Ed230B/C

Linear Statistical Models

More Split-Plot Factorial Designs

Updated for Stata 11


SPF-pr.q

Linear Model

Yijkl = μ + αj + γl + αγjl + πi(jl) + βk + αβjk + βγkl + αβγjkl + βπki(jl) + εijkl

Let's break the linear model into chunks with an error term at the end of each line.

Yijkl = μ + αj + γl + αγjl + πi(jl)       [between subjects]
+ βk + αβjk + βγkl + αβγjkl + βπki(jl) + εijkl       [within subjects]

Schematic

b1b2b3b4
a1c1S1S1S1S1
a1c2S2S2S2S2
a2c1S3S3S3S3
a2c2S4S4S4S4

ANOVA Summary Table (A, B, C fixed)

SourceError Term
Between Blocks
1A[4]
2C[4]
3A#C[4]
4Blks(A#C)
Within Blocks
5B[9]
6A#B[9]
7B#C[9]
8A#B#C[9]
9B#Blks(A#C)
Total

Stata Command

anova y a c a#c / s|a#c  b a#b b#c a#b#c /, repeated(b)

SPF-p.qr

Linear Model

Yijkl = μ + αj + πi(j) + βk + αβjk + βπki(j) + γl + αγjl + γπli(j) + βγkl + αβγjkl + βγπkli(j) + εijkl

Again, let's break it into chunks with an error term at the end of each line.

Yijkl = μ + αj + πi(j)       [between subjects]
+ βk + αβjk + βπki(j)       [within subjects - B]
+ γl + αγjl + γπli(j)       [within subjects - C]
+ βγkl + αβγjkl + βγπkli(j) + εijkl       [within subjects - B#C]

Schematic

b1
c1
b1
c2
b2
c1
b2
c2
a1S1S1S1S1
a2S2S2S2S2

ANOVA Summary Table (A, B, C fixed)

SourceError Term
Between Blocks
1A[2]
2Blks(A)
Within Blocks
3B[5]
4A#B[5]
5B#Blks(A)
 
6C[8]
7A#C[8]
8C#Blks(A)
 
9B#C[11]
10A#B#C[11]
11B#C#Blks(A)
Total

Stata Command

anova y a / s|a  b a#b / b#s|a  c a#c / c#s|a  b#c a#b#c /, repeated(b c)

SPF-pr.qt

Linear Model

There are so many terms in this linear model that we will break it up into chunks from the start.

Yijkl = μ + αj + γl + αγjl + πi(jl)       [between subjects]
+ βk + αβjk + βγkl + αβγjkl + βπki(jl)       [within subjects - B]
+ δm + αδjm + γδlm + αγδjlm + δπmi(jl)       [within subjects - D]
+ βδkm + αβδjkm + βγδklm + αβγδjklm + βδπkmi(jl) + εijklm       [within subjects - B#D]

Schematic

b1
d1
b1
d2
b2
d1
b2
d2
a1c1S1S1S1S1
a1c2S2S2S2S2
a2c1S3S3S3S3
a2c2S4S4S4S4

ANOVA Summary Table (A, B, C, D fixed)

SourceError Term
Between Blocks
1A[4]
2C[4]
3A#C[4]
4Blks(A#C)
Within Blocks
5B[9]
6A#B[9]
7B#C[9]
8A#B#C[9]
9B#Blks(A#C)
 
10D[14]
11A#D[14]
12C#D[14]
13A#C#D[14]
14D#Blks(A#C)
 
15B#D[19]
16A#B#D[19]
17B#C#D[19]
18A#B#C#D[19]
19B#D#Blks(A#C)
Total

Stata Command

anova y a c a#c / s|a#c  b a#b c#b a#b#c / b#s|a#c  d a#d c#d a#c#d / d#s|a#c  
  b#d a#b#d c#b#d a#b#c#d /, repeated(b d)


Linear Statistical Models Course

Phil Ender, 17sep10, 12Feb98