[R] Post-hoc tests on Split-plot design

[Md Newaz]

Dear R-help,


can you please post the following message to the r-nabble forum.


Thanks!


---------------------------------------------------------------------------------------------------------------------------------

Dear R users,


I have been attempting to carry out post-hoc tests on a split-plot design:


Model:
Yijkl = µ + Ci + ω(i)j + δ(ij) + Tk + CTik + ωT(i)jk + Pl + CPil + ωP(i)jl
+ TPkl + CTPikl + ωTP(i)jkl + Ɛ(ijkl)


I have successfully matched the appropriate degrees of freedom and mean
squares presented in the table below using aov().


*EMS Table:*





2

2

2

3









F

R

F

F









i

j

k

l

EMS

df

F(1,2)

Ci

0

2

2

3

δ2 + 6δ2δ + 6δ2ω + 12Φ(C)

1



ω(i)j

1

1

2

3

δ2 + 6δ2δ + 6δ2ω

2



δ(ij)

1

1

2

3

δ2 + 6δ2δ

0

F(1,2)

Tk

2

2

0

3

δ2 + 3δ2ωT + 12Φ(T)

1

F(1,2)

CTik

0

2

0

3

δ2 + 3δ2ωT + 6Φ(CT)

1



ωT(i)jk

1

1

0

3

δ2 + 3δ2ωT

2

F(2,4)

Pl

2

2

2

0

δ2 + 2δ2ωP + 8Φ(P)

2

F(2,4)

CPil

0

2

2

0

δ2 + 2δ2ωP + 4Φ(CP)

2



ωP(i)jl

1

1

2

0

δ2 + 2δ2ωP

4

F(2,4)

TPkl

2

2

0

0

δ2 + δ2ωTP + 4Φ(TP)

2

F(2,4)

CTPikl

0

2

0

0

δ2 + δ2ωTP + 2Φ(CTP)

2



ωTP(i)jkl

1

1

0

0

δ2 + δ2ωTP

4



Ɛ(ijkl)

1

1

1

1

δ2

0



Total











23



mod <- aov(Budburst ~ CO2*SoilTemp*Photoperiod +
Error(Greenhouse/(SoilTemp*Photoperiod)), data = data)

summary(mod)



Error: Greenhouse

                  Df    Sum Sq   Mean Sq   F value   Pr(>F)

CO2           1       1465.2    1465.2      38.81      0.0248

Residuals    2       75.5         37.8



Error: Greenhouse:SoilTemp

                           Df    Sum Sq   Mean Sq   F value   Pr(>F)

SoilTemp             1     238.00    238.00       80.57    0.0122

CO2:SoilTemp      1     145.70    145.70       49.32    0.0197

Residuals              2     5.91        2.95

Error: Greenhouse:Photoperiod

                                Df    Sum Sq  Mean Sq   F value  Pr(>F)

Photoperiod               2    986.9      493.4        6.965     0.0498

CO2:Photoperiod        2    0.2         0.1            0.001     0.9989

Residuals                   4    283.4      70.8



Error: Greenhouse:SoilTemp:Photoperiod

                                                   Df   Sum Sq   Mean Sq
  F value   Pr(>F)

SoilTemp:Photoperiod                   2    14.56       7.28
        0.514     0.6330

CO2:SoilTemp:Photoperiod            2    186.31     93.15         6.576
    0.0544

Residuals                                      4    56.67
      14.17



Error: Within

                    Df     Sum Sq   Mean Sq F value Pr(>F)

Residuals      216   2887        13.37



However, as neither TukeyHSD() nor glht() accept objects of class
“aovlist”, I cannot carry out the post-hoc tests. Is there any way to run a
post-hoc test on an object of class "aovlist"?



Alternatively, I tried modelling the data using lme() and lmer(), but the
problem is that I cannot match the appropriate degrees of freedom and mean
squares obtained from the above included expected mean squares table using
lme() or lmer().



Has anyone else encountered and overcome this issue?



Thanks in advance,


Md. Shah Newaz

Faculty of Natural Resources Management

Lakehead University

Thunder Bay, Ontario, Canada

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