R: Examples for 'stats::anova.mlm'

### ** Examples

require(graphics)
utils::example(SSD) # Brings in the mlmfit and reacttime objects

SSD> # Lifted from Baron+Li:
SSD> # "Notes on the use of R for psychology experiments and questionnaires"
SSD> # Maxwell and Delaney, p. 497
SSD> reacttime <- matrix(c(
SSD+ 420, 420, 480, 480, 600, 780,
SSD+ 420, 480, 480, 360, 480, 600,
SSD+ 480, 480, 540, 660, 780, 780,
SSD+ 420, 540, 540, 480, 780, 900,
SSD+ 540, 660, 540, 480, 660, 720,
SSD+ 360, 420, 360, 360, 480, 540,
SSD+ 480, 480, 600, 540, 720, 840,
SSD+ 480, 600, 660, 540, 720, 900,
SSD+ 540, 600, 540, 480, 720, 780,
SSD+ 480, 420, 540, 540, 660, 780),
SSD+ ncol = 6, byrow = TRUE,
SSD+ dimnames = list(subj = 1:10,
SSD+               cond = c("deg0NA", "deg4NA", "deg8NA",
SSD+                        "deg0NP", "deg4NP", "deg8NP")))

SSD> mlmfit <- lm(reacttime ~ 1)

SSD> SSD(mlmfit)
$SSD
        cond
cond     deg0NA deg4NA deg8NA deg0NP deg4NP deg8NP
  deg0NA  29160  30600  26640  23760  32400  25560
  deg4NA  30600  66600  32400   7200  36000  30600
  deg8NA  26640  32400  56160  41040  57600  69840
  deg0NP  23760   7200  41040  70560  72000  63360
  deg4NP  32400  36000  57600  72000 108000 100800
  deg8NP  25560  30600  69840  63360 100800 122760

$call
lm(formula = reacttime ~ 1)

$df
[1] 9

attr(,"class")
[1] "SSD"

SSD> estVar(mlmfit)
        cond
cond     deg0NA deg4NA deg8NA deg0NP deg4NP deg8NP
  deg0NA   3240   3400   2960   2640   3600   2840
  deg4NA   3400   7400   3600    800   4000   3400
  deg8NA   2960   3600   6240   4560   6400   7760
  deg0NP   2640    800   4560   7840   8000   7040
  deg4NP   3600   4000   6400   8000  12000  11200
  deg8NP   2840   3400   7760   7040  11200  13640

mlmfit0 <- update(mlmfit, ~0)

### Traditional tests of intrasubj. contrasts
## Using MANOVA techniques on contrasts:
anova(mlmfit, mlmfit0, X = ~1)

Analysis of Variance Table

Model 1: reacttime ~ 1
Model 2: reacttime ~ 1 - 1

Contrasts orthogonal to
~1

  Res.Df Df Gen.var. Pillai approx F num Df den Df   Pr(>F)   
1      9      1249.6                                          
2     10  1   2013.2 0.9456   17.381      5      5 0.003534 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Assuming sphericity
anova(mlmfit, mlmfit0, X = ~1, test = "Spherical")

Analysis of Variance Table

Model 1: reacttime ~ 1
Model 2: reacttime ~ 1 - 1

Contrasts orthogonal to
~1

Greenhouse-Geisser epsilon: 0.4855
Huynh-Feldt epsilon:        0.6778

  Res.Df Df Gen.var.      F num Df den Df     Pr(>F)    G-G Pr    H-F Pr
1      9      1249.6                                                    
2     10  1   2013.2 38.028      5     45 4.4711e-15 2.532e-08 7.393e-11

### tests using intra-subject 3x2 design
idata <- data.frame(deg = gl(3, 1, 6, labels = c(0, 4, 8)),
                    noise = gl(2, 3, 6, labels = c("A", "P")))

anova(mlmfit, mlmfit0, X = ~ deg + noise,
      idata = idata, test = "Spherical")

Analysis of Variance Table

Model 1: reacttime ~ 1
Model 2: reacttime ~ 1 - 1

Contrasts orthogonal to
~deg + noise

Greenhouse-Geisser epsilon: 0.904
Huynh-Feldt epsilon:        1.118

  Res.Df Df Gen.var.     F num Df den Df     Pr(>F)     G-G Pr     H-F Pr
1      9      316.58                                                     
2     10  1   996.34 45.31      2     18 9.4241e-08 3.4539e-07 9.4241e-08

anova(mlmfit, mlmfit0, M = ~ deg + noise, X = ~ noise,
      idata = idata, test = "Spherical" )

Analysis of Variance Table

Model 1: reacttime ~ 1
Model 2: reacttime ~ 1 - 1

Contrasts orthogonal to
~noise


Contrasts spanned by
~deg + noise

Greenhouse-Geisser epsilon: 0.9616
Huynh-Feldt epsilon:        1.2176

  Res.Df Df Gen.var.      F num Df den Df     Pr(>F)     G-G Pr     H-F Pr
1      9      1007.0                                                      
2     10  1   2703.2 40.719      2     18 2.0868e-07 3.4017e-07 2.0868e-07

anova(mlmfit, mlmfit0, M = ~ deg + noise, X = ~ deg,
      idata = idata, test = "Spherical" )

Analysis of Variance Table

Model 1: reacttime ~ 1
Model 2: reacttime ~ 1 - 1

Contrasts orthogonal to
~deg


Contrasts spanned by
~deg + noise

Greenhouse-Geisser epsilon: 1
Huynh-Feldt epsilon:        1

  Res.Df Df Gen.var.      F num Df den Df     Pr(>F)     G-G Pr     H-F Pr
1      9        1410                                                      
2     10  1     6030 33.766      1      9 0.00025597 0.00025597 0.00025597

f <- factor(rep(1:2, 5)) # bogus, just for illustration
mlmfit2 <- update(mlmfit, ~f)

Error in eval(predvars, data, env): object 'f' not found

anova(mlmfit2, mlmfit, mlmfit0, X = ~1, test = "Spherical")

Error in anova(mlmfit2, mlmfit, mlmfit0, X = ~1, test = "Spherical"): object 'mlmfit2' not found

anova(mlmfit2, X = ~1, test = "Spherical")

Error in anova(mlmfit2, X = ~1, test = "Spherical"): object 'mlmfit2' not found

# one-model form, eqiv. to previous

### There seems to be a strong interaction in these data
plot(colMeans(reacttime))

Examples for 'stats::anova.mlm'

Comparisons between Multivariate Linear Models