Chem97: Scores on A-level Chemistry in 1997
In mlmRev: Examples from Multilevel Modelling Software Review

Description Usage Format Details Source References Examples

Scores on the 1997 A-level Chemistry examination in Britain. Students are grouped into schools within local education authories. In addition some demographic and pre-test information is provided.

1	data(Chem97)

A data frame with 31022 observations on the following 8 variables.

lea: Local Education Authority - a factor
school: School identifier - a factor
student: Student identifier - a factor
score: Point score on A-level Chemistry in 1997
gender: Student's gender
age: Age in month, centred at 222 months or 18.5 years
gcsescore: Average GCSE score of individual.
gcsecnt: Average GCSE score of individual, centered at mean.

This data set is relatively large with 31,022 individuals in 2,280 schools. Note that while this is used, illustratively, to fit Normal response models, the distribution of the response is not well described by a Normal distribution.

http://www.bristol.ac.uk/cmm/learning/mmsoftware/data-rev.html

Yang, M., Fielding, A. and Goldstein, H. (2002). Multilevel ordinal models for examination grades (submitted to Statistical Modelling).

str(Chem97)
summary(Chem97)
(fm1 <- lmer(score ~ (1|school) + (1|lea), Chem97))
(fm2 <- lmer(score ~ gcsecnt + (1|school) + (1|lea), Chem97))

Loading required package: lme4
Loading required package: Matrix
'data.frame':	31022 obs. of  8 variables:
 $ lea      : Factor w/ 131 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ school   : Factor w/ 2410 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ student  : Factor w/ 31022 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
 $ score    : num  4 10 10 10 8 10 6 8 4 10 ...
 $ gender   : Factor w/ 2 levels "M","F": 2 2 2 2 2 2 2 2 2 2 ...
 $ age      : num  3 -3 -4 -2 -1 4 1 4 3 0 ...
 $ gcsescore: num  6.62 7.62 7.25 7.5 6.44 ...
 $ gcsecnt  : num  0.339 1.339 0.964 1.214 0.158 ...
      lea            school         student          score        gender   
 118    :  969   698    :  188   1      :    1   Min.   : 0.000   M:17262  
 116    :  931   1408   :  126   2      :    1   1st Qu.: 4.000   F:13760  
 119    :  916   431    :  118   3      :    1   Median : 6.000            
 109    :  802   416    :  111   4      :    1   Mean   : 5.813            
 113    :  791   1215   :   99   5      :    1   3rd Qu.: 8.000            
 129    :  762   908    :   94   6      :    1   Max.   :10.000            
 (Other):25851   (Other):30286   (Other):31016                             
      age            gcsescore        gcsecnt        
 Min.   :-6.0000   Min.   :0.000   Min.   :-6.28568  
 1st Qu.:-3.0000   1st Qu.:5.750   1st Qu.:-0.53568  
 Median :-1.0000   Median :6.375   Median : 0.08932  
 Mean   :-0.4678   Mean   :6.286   Mean   : 0.00000  
 3rd Qu.: 3.0000   3rd Qu.:6.900   3rd Qu.: 0.61432  
 Max.   : 5.0000   Max.   :8.000   Max.   : 1.71432  
                                                     
Linear mixed model fit by REML ['lmerMod']
Formula: score ~ (1 | school) + (1 | lea)
   Data: Chem97
REML criterion at convergence: 157873.8
Random effects:
 Groups   Name        Std.Dev.
 school   (Intercept) 1.6579  
 lea      (Intercept) 0.3918  
 Residual             2.9182  
Number of obs: 31022, groups:  school, 2410; lea, 131
Fixed Effects:
(Intercept)  
      5.319  
Linear mixed model fit by REML ['lmerMod']
Formula: score ~ gcsecnt + (1 | school) + (1 | lea)
   Data: Chem97
REML criterion at convergence: 141697
Random effects:
 Groups   Name        Std.Dev.
 school   (Intercept) 1.0799  
 lea      (Intercept) 0.1215  
 Residual             2.2703  
Number of obs: 31022, groups:  school, 2410; lea, 131
Fixed Effects:
(Intercept)      gcsecnt  
      5.635        2.473