Week12

library(lme4)

## Loading required package: Matrix

library(faraway)

## Warning: package 'faraway' was built under R version 4.0.3

library(nlme)

## 
## Attaching package: 'nlme'

## The following object is masked from 'package:lme4':
## 
##     lmList

fatmodel <- lmer(Fat ~ 1 + (1|Lab/Technician/Sample),data = eggs)
summary(fatmodel)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Fat ~ 1 + (1 | Lab/Technician/Sample)
##    Data: eggs
## 
## REML criterion at convergence: -64.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.04098 -0.46576  0.00927  0.59713  1.54276 
## 
## Random effects:
##  Groups                  Name        Variance Std.Dev.
##  Sample:(Technician:Lab) (Intercept) 0.003065 0.05536 
##  Technician:Lab          (Intercept) 0.006980 0.08355 
##  Lab                     (Intercept) 0.005920 0.07694 
##  Residual                            0.007196 0.08483 
## Number of obs: 48, groups:  
## Sample:(Technician:Lab), 24; Technician:Lab, 12; Lab, 6
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  0.38750    0.04296   9.019

refitmodel <- lmer(Fat ~ 1 + (1|Lab/Technician),data = eggs)
summary(refitmodel)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Fat ~ 1 + (1 | Lab/Technician)
##    Data: eggs
## 
## REML criterion at convergence: -62.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.17799 -0.42424  0.08043  0.67361  1.77544 
## 
## Random effects:
##  Groups         Name        Variance Std.Dev.
##  Technician:Lab (Intercept) 0.008002 0.08945 
##  Lab            (Intercept) 0.005920 0.07694 
##  Residual                   0.009239 0.09612 
## Number of obs: 48, groups:  Technician:Lab, 12; Lab, 6
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  0.38750    0.04296   9.019

a. Fat is the response variable here
b. Lab, Technician, and Sample are all random effects.
c. Due to the natural progression I believe these are nested random effects.
d. Lab one appears to have higher fat contents, other labs are pretty consistent
e. .3875
f. 0.006980
g. 0.005920
h. The variance goes up, fixed effects stay the same