unibiv has the purpose of detecting univariate and bivariate outliers

Run this code to see the output shown in the help file

n=500; p=5; randn('state', 123456); Y=randn(n,p); [out]=unibiv(Y);

Stack loss data.

Y=load('stack_loss.txt'); % Show robust confidence ellipses out=unibiv(Y,'plots',1,'textlab',1);

`Y`

— Input data.
Matrix.n x v data matrix; n observations and v variables. Rows of Y represent observations, and columns represent variables.

Missing values (NaN's) and infinite values (Inf's) are allowed, since observations (rows) with missing or infinite values will automatically be excluded from the computations.

**
Data Types: **`single|double`

Specify optional comma-separated pairs of `Name,Value`

arguments.
`Name`

is the argument name and `Value`

is the corresponding value. `Name`

must appear
inside single quotes (`' '`

).
You can specify several name and value pair arguments in any order as ```
Name1,Value1,...,NameN,ValueN
```

.

```
'rf',0.99
```

,```
'robscale',2
```

,```
'plots',2
```

,```
'textlab',0
```

,```
'tag','new_tag'
```

,```
'madcoef',2
```

`rf`

—It specifies the confidence
level of the robust bivariate ellipses.scalar.0<rf<1.

The default value is 0.95 that is the outer contour in presence of normality for each ellipse should leave outside 5% of the values.

**Example: **```
'rf',0.99
```

**Data Types: **`double`

`robscale`

—how to compute dispersion.scalar.It specifies the statistical indexes to use to compute the dispersion of each variable and the correlation among each pair of variables.

robscale=1 (default): the program uses the median correlation and the MAD as estimate of the dispersion of each variable;

robscale=2: the correlation coefficient among ranks is used (Spearman's rho) and the MAD as estimate of the dispersion of each variable;

robscale=3: the correlation coefficient is based on Kendall's tau b and the MAD as estimate of the dispersion of each variable;

robscale=4: tetracoric correlation coefficient is used and the MAD as estimate of the dispersion of each variable;

otherwise the correlation and the dispersion of the variables are computed using the traditional (non robust) formulae around the univariate medians.

**Example: **```
'robscale',2
```

**Data Types: **`double`

`plots`

—Plot on the screen.scalar.It specifies whether it is necessary to produce a plot with univariate standardized boxplots on the main diagonal and bivariate confidence ellipses out of the main diagonal. If plots is equal to 1 a plot which contains univariate standardized boxplots on the main diagonal and bivariate confidence ellipses out of the main diagonal is produced on the screen. If plots is <> 1 no plot is produced. As default no plot is produced.

**Example: **```
'plots',2
```

**Data Types: **`double`

`textlab`

—plot labels.scalar.Scalar which controls the labels in the plots. If textlab=1 and plots=1 the labels associated to the units which are univariate outliers or which are outside the confidence levels of the contours are displayed on the screen.

**Example: **```
'textlab',0
```

**Data Types: **`double`

`tag`

—plot tag.character.It identifies the handle of the plot which is about to be created. The default is to use tag 'pl_unibiv'. Notice that if the program finds a plot which has a tag equal to the one specified by the user, then the output of the new plot overwrites the existing one in the same window else a new window is created.

**Example: **```
'tag','new_tag'
```

**Data Types: **`char`

`madcoef`

—scaled MAD.scalar.Coefficient which is used to scale MAD coefficient to have a robust estimate of dispersion. The default is 1.4815 so that 1.4815*MAD(N(0,1))=1.

Remark: if mad =median(y-median(y))=0 then the interquartile range is used. If also the interquartile range is 0 than the MD (mean absolute deviation) is used. In other words MD=mean(abs(y-mean(Y))

**Example: **```
'madcoef',2
```

**Data Types: **`double`

`fre`

—Details about the univariate and
bivariate outliers.
`n -by- 4 `

matrix1st col = index of the units;

2nd col = number of times unit has been declared univariate outliers;

3rd col = number of times unit has been declared bivariate outlier;

4th col = pseudo MD as sum of bivariate MD.

Riani, M., Zani S. (1997). An iterative method for the detection of multivariate outliers, Metron, vol. LV, pp. 101-117.