Content Review 6

library(tidyverse)

Registered S3 methods overwritten by 'dbplyr':
  method         from
  print.tbl_lazy     
  print.tbl_sql      
-- Attaching packages --------------------------------------- tidyverse 1.3.0 --
v ggplot2 3.3.2     v purrr   0.3.4
v tibble  3.0.3     v dplyr   1.0.2
v tidyr   1.1.1     v stringr 1.4.0
v readr   1.3.1     v forcats 0.5.0
-- Conflicts ------------------------------------------ tidyverse_conflicts() --
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()

library(lme4)

Loading required package: Matrix

Attaching package: 㤼㸱Matrix㤼㸲

The following objects are masked from 㤼㸱package:tidyr㤼㸲:

    expand, pack, unpack

library(lmerTest)

Attaching package: 㤼㸱lmerTest㤼㸲

The following object is masked from 㤼㸱package:lme4㤼㸲:

    lmer

The following object is masked from 㤼㸱package:stats㤼㸲:

    step

model.null <- lmer(mathach~(1|schoolid), REML = FALSE, data = hsbmerged)
summary(model.null)

Linear mixed model fit by maximum likelihood . t-tests use
  Satterthwaite's method [lmerModLmerTest]
Formula: mathach ~ (1 | schoolid)
   Data: hsbmerged

     AIC      BIC   logLik deviance df.resid 
 47121.8  47142.4 -23557.9  47115.8     7182 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-3.06262 -0.75365  0.02676  0.76070  2.74184 

Random effects:
 Groups   Name        Variance Std.Dev.
 schoolid (Intercept)  8.553   2.925   
 Residual             39.148   6.257   
Number of obs: 7185, groups:  schoolid, 160

Fixed effects:
            Estimate Std. Error       df t value Pr(>|t|)    
(Intercept)  12.6371     0.2436 157.6209   51.87   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

model.1 <- lmer(mathach ~ female + ses + size + sector + (1|schoolid), REML = FALSE, data=hsbmerged)
summary(model.1)

Linear mixed model fit by maximum likelihood . t-tests use
  Satterthwaite's method [lmerModLmerTest]
Formula: mathach ~ female + ses + size + sector + (1 | schoolid)
   Data: hsbmerged

     AIC      BIC   logLik deviance df.resid 
 46564.2  46612.3 -23275.1  46550.2     7178 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.2032 -0.7404  0.0323  0.7584  2.8130 

Random effects:
 Groups   Name        Variance Std.Dev.
 schoolid (Intercept)  3.27    1.808   
 Residual             36.81    6.067   
Number of obs: 7185, groups:  schoolid, 160

Fixed effects:
              Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)  1.168e+01  4.543e-01  1.613e+02  25.707  < 2e-16 ***
female      -1.201e+00  1.641e-01  6.464e+03  -7.318 2.81e-13 ***
ses          2.345e+00  1.050e-01  6.643e+03  22.325  < 2e-16 ***
size         4.972e-04  2.894e-04  1.506e+02   1.718   0.0878 .  
sector       2.378e+00  3.633e-01  1.465e+02   6.544 9.40e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
       (Intr) female ses    size  
female -0.202                     
ses     0.028  0.057              
size   -0.858  0.016 -0.008       
sector -0.671  0.006 -0.089  0.447

model.2 <- lmer(mathach ~ female + ses + size + sector + (ses|schoolid), REML = FALSE, data=hsbmerged)
summary(model.2)

Linear mixed model fit by maximum likelihood . t-tests use
  Satterthwaite's method [lmerModLmerTest]
Formula: mathach ~ female + ses + size + sector + (ses | schoolid)
   Data: hsbmerged

     AIC      BIC   logLik deviance df.resid 
 46560.0  46621.9 -23271.0  46542.0     7176 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.2053 -0.7384  0.0281  0.7570  2.8322 

Random effects:
 Groups   Name        Variance Std.Dev. Corr
 schoolid (Intercept)  3.5435  1.8824       
          ses          0.3548  0.5956   0.60
 Residual             36.6025  6.0500       
Number of obs: 7185, groups:  schoolid, 160

Fixed effects:
              Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)  1.148e+01  4.505e-01  1.580e+02  25.471  < 2e-16 ***
female      -1.194e+00  1.641e-01  6.561e+03  -7.275 3.86e-13 ***
ses          2.353e+00  1.152e-01  1.609e+02  20.423  < 2e-16 ***
size         4.656e-04  2.850e-04  1.416e+02   1.634    0.104    
sector       2.789e+00  3.651e-01  1.496e+02   7.639 2.42e-12 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
       (Intr) female ses    size  
female -0.207                     
ses     0.109  0.055              
size   -0.850  0.019 -0.006       
sector -0.660  0.009 -0.078  0.436

rand(model.2)

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

Model:
mathach ~ female + ses + size + sector + (ses | schoolid)
                        npar logLik   AIC    LRT Df Pr(>Chisq)  
<none>                     9 -23271 46560                       
ses in (ses | schoolid)    7 -23275 46564 8.1673  2    0.01685 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1