R_lme4_mixed-effects_modelling_SPSSexample_replication_cross-platform

Question

Hello stackoverflow community! I am new to mixed-effects modelling (MEM) or mixed-models . In order to gain a better understanding of MEM, I decided to replicate two examples in r ( lme4 package) from the textbook "Experimental Design and Analysis" by Dr. Howard J. Seltman . In the textbook, the author used SPSS to solve the two examples and included the relevant output tables.

Model 1, referred to as [tag:video game example], models " the linear relationship between trial and score with separate intercepts and slopes for each age group, and including a random per-subject intercept. "
The data for the video game example is available at the link below : https://www.stat.cmu.edu/~hseltman/309/Book/data/MMvideo.txt

The model 1 output tables are found on the page no. 370/382 (actual book/pdf book) of the textbook which is also linked below (or see image): https://www.stat.cmu.edu/~hseltman/309/Book/Book.pdf

My model 1 ( video game example ) is:

lmer(score ~ trial + (1|id) + (1+agegrp|agegrp), data=data)

where, trial is a fixed-effect.
(1|id) is a random per-subject intercept.
(1+agegrp|agegrp) is a random slope and random intercept for each age group.

The model 1 returns an error: boundary (singular) fit: see help('isSingular')

Model 2, referred to as [tag:classroom example], includes " main effects for stdTest, grade level, and treatment group " and " random effect (intercept) to account for school to school differences that induces correlation among scores for students within a school. " Link for the classroom example data is included below: https://www.stat.cmu.edu/~hseltman/309/Book/data/schools.txt

The model 2 output tables are found on the page no. 377/391 (actual book/pdf book) of the textbook which is also linked below (or see image): [https://www.stat.cmu.edu/~hseltman/309/Book/Book.pdf]

My model 2 ( classroom example ) is:

lmer(score ~ stdTest + grade + treatment + (1|student) + (1|student:classroom), data=data)

where, stdTest, grade level, and treatment group are the fixed-effect.
(1|student) is a random effect (intercept).
(1|student:classroom) for students nested within a school.

The model 2 returns an error: number of levels of each grouping factor must be < number of observations (problems: student, classroom:student )

Could someone please help me model these two examples correctly to produce the desired outputs?

Answer 1

I think you had the models specified the wrong way. This looks like the way to replicate those two models:

library(lme4)
library(lmerTest)
library(dplyr)
dat <- rio::import("https://www.stat.cmu.edu/~hseltman/309/Book/data/MMvideo.txt")
dat <- dat %>% 
  mutate(agegrp = factor(agegrp, levels=c("(40,50]", "(20,30]", "(30,40]")))

m1 <- lmer(score ~ agegrp*trial + (1|id) , data=dat)
summary(m1)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: score ~ agegrp * trial + (1 | id)
#>    Data: dat
#> 
#> REML criterion at convergence: 708.4
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -2.39575 -0.54403  0.07855  0.65601  2.02271 
#> 
#> Random effects:
#>  Groups   Name        Variance Std.Dev.
#>  id       (Intercept) 6.457    2.541   
#>  Residual             4.633    2.152   
#> Number of obs: 150, groups:  id, 28
#> 
#> Fixed effects:
#>                     Estimate Std. Error       df t value Pr(>|t|)    
#> (Intercept)          14.0223     1.1097  55.4281  12.637  < 2e-16 ***
#> agegrp(20,30]        -7.2586     1.5704  72.9807  -4.622 1.60e-05 ***
#> agegrp(30,40]        -3.4887     1.4510  64.2373  -2.404   0.0191 *  
#> trial                 3.3150     0.2152 118.8662  15.401  < 2e-16 ***
#> agegrp(20,30]:trial   3.7988     0.3229 118.8662  11.766  < 2e-16 ***
#> agegrp(30,40]:trial   2.1433     0.2914 118.8662   7.354 2.68e-11 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Correlation of Fixed Effects:
#>             (Intr) ag(20,30] ag(30,40] trial  a(20,30]:
#> aggr(20,30] -0.707                                     
#> aggr(30,40] -0.765  0.617                              
#> trial       -0.582  0.411     0.445                    
#> agg(20,30]:  0.388 -0.617    -0.297    -0.667          
#> agg(30,40]:  0.430 -0.304    -0.603    -0.739  0.492

dat2 <- rio::import("https://www.stat.cmu.edu/~hseltman/309/Book/data/schools.txt")
dat2 <- dat2 %>% 
  mutate(grade =factor(grade, levels=c(5,3)), 
         treatment = factor(treatment, levels=c(1,0)))

m2 <- lmer(score ~ grade + treatment + stdTest + (1|classroom), data=dat2)
summary(m2)
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: score ~ grade + treatment + stdTest + (1 | classroom)
#>    Data: dat2
#> 
#> REML criterion at convergence: 3023.7
#> 
#> Scaled residuals: 
#>      Min       1Q   Median       3Q      Max 
#> -3.02847 -0.68306  0.03838  0.64510  2.94562 
#> 
#> Random effects:
#>  Groups    Name        Variance Std.Dev.
#>  classroom (Intercept) 10.05    3.170   
#>  Residual              25.87    5.086   
#> Number of obs: 490, groups:  classroom, 20
#> 
#> Fixed effects:
#>             Estimate Std. Error       df t value Pr(>|t|)    
#> (Intercept) -23.0943     6.8025  15.9160  -3.395 0.003722 ** 
#> grade3       -5.9424     1.6566  16.0861  -3.587 0.002447 ** 
#> treatment0    1.7941     1.6351  16.0676   1.097 0.288698    
#> stdTest       0.4438     0.0879  15.8672   5.049 0.000122 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Correlation of Fixed Effects:
#>            (Intr) grade3 trtmn0
#> grade3     -0.246              
#> treatment0  0.007 -0.410       
#> stdTest    -0.985  0.179 -0.079

^{Created on 2022-12-04 by the reprex package (v2.0.1)}

One thing to note is that the default behaviour in R is to have the first level of the factor be the reference. In the book examples, the last level was the reference, so you have to make that explicit in the data managing as above.