IntervalQuestionStat (version 0.2.0)

ivs2likert: Convert interval-valued responses into their equivalent numerically encoded Likert-type scale answers with minimum \(\theta\)-distance criterion

Description

This function allows to associate each nonempty compact real interval collected as a response in a questionnaire designed with interval-valued scales to its equivalent numerically encoded Likert-type scale answer following the minimum \(\theta\)-distance criterion.

Usage

ivs2likert(x, k = 7, minimum = 1, maximum = 7, theta = 1)

Value

This function returns the nearest Likert-type responses for the given interval-valued data following the minimum \(\theta\)-distance criterion stored either as a numeric object if x argument is a single interval or a list of intervals, that is, an IntervalData or IntervalList instance, or either as a data.frame object whether x is a matrix of intervals, that is, an IntervalMatrix object.

Arguments

x

Either a single interval or either a list or matrix with several intervals stored as an IntervalData object or as an IntervalList or IntervalMatrix instance.

k

A single positive integer number stored as a numeric object which indicates the number of different Likert-type responses to be considered. By default, k = 7.

minimum

A single real number indicating the lower bound of the interval-valued scale used saved as a unique numeric value. By default, minimum = 1.

maximum

A single real number indicating the upper bound of the interval-valued scale used saved as a unique numeric value. By default, maximum = 7.

theta

A single positive real number stored as a unique numeric value which is used for distance computations. By default, theta = 1.

Author

José García-García

Details

If a \(k\)-point Likert-type scale with reference interval \([l,u]\) is considered, then the minimum distance criterion consists on associating each interval-valued scale response with the real number in the set defined by \(\{L_{1},L_{2},\ldots,L_{k}\},\) where each \(L_{i}\) is defined as follows, $$L_{i}=l+(i-1)\frac{u-l}{k-1}, \qquad i=1,2,\ldots,k,$$ with the smallest \(\theta\)-distance to the given data. That is, each interval \(A\) is associated with the real number \(L(A)\) such that $$L(A)=\arg\min_{L\in\{L_{1},L_{2},\ldots, L_{k}\}} d_{\theta} \left(A,\{L\}\right).$$ If ties are produced, they are broken at random.

See Also

Interval-valued responses can be also associated to their corresponding answers in a visual analogue scale through the mid-point criterion implemented in the ivs2vas() function.

Examples

## Some ivs2likert() examples using an interval-valued scale bounded
## between 0 and 10, a 11-point Likert scale, and rho2 distance (theta = 1)

## A single interval-valued response
i <- IntervalData(3, 3.2)
ivs2likert(i, k = 11, minimum = 0, maximum = 10)

## A list of interval-valued responses
list <- IntervalList(c(3, 8.7), c(3.2, 9))
ivs2likert(list, k = 11, minimum = 0, maximum = 10)

## A matrix of interval-valued responses
matrix <- IntervalMatrix(matrix(c(1, 2.6, 1.5, 3, 3.8, 6, 4, 7), 2, 4))
ivs2likert(matrix, k = 11, minimum = 0, maximum = 10)