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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.

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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://multilevel.ioe.ac.uk/softrev/chem97.html

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

1 2 3 4 |

```
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
```

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