ffAnova | R Documentation |

Analysis of variance table for a linear model using type `II`

* sums of squares,
which are described in Langsrud et al. (2007).
Type `II`

* extends the type `II`

philosophy to continuous variables.
The results are invariant to scale changes and pitfalls are avoided.

```
ffAnova(formula, data = NULL)
```

`formula` |
A model |

`data` |
An optional data frame, list or environment. |

This function is a variant of `ffmanova`

for the univariate special case.
The two input parameters will be interpreted by `model.frame`

.

An object of class `"anova"`

(see `anova`

).

Øyvind Langsrud and Bjørn-Helge Mevik

Langsrud, Ø., Jørgensen, K., Ofstad, R. and Næs, T. (2007):
“Analyzing Designed Experiments with Multiple Responses”,
*Journal of Applied Statistics*, **34**, 1275-1296.

```
# Generate example data
set.seed(123)
a <- c(0, 0, 0, 10, 10, 10, 1, 1, 1)
A <- as.character(a) # A is categorical
b <- 1:9
y <- rnorm(9)/10 + a # y depends strongly on a (and A)
a100 <- a + 100 # change of scale (origin)
b100 <- b + 100 # change of scale (origin)
# Four ways of obtaining the same results
ffAnova(y ~ A * b)
ffAnova(y ~ A * b100)
ffAnova(lm(y ~ A * b))
ffAnova(y ~ A * b, data.frame(A = A, y = y, b = 1:9))
# Second order continuous variable
ffAnova(y ~ a + I(a^2))
# Model equivalent to 'y ~ A * b'
ffAnova(y ~ (a + I(a^2)) * b)
# Demonstrating similarities and differences using package car
if (!require(car)) # Package car is loaded if available
Anova <- function(...) { # Replacement function if car not available
warning("No results since package car is not available")}
lm_Ab <- lm(y ~ A * b)
lm_Ab100 <- lm(y ~ A * b100)
# Type II same as type II* in this case
Anova(lm_Ab) # Type II
Anova(lm_Ab100) # Type II
ffAnova(lm_Ab) # Type II*
ffAnova(lm_Ab100) # Type II*
# Type III depends on scale
Anova(lm_Ab, type = 3)
Anova(lm_Ab100, type = 3)
lm_a <- lm(y ~ a + I(a^2))
lm_a100 <- lm(y ~ a100 + I(a100^2))
# Now Type II depends on scale
Anova(lm_a) # Type II
Anova(lm_a100) # Type II
ffAnova(lm_a) # Type II*
ffAnova(lm_a100) # Type II*
```

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