Content Review 5

suppressPackageStartupMessages(library(tidyverse))
suppressPackageStartupMessages(library(lme4))

model.1 <- lmer(thk ~ prethk + cc + gprethk + (1|school), REML=FALSE, data=schoolsmoke)
summary(model.1)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: thk ~ prethk + cc + gprethk + (1 | school)
   Data: schoolsmoke

     AIC      BIC   logLik deviance df.resid 
  4712.6   4744.9  -2350.3   4700.6     1594 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.23332 -0.79567  0.02374  0.79254  2.16704 

Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.01734  0.1317  
 Residual             1.09334  1.0456  
Number of obs: 1600, groups:  school, 28

Fixed effects:
            Estimate Std. Error t value
(Intercept)  1.07609    0.25478   4.224
prethk       0.21260    0.02138   9.944
cc           0.43075    0.07554   5.702
gprethk      0.41835    0.11930   3.507

Correlation of Fixed Effects:
        (Intr) prethk cc    
prethk   0.000              
cc      -0.288  0.000       
gprethk -0.963 -0.179  0.148

model.2 <- lmer(thk ~ prethk + cc + gprethk + (gprethk|school), REML=FALSE, data=schoolsmoke.2)

boundary (singular) fit: see ?isSingular

summary(model.2)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: thk ~ prethk + cc + gprethk + (gprethk | school)
   Data: schoolsmoke.2

     AIC      BIC   logLik deviance df.resid 
  4715.0   4758.0  -2349.5   4699.0     1592 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.24405 -0.80342  0.04777  0.80128  2.19526 

Random effects:
 Groups   Name        Variance Std.Dev. Corr 
 school   (Intercept) 0.26850  0.5182        
          gprethk     0.03524  0.1877   -1.00
 Residual             1.09200  1.0450        
Number of obs: 1600, groups:  school, 28

Fixed effects:
            Estimate Std. Error t value
(Intercept)  0.99684    0.25560   3.900
prethk       0.21260    0.02137   9.951
cc           0.43532    0.07457   5.838
gprethk      0.45284    0.11410   3.969

Correlation of Fixed Effects:
        (Intr) prethk cc    
prethk   0.000              
cc      -0.306  0.000       
gprethk -0.964 -0.187  0.179
convergence code: 0
boundary (singular) fit: see ?isSingular

lmerTest::rand(model.2)

ANOVA-like table for random-effects: Single term deletions

Model:
thk ~ prethk + cc + gprethk + (gprethk | school)
                              npar  logLik    AIC    LRT Df Pr(>Chisq)
<none>                           8 -2349.5 4715.0                     
gprethk in (gprethk | school)    6 -2350.3 4712.6 1.6116  2     0.4467

schoolsmoke.2 <- schoolsmoke %>%
  mutate(.,
         prethk.cent = prethk - mean(prethk),
         gprethk.cent = gprethk - mean(gprethk))
psych::describe(schoolsmoke.2, fast=TRUE)

model.3 <- lmer(thk ~ prethk.cent + cc + gprethk.cent + prethk.cent:gprethk.cent + (1|school), REML=FALSE, data = schoolsmoke.2)
summary(model.3)

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: 
thk ~ prethk.cent + cc + gprethk.cent + prethk.cent:gprethk.cent +  
    (1 | school)
   Data: schoolsmoke.2

     AIC      BIC   logLik deviance df.resid 
  4702.9   4740.5  -2344.4   4688.9     1593 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.24644 -0.81395  0.04367  0.80525  2.07026 

Random effects:
 Groups   Name        Variance Std.Dev.
 school   (Intercept) 0.0165   0.1284  
 Residual             1.0857   1.0420  
Number of obs: 1600, groups:  school, 28

Fixed effects:
                         Estimate Std. Error t value
(Intercept)               2.35901    0.05205  45.322
prethk.cent               0.20797    0.02135   9.743
cc                        0.43001    0.07453   5.770
gprethk.cent              0.36513    0.11890   3.071
prethk.cent:gprethk.cent  0.22898    0.06663   3.437

Correlation of Fixed Effects:
            (Intr) prthk. cc     gprth.
prethk.cent  0.008                     
cc          -0.695  0.000              
gprethk.cnt -0.104 -0.171  0.148       
prthk.cnt:. -0.128 -0.063 -0.003 -0.130

anova(model.2, model.3)

Data: schoolsmoke.2
Models:
model.3: thk ~ prethk.cent + cc + gprethk.cent + prethk.cent:gprethk.cent + 
model.3:     (1 | school)
model.2: thk ~ prethk + cc + gprethk + (gprethk | school)
        npar    AIC    BIC  logLik deviance Chisq Df Pr(>Chisq)
model.3    7 4702.9 4740.5 -2344.4   4688.9                    
model.2    8 4715.0 4758.0 -2349.5   4699.0     0  1          1

interplot::interplot(model.3, var1 = "gprethk.cent", var2 = "prethk.cent")

output:plot 

Error: object 'output' not found