# mona

##### MONothetic Analysis Clustering of Binary Variables

Returns a list representing a divisive hierarchical clustering of a dataset with binary variables only.

- Keywords
- cluster

##### Usage

`mona(x, trace.lev = 0)`

##### Arguments

- x
data matrix or data frame in which each row corresponds to an observation, and each column corresponds to a variable. All variables must be binary. A limited number of missing values (

`NA`

s) is allowed. Every observation must have at least one value different from`NA`

. No variable should have half of its values missing. There must be at least one variable which has no missing values. A variable with all its non-missing values identical is not allowed.- trace.lev
logical or integer indicating if (and how much) the algorithm should produce progress output.

##### Details

`mona`

is fully described in chapter 7 of Kaufman and Rousseeuw (1990).
It is “monothetic” in the sense that each division is based on a
single (well-chosen) variable, whereas most other hierarchical methods
(including `agnes`

and `diana`

) are “polythetic”, i.e. they use
all variables together.

The `mona`

-algorithm constructs a hierarchy of clusterings,
starting with one large cluster. Clusters are divided until all
observations in the same cluster have identical values for all variables.

At each stage, all clusters are divided according to the values of one variable. A cluster is divided into one cluster with all observations having value 1 for that variable, and another cluster with all observations having value 0 for that variable.

The variable used for splitting a cluster is the variable with the maximal total association to the other variables, according to the observations in the cluster to be splitted. The association between variables f and g is given by a(f,g)*d(f,g) - b(f,g)*c(f,g), where a(f,g), b(f,g), c(f,g), and d(f,g) are the numbers in the contingency table of f and g. [That is, a(f,g) (resp. d(f,g)) is the number of observations for which f and g both have value 0 (resp. value 1); b(f,g) (resp. c(f,g)) is the number of observations for which f has value 0 (resp. 1) and g has value 1 (resp. 0).] The total association of a variable f is the sum of its associations to all variables.

##### Value

an object of class `"mona"`

representing the clustering.
See `mona.object`

for details.

##### Note

In cluster versions before 2.0.6, the algorithm entered an
infinite loop in the boundary case of one variable, i.e.,
`ncol(x) == 1`

, which currently signals an error (because the
algorithm now in C, haes not correctly taken account of this special case).

##### Missing Values (`NA`

s)

The mona-algorithm requires “pure” 0-1 values. However,
`mona(x)`

allows `x`

to contain (not too many)
`NA`

s. In a preliminary step, these are “imputed”,
i.e., all missing values are filled in. To do this, the same measure
of association between variables is used as in the algorithm. When variable
f has missing values, the variable g with the largest absolute association
to f is looked up. When the association between f and g is positive,
any missing value of f is replaced by the value of g for the same
observation. If the association between f and g is negative, then any missing
value of f is replaced by the value of 1-g for the same
observation.

##### See Also

`agnes`

for background and references;
`mona.object`

, `plot.mona`

.

##### Examples

```
# NOT RUN {
data(animals)
ma <- mona(animals)
ma
## Plot similar to Figure 10 in Struyf et al (1996)
plot(ma)
## One place to see if/how error messages are *translated* (to 'de' / 'pl'):
ani.NA <- animals; ani.NA[4,] <- NA
aniNA <- within(animals, { end[2:9] <- NA })
aniN2 <- animals; aniN2[cbind(1:6, c(3, 1, 4:6, 2))] <- NA
ani.non2 <- within(animals, end[7] <- 3 )
ani.idNA <- within(animals, end[!is.na(end)] <- 1 )
try( mona(ani.NA) ) ## error: .. object with all values missing
try( mona(aniNA) ) ## error: .. more than half missing values
try( mona(aniN2) ) ## error: all have at least one missing
try( mona(ani.non2) ) ## error: all must be binary
try( mona(ani.idNA) ) ## error: ditto
# }
```

*Documentation reproduced from package cluster, version 2.0.7-1, License: GPL (>= 2)*