## Multiple Factorial Analysis

### Description

performs a multiple factorial analysis, using an object of class `ktab`.

### Usage

```mfa(X, option = c("lambda1", "inertia", "uniform", "internal"),
scannf = TRUE, nf = 3)
## S3 method for class 'mfa':
plot(x, xax = 1, yax = 2, option.plot = 1:4, ...)
## S3 method for class 'mfa':
print(x, ...)
## S3 method for class 'mfa':
summary(object, ...)
```

### Arguments

 `X` K-tables, an object of class `ktab` `option` a string of characters for the weighting of arrays options : `lambda1`weighting of group k by the inverse of the first eigenvalue of the k analysis `inertia`weighting of group k by the inverse of the total inertia of the array k `uniform`uniform weighting of groups `internal`weighting included in `X\$tabw` `scannf` a logical value indicating whether the eigenvalues bar plot should be displayed `nf` if scannf FALSE, an integer indicating the number of kept axes `x, object` an object of class 'mfa' `xax, yax` the numbers of the x-axis and the y-axis `option.plot` an integer between 1 and 4, otherwise the 4 components of the plot are displayed `...` further arguments passed to or from other methods

### Value

Returns a list including :
 `tab` a data frame with the modified array `rank` a vector of ranks for the analyses `eig` a numeric vector with the all eigenvalues `li` a data frame with the coordinates of rows `TL` a data frame with the factors associated to the rows (indicators of table) `co` a data frame with the coordinates of columns `TC` a data frame with the factors associated to the columns (indicators of table) `blo` a vector indicating the number of variables for each table `lisup` a data frame with the projections of normalized scores of rows for each table `cg` a data frame with the gravity center for the lisup `link` a data frame containing the projected inertia and the links between the arrays and the reference array `corli` a data frame giving the correlations between the \\$lisup and the \\$li

### Author(s)

Daniel Chessel
Anne B Dufour dufour@biomserv.univ-lyon1.fr

### References

Escofier, B. and Pagès, J. (1994) Multiple factor analysis (AFMULT package), Computational Statistics and Data Analysis, 18, 121–140.

### Examples

```data(friday87)
w1 <- data.frame(scale(friday87\$fau, scal = FALSE))
w2 <- ktab.data.frame(w1, friday87\$fau.blo,
tabnames = friday87\$tab.names)
mfa1 <- mfa(w2, scann = FALSE)
mfa1
plot(mfa1)

data(escopage)
w <- data.frame(scale(escopage\$tab))
w <- ktab.data.frame(w, escopage\$blo, tabnames = escopage\$tab.names)
plot(mfa(w, scann = FALSE))
```

### Worked out examples

```
> ### Name: mfa
> ### Title: Multiple Factorial Analysis
> ### Aliases: mfa print.mfa plot.mfa summary.mfa
> ### Keywords: multivariate
>
> ### ** Examples
>
> data(friday87)
> w1 <- data.frame(scale(friday87\$fau, scal = FALSE))
> w2 <- ktab.data.frame(w1, friday87\$fau.blo,
+     tabnames = friday87\$tab.names)
> mfa1 <- mfa(w2, scann = FALSE)
> mfa1
Multiple Factorial Analysis
list of class function
\$call: mfa(X = w2, scannf = FALSE)
\$nf: 3 axis-components saved

vector     length mode      content
1 \$tab.names 10     character tab names
2 \$blo       10     numeric   column number
3 \$rank      1      numeric   tab rank
4 \$eig       15     numeric   eigen values
5 \$lw        16     numeric   row weights
6 \$tabw      0      NULL      array weights

data.frame nrow ncol content
1  \$tab       16   91   modified array
2  \$li        16   3    row coordinates
3  \$l1        16   3    row normed scores
4  \$co        91   3    column coordinates
5  \$c1        91   3    column normed scores
6  \$lisup     160  3    row coordinates from each table
7  \$TL        160  2    factors for li l1
8  \$TC        91   2    factors for co c1
9  \$T4        40   2    factors for T4comp
10 \$T4comp    40   3    component projection
other elements: NULL
> plot(mfa1)
```
```>
> data(escopage)
> w <- data.frame(scale(escopage\$tab))
> w <- ktab.data.frame(w, escopage\$blo, tabnames = escopage\$tab.names)
> plot(mfa(w, scann = FALSE))
>
>
>
>
```