingular')
Warning message:
Model failed to converge with 1 negative eigenvalue: -3.1e+02 
> step(model)
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                                    Eliminated npar  logLik    AIC    LRT Df
<none>                                           10 -1874.4 3768.8          
sens1 in (sens1 + sens2 | Consumer)          1    7 -1874.5 3762.9 0.1333  3
sens2 in (sens2 | Consumer)                  0    5 -1878.0 3765.9 6.9944  2
                                    Pr(>Chisq)  
<none>                                          
sens1 in (sens1 + sens2 | Consumer)    0.98757  
sens2 in (sens2 | Consumer)            0.03028 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

         Eliminated Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
sens2             0 58.685  58.685     1 102.02 54.8236 3.888e-11 ***
Homesize          0  5.979   5.979     1 100.95  5.5852   0.02003 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + Homesize + (sens2 | Consumer)
> stopifnot(
+   nrow(ranova(model)) == 3L,
+   nrow(ranova(model, reduce.terms = FALSE)) == 2L
+ )
boundary (singular) fit: see help('isSingular')
> 
> # Model of the form (f1 + f2 | gr):
> model <- lmer(Preference ~ sens2 + Homesize + Gender +
+                 (Gender+Homesize|Consumer), data=carrots)
boundary (singular) fit: see help('isSingular')
> step(model)
Backward reduced random-effect table:

                                         Eliminated npar  logLik    AIC    LRT
<none>                                                11 -1872.3 3766.5       
Gender in (Gender + Homesize | Consumer)          1    8 -1875.1 3766.3 5.7408
Homesize in (Homesize | Consumer)                 0    6 -1878.4 3768.7 6.4705
                                         Df Pr(>Chisq)  
<none>                                                  
Gender in (Gender + Homesize | Consumer)  3    0.12493  
Homesize in (Homesize | Consumer)         2    0.03935 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

         Eliminated Sum Sq Mean Sq NumDF   DenDF F value  Pr(>F)    
Gender            1  0.632   0.632     1   91.80  0.5686 0.45275    
sens2             0 83.385  83.385     1 1129.09 75.0490 < 2e-16 ***
Homesize          0  6.212   6.212     1   97.82  5.5910 0.02003 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + Homesize + (Homesize | Consumer)
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  unable to evaluate scaled gradient
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
  See ?lme4::convergence and ?lme4::troubleshooting.
3: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  unable to evaluate scaled gradient
4: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
  See ?lme4::convergence and ?lme4::troubleshooting.
5: Model failed to converge with 1 negative eigenvalue: -2.7e-04 
> stopifnot(
+   nrow(ranova(model)) == 3L,
+   nrow(ranova(model, reduce.terms = FALSE)) == 2L
+ )
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  unable to evaluate scaled gradient
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
  See ?lme4::convergence and ?lme4::troubleshooting.
> 
> # Model of the form (-1 + f2 | gr):
> model <- lmer(Preference ~ sens2 + Homesize + Gender +
+                 (Gender -1 |Consumer), data=carrots)
Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?
> step(model)
Backward reduced random-effect table:

                                  Eliminated npar  logLik    AIC    LRT Df
<none>                                          8 -1876.4 3768.9          
Gender in (Gender - 1 | Consumer)          1    6 -1878.4 3768.7  3.863  2
(1 | Consumer)                             0    5 -1917.2 3844.5 77.714  1
                                  Pr(>Chisq)    
<none>                                          
Gender in (Gender - 1 | Consumer)      0.145    
(1 | Consumer)                        <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

         Eliminated Sum Sq Mean Sq NumDF   DenDF F value  Pr(>F)    
Gender            1  1.879   1.879     1   99.98  1.6909 0.19647    
sens2             0 83.363  83.363     1 1129.00 75.0256 < 2e-16 ***
Homesize          0  5.729   5.729     1  100.97  5.1557 0.02529 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + Homesize + (1 | Consumer)
> an1 <- ranova(model)
> an1b <- ranova(model, reduce.terms = FALSE)
> 
> model <- lmer(Preference ~ sens2 + Homesize + Gender +
+                 (0 + Gender|Consumer), data=carrots)
Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?
> step(model)
Backward reduced random-effect table:

                                  Eliminated npar  logLik    AIC    LRT Df
<none>                                          8 -1876.4 3768.9          
Gender in (0 + Gender | Consumer)          1    6 -1878.4 3768.7  3.863  2
(1 | Consumer)                             0    5 -1917.2 3844.5 77.714  1
                                  Pr(>Chisq)    
<none>                                          
Gender in (0 + Gender | Consumer)      0.145    
(1 | Consumer)                        <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

         Eliminated Sum Sq Mean Sq NumDF   DenDF F value  Pr(>F)    
Gender            1  1.879   1.879     1   99.98  1.6909 0.19647    
sens2             0 83.363  83.363     1 1129.00 75.0256 < 2e-16 ***
Homesize          0  5.729   5.729     1  100.97  5.1557 0.02529 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + Homesize + (1 | Consumer)
> an2 <- ranova(model)
> an2b <- ranova(model, reduce.terms = FALSE)
> 
> stopifnot(
+   all.equal(an1, an2, check.attributes=FALSE, tolerance=TOL),
+   all.equal(an1b, an2b, check.attributes=FALSE, tolerance=TOL)
+ )
> 
> ####### Polynomial terms:
> model <- lmer(Preference ~ sens2 + Gender + (poly(sens2, 2) | Consumer),
+               data=carrots)
> (an <- ranova(model))
ANOVA-like table for random-effects: Single term deletions

Model:
Preference ~ sens2 + Gender + (poly(sens2, 2) | Consumer)
                                              npar  logLik    AIC    LRT Df
<none>                                          10 -1874.1 3768.2          
poly(sens2, 2) in (poly(sens2, 2) | Consumer)    5 -1879.9 3769.7 11.552  5
                                              Pr(>Chisq)  
<none>                                                    
poly(sens2, 2) in (poly(sens2, 2) | Consumer)    0.04147 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step(model)
Backward reduced random-effect table:

                                              Eliminated npar  logLik    AIC
<none>                                                     10 -1874.1 3768.2
poly(sens2, 2) in (poly(sens2, 2) | Consumer)          0    5 -1879.9 3769.7
                                                 LRT Df Pr(>Chisq)  
<none>                                                              
poly(sens2, 2) in (poly(sens2, 2) | Consumer) 11.552  5    0.04147 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

       Eliminated Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
Gender          1  1.188   1.188     1 101.03  1.1262    0.2911    
sens2           0 53.447  53.447     1 114.59 50.6761 1.019e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + (poly(sens2, 2) | Consumer)
Warning message:
Model failed to converge with 1 negative eigenvalue: -2.7e-02 
> 
> model <- lmer(Preference ~ sens2 + Gender + (sens2 + I(sens2^2) | Consumer),
+               data=carrots)
Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge with max|grad| = 0.099278 (tol = 0.002, component 1)
  See ?lme4::convergence and ?lme4::troubleshooting.
> (an2 <- ranova(model))
boundary (singular) fit: see help('isSingular')
ANOVA-like table for random-effects: Single term deletions

Model:
Preference ~ sens2 + Gender + (sens2 + I(sens2^2) | Consumer)
                                              npar  logLik    AIC     LRT Df
<none>                                          10 -1874.1 3768.2           
sens2 in (sens2 + I(sens2^2) | Consumer)         7 -1879.8 3773.5 11.3637  3
I(sens2^2) in (sens2 + I(sens2^2) | Consumer)    7 -1876.5 3767.0  4.8755  3
                                              Pr(>Chisq)   
<none>                                                     
sens2 in (sens2 + I(sens2^2) | Consumer)        0.009913 **
I(sens2^2) in (sens2 + I(sens2^2) | Consumer)   0.181146   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step(model)
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                                              Eliminated npar  logLik    AIC
<none>                                                     10 -1874.1 3768.2
I(sens2^2) in (sens2 + I(sens2^2) | Consumer)          1    7 -1876.5 3767.0
sens2 in (sens2 | Consumer)                            0    5 -1879.9 3769.7
                                                 LRT Df Pr(>Chisq)  
<none>                                                              
I(sens2^2) in (sens2 + I(sens2^2) | Consumer) 4.8755  3    0.18115  
sens2 in (sens2 | Consumer)                   6.6735  2    0.03555 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

       Eliminated Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
Gender          1  1.211   1.211     1 101.02  1.1309    0.2901    
sens2           0 58.688  58.688     1 102.01 54.8276 3.883e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + (sens2 | Consumer)
> stopifnot(
+   nrow(an) == 2L,
+   an[2L, "Df"] == 5L,
+   nrow(an2) == 3L,
+   all(an2[2:3, "Df"] == 3L)
+ )
> 
> ######## Functions of terms in random effects:
> model <- lmer(Preference ~ sens2 + Gender + (log(10+sens2) | Consumer),
+               data=carrots)
> ranova(model) # Works
ANOVA-like table for random-effects: Single term deletions

Model:
Preference ~ sens2 + Gender + (log(10 + sens2) | Consumer)
                                                npar  logLik    AIC    LRT Df
<none>                                             7 -1875.3 3764.6          
log(10 + sens2) in (log(10 + sens2) | Consumer)    5 -1879.9 3769.7 9.0854  2
                                                Pr(>Chisq)  
<none>                                                      
log(10 + sens2) in (log(10 + sens2) | Consumer)    0.01064 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step(model)
Backward reduced random-effect table:

                                                Eliminated npar  logLik    AIC
<none>                                                        7 -1875.3 3764.6
log(10 + sens2) in (log(10 + sens2) | Consumer)          0    5 -1879.9 3769.7
                                                   LRT Df Pr(>Chisq)  
<none>                                                                
log(10 + sens2) in (log(10 + sens2) | Consumer) 9.0854  2    0.01064 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

       Eliminated Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
Gender          1  1.200   1.200     1 101.03  1.1296    0.2904    
sens2           0 54.185  54.185     1 109.20 51.0020 1.083e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + (log(10 + sens2) | Consumer)
> 
> #####################################################################
> 
> # Missing values changes the number of observations in use:
> m <- lmer(Preference ~ sens2 + Homesize +
+             (1 |Consumer:Income), data=carrots)
> assertError(step(m))
> ans <- try(ranova(m), silent = TRUE)
> stopifnot(
+   inherits(ans, "try-error"),
+   grepl("number of rows in use has changed", ans)
+ )
> 
> ## Removing missing values solves the problem:
> m2 <- lmer(Preference ~ sens2 + Homesize +
+              (1 |Consumer:Income), data=carrots[complete.cases(carrots), ])
> ranova(m2) # Works
ANOVA-like table for random-effects: Single term deletions

Model:
Preference ~ sens2 + Homesize + (1 | Consumer:Income)
                      npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                   5 -1752.0 3513.9                         
(1 | Consumer:Income)    4 -1778.6 3565.2 53.272  1  2.904e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step(m2)
Backward reduced random-effect table:

                      Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                              5 -1752.0 3513.9                         
(1 | Consumer:Income)          0    4 -1778.6 3565.2 53.272  1  2.904e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

         Eliminated Sum Sq Mean Sq NumDF   DenDF F value    Pr(>F)    
sens2             0 77.308  77.308     1 1058.49 69.7915 < 2.2e-16 ***
Homesize          0  8.569   8.569     1   95.23  7.7355  0.006527 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + Homesize + (1 | Consumer:Income)
> 
> ## Including the variable with missing values (Income) among the fixed effects
> ## also solves the problem:
> m <- lmer(Preference ~ sens2 + Homesize + Income + #(1 + sens2 | Consumer) +
+             (1 |Consumer:Income), data=carrots)
> ranova(m)
ANOVA-like table for random-effects: Single term deletions

Model:
Preference ~ sens2 + Homesize + Income + (1 | Consumer:Income)
                      npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                   8 -1766.0 3547.9                         
(1 | Consumer:Income)    7 -1791.1 3596.3 50.395  1  1.257e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> step(m)
Backward reduced random-effect table:

                      Eliminated npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>                              8 -1766.0 3547.9                         
(1 | Consumer:Income)          0    7 -1791.1 3596.3 50.395  1  1.257e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

         Eliminated Sum Sq Mean Sq NumDF   DenDF F value    Pr(>F)    
Income            1  3.567   1.189     3   91.92  1.0627  0.368918    
sens2             0 78.191  78.191     1 1062.96 69.8919 < 2.2e-16 ***
Homesize          0  7.983   7.983     1   94.93  7.1355  0.008894 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Preference ~ sens2 + Homesize + (1 | Consumer:Income)
> 
> # Missing values in a an insignificant fixed effect causes the an error in step:
> m0 <- lmer(Preference ~ sens2 + Homesize + Income + #(1 + sens2 | Consumer) +
+             (1 |Consumer), data=carrots)
> ranova(m0)
ANOVA-like table for random-effects: Single term deletions

Model:
Preference ~ sens2 + Homesize + Income + (1 | Consumer)
               npar  logLik    AIC    LRT Df Pr(>Chisq)    
<none>            8 -1766.0 3547.9                         
(1 | Consumer)    7 -1791.1 3596.3 50.395  1  1.257e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> ans <- try(step(m0), silent = TRUE)
> stopifnot(
+   inherits(ans, "try-error"),
+   grepl("number of rows in use has changed", ans)
+ )
> 
> # Check that step still works for linear models (etc.)
> flm <- lm(Coloursaturation ~ TVset * Picture, data=TVbo)
> res <- step(flm, trace=0)
> stopifnot(
+   inherits(res, "lm")
+ )
> 
> ##################### Using reduce and keep args:
> # Fit a model to the ham dataset:
> m <- lmer(Informed.liking ~ Product*Information+
+             (1|Consumer) + (1|Product:Consumer)
+           + (1|Information:Consumer), data=ham)
> 
> # Backward elimination using terms with default alpha-levels:
> (step_res <- step(m))
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                           Eliminated npar  logLik    AIC     LRT Df Pr(>Chisq)
<none>                                  12 -1352.0 2728.1                      
(1 | Information:Consumer)          1   11 -1352.8 2727.5   1.444  1    0.22952
(1 | Consumer)                      0   10 -1354.4 2728.7   3.184  1    0.07437
(1 | Product:Consumer)              0   10 -1435.0 2890.0 164.443  1    < 2e-16
                              
<none>                        
(1 | Information:Consumer)    
(1 | Consumer)             .  
(1 | Product:Consumer)     ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

                    Eliminated  Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
Product:Information          1 10.3873  3.4624     3   320  2.0765 0.10321  
Product                      0 19.3466  6.4489     3   240  3.8291 0.01048 *
Information                  0  6.5201  6.5201     1   323  3.8714 0.04997 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Informed.liking ~ Product + Information + (1 | Consumer) + (1 | Product:Consumer)
> 
> (step_res <- step(m, reduce.random = FALSE))
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                           Eliminated npar  logLik    AIC     LRT Df Pr(>Chisq)
<none>                                  12 -1352.0 2728.1                      
(1 | Consumer)                      0   11 -1353.2 2728.3   2.252  1     0.1335
(1 | Product:Consumer)              0   11 -1435.0 2892.0 165.887  1     <2e-16
(1 | Information:Consumer)          0   11 -1352.8 2727.5   1.444  1     0.2295
                              
<none>                        
(1 | Consumer)                
(1 | Product:Consumer)     ***
(1 | Information:Consumer)    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

                    Eliminated  Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
Product:Information          1 10.3873  3.4624     3   240  2.2014 0.08855 .
Information                  2  5.3335  5.3335     1    80  3.3414 0.07129 .
Product                      0 18.3361  6.1120     3   240  3.8291 0.01048 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Informed.liking ~ Product + (1 | Consumer) + (1 | Product:Consumer) + (1 | Information:Consumer)
> (step_res <- step(m, reduce.fixed = FALSE))
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                           Eliminated npar  logLik    AIC     LRT Df Pr(>Chisq)
<none>                                  12 -1352.0 2728.1                      
(1 | Information:Consumer)          1   11 -1352.8 2727.5   1.444  1    0.22952
(1 | Consumer)                      0   10 -1354.4 2728.7   3.184  1    0.07437
(1 | Product:Consumer)              0   10 -1435.0 2890.0 164.443  1    < 2e-16
                              
<none>                        
(1 | Information:Consumer)    
(1 | Consumer)             .  
(1 | Product:Consumer)     ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

                    Eliminated Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Product:Information          0 10.387  3.4624     3   320  2.0765 0.1032

Model found:
Informed.liking ~ Product + Information + (1 | Consumer) + (1 | Product:Consumer) + Product:Information
> (step_res <- step(m, reduce.fixed = FALSE, reduce.random = FALSE))
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                           Eliminated npar  logLik    AIC     LRT Df Pr(>Chisq)
<none>                                  12 -1352.0 2728.1                      
(1 | Consumer)                      0   11 -1353.2 2728.3   2.252  1     0.1335
(1 | Product:Consumer)              0   11 -1435.0 2892.0 165.887  1     <2e-16
(1 | Information:Consumer)          0   11 -1352.8 2727.5   1.444  1     0.2295
                              
<none>                        
(1 | Consumer)                
(1 | Product:Consumer)     ***
(1 | Information:Consumer)    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

                    Eliminated Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
Product:Information          0 10.387  3.4624     3   240  2.2014 0.08855 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Informed.liking ~ Product * Information + (1 | Consumer) + (1 | Product:Consumer) + (1 | Information:Consumer)
> 
> (step_res <- step(m, reduce.random = FALSE, keep="Information"))
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                           Eliminated npar  logLik    AIC     LRT Df Pr(>Chisq)
<none>                                  12 -1352.0 2728.1                      
(1 | Consumer)                      0   11 -1353.2 2728.3   2.252  1     0.1335
(1 | Product:Consumer)              0   11 -1435.0 2892.0 165.887  1     <2e-16
(1 | Information:Consumer)          0   11 -1352.8 2727.5   1.444  1     0.2295
                              
<none>                        
(1 | Consumer)                
(1 | Product:Consumer)     ***
(1 | Information:Consumer)    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

                    Eliminated  Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
Product:Information          1 10.3873  3.4624     3   240  2.2014 0.08855 .
Product                      0 18.3363  6.1121     3   240  3.8292 0.01048 *
Information                  0  5.3335  5.3335     1    80  3.3414 0.07129 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Informed.liking ~ Product + Information + (1 | Consumer) + (1 | Product:Consumer) + (1 | Information:Consumer)
> (step_res <- step(m, reduce.random = FALSE, keep="Product:Information"))
boundary (singular) fit: see help('isSingular')
Backward reduced random-effect table:

                           Eliminated npar  logLik    AIC     LRT Df Pr(>Chisq)
<none>                                  12 -1352.0 2728.1                      
(1 | Consumer)                      0   11 -1353.2 2728.3   2.252  1     0.1335
(1 | Product:Consumer)              0   11 -1435.0 2892.0 165.887  1     <2e-16
(1 | Information:Consumer)          0   11 -1352.8 2727.5   1.444  1     0.2295
                              
<none>                        
(1 | Consumer)                
(1 | Product:Consumer)     ***
(1 | Information:Consumer)    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Backward reduced fixed-effect table:
Degrees of freedom method: Satterthwaite 

                    Eliminated Sum Sq Mean Sq NumDF DenDF F value  Pr(>F)  
Product:Information          0 10.387  3.4624     3   240  2.2014 0.08855 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model found:
Informed.liking ~ Product * Information + (1 | Consumer) + (1 | Product:Consumer) + (1 | Information:Consumer)
> 
> 
> ###########################
> ## Test that `step` works even if all random terms are reduced away:
> set.seed(101)
> test <- data.frame(TM = factor(rep(rep(c("org","min"),each=3),3)),
+                    dep = runif(18,0,20),
+                    ind = runif(18,0,7),
+                    dorp = factor(rep(1:3,each=6)))
> full.model <- lmer(dep ~ TM + ind + (1 | dorp),  data=test)
> res <- step(full.model)
> # res$random
> # res$fixed
> # attr(res, "model")
> # attr(res, "drop1")
> 
> 
> 
> proc.time()
   user  system elapsed 
  13.12    0.40   13.51