R version 3.4.4 (2018-03-15) -- "Someone to Lean On"                         ### Stat222, WEEK 2 
Copyright (C) 2018 The R Foundation for Statistical Computing
> library(lme4)
Loading required package: Matrix
### Sleepstudy descriptives SFYS
> data(sleepstudy)  # sleep deprivation 3hrs/night truckers
> dim(sleepstudy)   
[1] 180   3
> head(sleepstudy)
  Reaction Days Subject
1 249.5600    0     308
2 258.7047    1     308
3 250.8006    2     308
4 321.4398    3     308
5 356.8519    4     308
6 414.6901    5     308
## note initial observation time = 0
> attach(sleepstudy) 
> table(Subject)
Subject
308 309 310 330 331 332 333 334 335 337 349 350 351 352 369 370 371 372 
 10  10  10  10  10  10  10  10  10  10  10  10  10  10  10  10  10  10 
> #yes 18 subjects (3hrs sleep) 10 observations on each, page 64 of bates ch4
> 
> 
>   #lmList has the old nlme syntax, even in lme4
>  sleeplmList = lmList(Reaction ~ Days |Subject, data = sleepstudy)
>  sleeplmList
Call: lmList(formula = Reaction ~ Days | Subject, data = sleepstudy) 
Coefficients:
    (Intercept)      Days
308    244.1927 21.764702
309    205.0549  2.261785
310    203.4842  6.114899
330    289.6851  3.008073
331    285.7390  5.266019
332    264.2516  9.566768
333    275.0191  9.142045
334    240.1629 12.253141
335    263.0347 -2.881034
337    290.1041 19.025974
349    215.1118 13.493933
350    225.8346 19.504017
351    261.1470  6.433498
352    276.3721 13.566549
369    254.9681 11.348109
370    210.4491 18.056151
371    253.6360  9.188445
372    267.0448 11.298073

Degrees of freedom: 180 total; 144 residual
Residual standard error: 25.59182
> # note this matches lmer Residual (random eff)
>  mean(coef(sleeplmList)[,1])   
[1] 251.4051
>  mean(coef(sleeplmList)[,2])   
[1] 10.46729
> #mean int and slope match lmer Fixed effects results 
> 
> #### Random -> varies over units (subj); Fixed -> not vary

> # heterogeneity across units
>  var(coef(sleeplmList)[,1])   
[1] 838.3423
>  var(coef(sleeplmList)[,2])   
[1] 43.01034

>  #these are too big as they should be, compare with variance random effects lmer
>  # mle subtracts off wobble in estimated indiv regressions Y on t
>  # method of moments - SSR/SST, see Review Question
> 
> ## more useful descriptives using lmList results
>  quantile(coef(sleeplmList)[,1])
      0%      25%      50%      75%     100% 
203.4842 229.4167 258.0576 273.0255 290.1041 
> 
>  quantile(coef(sleeplmList)[,2])
       0%       25%       50%       75%      100% 
-2.881034  6.194548 10.432421 13.548395 21.764702 
>  
>  stem(coef(sleeplmList)[,2])

  The decimal point is 1 digit(s) to the right of the |

  -0 | 3
  0 | 23
  0 | 56699
  1 | 011234
  1 | 89
  2 | 02

> ## can also rename quantities
>  rate = coef(sleeplmList)[,2]
> quantile(rate)
       0%       25%       50%       75%      100% 
-2.881034  6.194548 10.432421 13.548395 21.764702 
>