# intervalPVA

##### Selects a subset of variables observed within a specified time interval using Principal Variable Analysis (PVA)

Principal Variable Analysis (PVA) (Cummings, 2007) selects a subset from a set of the variables such that the variables in the subset are as uncorrelated as possible, in an effort to ensure that all aspects of the variation in the data are covered. Here, all observations in a specified time interval are used for calculation the correlations on which the selection is based.

##### Usage

```
intervalPVA(responses, data, times.factor = "Days", start.time, end.time,
nvarselect = NULL, p.variance = 1, include = NULL,
plot = TRUE, ...)
```

##### Arguments

- responses
A

`character`

giving the names of the columns in`data`

from which the variables are to be selected.- data
A

`data.frame`

containing the columns of variables from which the selection is to be made.- times.factor
A

`character`

giving the name of the column in`data`

containing the factor for times at which the data was collected. Its levels will be used to identify the subset and should be numeric values stored as characters.- start.time
A

`numeric`

giving the time, in terms of a level of`times.factor`

, at which the time interval begins; observations at this time and up to and including`end.time`

will be included.- end.time
A

`numeric`

giving the time, in terms of levels of`times.factor`

, at the end of the interval; observations after this time will not be included.- nvarselect
A

`numeric`

specifying the number of variables to be selected, which includes those listed in`include`

. If`nvarselect = 1`

, as many variables are selected as is need to satisfy`p.variance`

.- p.variance
A

`numeric`

specifying the minimum proportion of the variance that the selected variables must account for,- include
A

`character`

giving the names of the columns in`data`

for the variables whose selection is mandatory.- plot
A

`logical`

indicating whether a plot of the cumulative proportion of the variance explained is to be produced.- ...
allows passing of arguments to other functions.

##### Details

The variable that is most correlated with the other variables is selected first for inclusion. The partial correlation for each of the remaining variables, given the first selected variable, is calculated and the most correlated of these variables is selects for inclusion next. Then the partial correlations are adjust for the second included variables. This process is repeated until the specified criteria have been satisfied. The possibilities are to:

the default (

`nvarselect = NULL`

and`p.variance = 1`

) select all variables in increasing order of amount of information they provide;select exactly

`nvarselect`

variables;select just enough variables, up to a maximum of

`nvarselect`

variables, to explain at least`p.variance`

*100 per cent of the total variance.

##### Value

A `data.frame`

giving the results of the variable selection.
It will contain the columns `Variable`

, `Selected`

,
`h.partial`

, `Added.Propn`

and `Cumulative.Propn`

.

##### References

Cumming, J. A. and D. A. Wood (2007) Dimension reduction via principal variables. *Computational Statistics
and Data Analysis*, **52**, 550--565.

##### See Also

##### Examples

```
# NOT RUN {
data(exampleData)
responses <- c("Area","Area.SV","Area.TV", "Image.Biomass", "Max.Height","Centre.Mass",
"Density", "Compactness.TV", "Compactness.SV")
results <- intervalPVA(responses, longi.dat,
start.time = "31", end.time = "31",
p.variance=0.9, plot = FALSE)
# }
```

*Documentation reproduced from package growthPheno, version 1.0-13, License: GPL (>= 2)*