Calculate Concentration and Dispersion in Ordered Rating Scales

Description

This package calculates concentration and dispersion in ordered rating scales. It implements various measures of concentration and dispersion to describe what researchers variably call agreement, concentration, consensus, dispersion, or polarization among respondents in ordered data. It also implements other related measures to classify distributions.

Details

In ordered rating scales, concentration occurs if many values on the scale cluster around one value. Dispersion describes the absense of concentration. Various measures exist to calculate concentration and dispersion.

The package provides a generic city-block based (concentration) measure, and a generic measure of dispersion (disper). To use Van der Eijk's (2001) algorithmic approach agreement "A", call agreement. The derived polarization lets you calculate a polarization score based on agreement A. Values are inverted and standardized to [0, 1]. Other specific measures: Leik's measure of ordinal dispersion (Leik), Tatsle and Wierman's (consensus), Blair and Lacy's (dsquared, lsquared, and BlairLacy), the measure by Kvalseth (Kvalseth), Berry and Mielke's IOV (BerryMielke), Reardon (Reardon) or Garcia-Montalvo and Reynal-Querol's (MRQ).

The package also includes functions to classify distributions according to Galtung's (1969) AJUS-system (ajus), and changes over time according to Galtung's (1969) ISD-system (isd). Moreover, the function modes can identify the position of multiple modes.

Author(s)

Didier Ruedin

Contributor: Clem Aeppli

Maintainer: Didier Ruedin <didier.ruedin@unine.ch>

References

van der Eijk, C. (2001) Measuring agreement in ordered rating scales, Quality and Quantity 35(3):325-341.

Galtung, J. (1969) Theory and Methods of Social Research. Oslo: Universitetsforlaget.

Calculate IOV

Description

Calculate Berry and Mielke's IOV.

Usage

BerryMielke(V)

Arguments

Details

This function calculates Berry and Mielke's IOV, a measure of dispersion based on squared Euclidean distances. This function follows the presentation by Blair and Lacy 2000, but includes the adjustment for Tmax omitted by Blair and Lacy as there is no reason to leave it out. The derived measure COV by Kvalseth is implemented as Kvalseth. Usually, the IOV is equivalent to 1-lsquared.

Value

The function returns the IOV.

Author(s)

Didier Ruedin

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

Berry, K., and P. Mielke. 1992. Assessment of Variation in Ordinal Data. Perceptual and Motor Skills 74 (1): 63-66.

See Also

lsquared, Kvalseth

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
BerryMielke(V)

Calculate l

Description

Calculate Blair and Lacy's l.

Usage

BlairLacy(V)

Arguments

Details

This function calculates Blair and Lacy's l, a measure of concentration based on linear Euclidean distances. This function follows the presentation by Blair and Lacy 2000. The measure l-squared by Blair and Lacy is implemented as lsquared.

Value

The function returns the l.

Author(s)

Didier Ruedin

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

lsquared

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
BlairLacy(V)

Approximate variance of Leik's D

Description

Calculate approximate variance of Leik's D

Usage

D.variance(V)

Arguments

Details

Helper function to calculate approximate variance of Leik's (1966) D.

Value

Approximate variance of D

Author(s)

Clem Aeppli

References

Leik, R. (1966) A measure of ordinal consensus, Pacific Sociological Review 9(2):85-90.

See Also

Leik

Calculate Kvalseth's COV

Description

Calculate Kvalseth's COV.

Usage

Kvalseth(V)

Arguments

Details

This function calculates Kvalseth's COV, a measure of dispersion based on linear Euclidean distances. It is based on the IOV measure, implemented as BerryMielke. This function follows the presentation by Blair and Lacy 2000.

Value

The function returns the COV.

Author(s)

Didier Ruedin

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

BerryMielke, lsquared

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
Kvalseth(V)

Calculate ordinal dispersion

Description

Calculates ordinal dispersion as introduced by Leik (1966)

Usage

Leik(V)

Arguments

Details

This function calculates ordinal dispersion as introduced by Robert K. Leik (1966). It uses the cumulative frequency distribution to determine ordinal dispersion. The extremes (agreement, polarization) largely correspond to the types used by Cees van der Eijk. By contrast, the mid-point depends on the number of categories: it tends toward 0.5 as the number of categories increases. Leik defends this difference by highlighting the increased probability of falling into polarized patterns when there are fewer categories. If all observations are in the same category, ordinal dispersion is 0. With half the observations in one extreme category, and half the observations in the other extreme, Leik's measure gives a value of 1.

The dispersion measure is a percentage, and can be interpreted accordingly. Ordinal dispersion can be used to express consensus or agreement, simply by taking: 1 - ordinal dispersion.

Value

The function returns the ordinal dispersion

Author(s)

Didier Ruedin

References

Leik, R. (1966) A measure of ordinal consensus, Pacific Sociological Review 9(2):85-90.

See Also

polarization, agreement

Examples

# Example 1:
V <- c(30,40,210,130,530,50,10)
# Calculate polarization
Leik(V)
# The ordinal dispersion is given as 0.287
polarization(V)
# Polarization is given as 0.194 (as contrast)

Calculates MRQ polarization index

Description

This function calculates the MRQ polarization index from a population vector.

Usage

MRQ(Z)

Arguments

Details

This function implements the polarization index introduced by Garcia-Montalvo and Reynal-Querol (2005), also known as the Reynal-Querol index of polarization (RQ). It is a measure of dispersion based on squared Euclidean distances. The frequency vector needs to be standardized for the Reynal-Querol index to work; if the sum of the frequency vector is not 1 (i.e. it is not standardized), the function automatically standardizes the frequency vector by dividing each element of the vector by the sum of the vector. The assumption is that the frequencies are complete.

Value

Index of polarization (RQ).

Author(s)

Didier Ruedin

References

Garcia-Montalvo, Jose, and Marta Reynal-Querol. 2005. Ethnic Polarization, Potential Conflict, and Civil Wars. American Economic Review 95(3): 796-816.

Reynal-Querol, Marta. 2002. Ethnicity, Political Systems, and Civil Wars. Journal of Conflict Resolution 46(1): 29-54.

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
MRQ(V)

Reardon's entropy

Description

This function calculates Reardon's (2009) entropy from a frequency vector

Usage

Reardon(V)

Arguments

Details

Calculate Reardon's (2009) entropy.

Value

measure of entropy

Author(s)

Clem Aeppli

References

Reardon, S. 2009. Measures of Ordinal Segregation. Research on Economic Inequality 17:129-55. <DOI: 10.1108/S1049-2585(2009)0000017011>

See Also

disper

Calculate van der Eijk's measure of agreement A

Description

Calculate agreement in ordered rating scales. This function implements van der Eijk's (2001) measure of agreement A, which can be used to describe agreement or consensus among respondents.

Usage

agreement(V, old = FALSE)

Arguments

Details

This is the main function to calculate agreement. A frequency vector describes the number of observations in a given category. For example, the vector [10,20,30,15,4] describes 10 observations with position 1, 20 observations with position 2, 30 observations with position 3, 15 observations with position 4, and 4 observations with position 5. At least three categories are required to calculate agreement.

Polarization can be measured by extension. A convenience function polarization is provided.

Value

The function returns the measure of agreement A. A is 1 if there is perfect unimodality (=agreement); A is 0 if there is perfect uniformity; A is -1 if there is perfect bimodality (=lack of agreement)

Author(s)

Didier Ruedin

References

van der Eijk, C. 2001. Measuring agreement in ordered rating scales. Quality and Quantity 35(3):325-341. <DOI: 10.1023/A:1010374114305>

See Also

polarization

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
# Calculate agreement A
agreement(V)
# The rate of agreement is given as 0.6113333

Simulated coding error for agreement A

Description

Calculate agreement in ordered rating scales, but simulates coding error.

Usage

agreementError(V, n=500, e=0.01, pos=FALSE)

Arguments

Details

This function calculates agreement A, but simulates coding error. This can be useful to estimate standard errors and central tendency if certain positions are not observed. If all positions are observed in the vector V, bootstrapping can be used to estimate standard errors. If certain positions are not observed, bootstrapping is limited. Take an extreme example: [3 0 0 0 0]. Here we have three observations at the first position, but none at the others. Bootstrapping will always lead to the same agreement score. This can be misleading if coding error can be assumed. For example, if these three observations refer to a ‘strongly agree’ answer, it is usually conceivable that some or all of these answers could refer to ‘somewhat agree’. This function lets you specify how many of the observations should be assumed to be potentially mis-coded, and calculates agreement accordingly. If an observation is assumed to be potentially mis-coded, it is randomly set to the position to the left, the position to the right, or the position itself. If the first or last observation is chosen, the simulation takes care not to suggest values that could not occur.

You can run the function a few (hundred) times to get summary statistics of the result (mean, median, standard deviation, etc.). The function compareAgreement does just this, and compares the result with the agreement score if no coding error is assumed.

Value

The function returns the measure of agreement A.

Author(s)

Didier Ruedin

See Also

agreement, compareAgreement, collapse

Examples

# Sample data:
V <- c(1,1,1,1,2,3,3,3,3,4,4,4,4,4,4)
# calculate agreement; using collapse() to create the frequency vector
agreement(collapse(V))
# Calculate agreement A with coding error:
agreementError(V)
# Assume that all values could have coding error:
agreementError(V, e=1)
# Run the function a few times and show the mean:
z <- replicate(1000, agreementError(V))
mean(z) 
hist(z) # etc.
# the example mentioned, population vector [3 0 0 0 0]:
V2 <- c(1,1,1)
agreementError(V2, pos=1:5)
# you can also use the compareAgreement function
compareAgreement(V2, pos=1:5)

Classify distributions

Description

Classify distributions using the AJUS-system introduced by Galtung (1969).

Usage

ajus(V, tolerance=0.1, variant="modified")

Arguments

Details

This function implements the AJUS-system introduced by Galtung (1969). The input is a frequency vector; the output is a classification of the distribution.

Distributions are classified as A if they are unimodal with a peak in the centre, as J if they are unimodal with a peak at either end, as U if they are bimodal with a peak at both ends, and as S if they are multimodal. In addition to Galtung's classification, the function classifies distributions as F if there is no peak and all values are more or less the same (flat). Furthermore, a distinction is drawn between J and L distributions, depending on whether they increase or decrease: J types have a peak on the right, L types have the peak on the left. The skew is given as +1 for a positive skew, as 0 for no skew, and -1 for a negative skew.

The skew is identified by comparing the sum of values left and right of the midpoint respectively. For J-type of distributions, the skew is identified on the basis of the changes between values. This way, long tails cannot influence the skew, and a single peak at the left and right-hand end can be differentiated in all cases.

The aim of the AJUS system is to reduce complexity. Initially the intuition was to classify distributions on an ad-hoc basis (i.e. eye-balling). Using an algorithm is certainly more reliable, and useful if one is interested in classifying (and comparing) a large number of distributions. The argument tolerance, however is not a trivial choice and can affect results. Use the helper function ajusCheck to check sensitivity to different values of the tolerance parameter.

You can choose between a strict AJUS classification and a modified AJUSFL classification (default). The AJUS classification does not include a type for distributions without peaks (F type), and NA is returned instead. The AJUS classification does not draw a distinction between unimodal distributions with a peak at the end: the skew needs to be considered to distinguish between increasing and decreasing cases. The modified variant (default) includes the F type and the L type along with the original AJUS types.

Value

The function returns a list. The type returns a string corresponding to the pattern described by Galtung (A,J,U,S) or (F,L). The skew returns a number to describe the direction of the skew. The pattern returns the simplified pattern of the distribution. It indicates whether two values were considered the same (0), or if there was an increase (1) or decrease (-1) between two consecutive values. The length of the pattern is equal to the length of the frequency vector minus one.

Author(s)

Didier Ruedin

References

Galtung, J. (1969) Theory and Methods of Social Research. Oslo: Universitetsforlaget.

See Also

isd, ajusCheck, ajusPlot

Sensitivity test for AJUS

Description

Check sensitivity of AJUS to different tolerance parameters.

Usage

ajusCheck(V, t=seq(from=0.05, to=0.2, by=0.05), variant="modified")

Arguments

Details

This function runs the AJUS system with a range of tolerance parameters. This way, you can easily check how sensitive the classification of the distribution is to the tolerance parameter.

Value

The function returns a list. The tolerance returns the tolerance parameters tested. The type returns a series of strings corresponding to the pattern described by Galtung (A,J,U,S) or (F, L) for each tolerance parameter. The skew returns a number to describe the direction of the skew. See ajus for a description of the different arguments and the AJUS types.

Author(s)

Didier Ruedin

See Also

ajus

Plot vector with AJUS type

Description

Plot a frequency vector among with its AJUS type.

Usage

ajusPlot(V, tolerance=0.1, variant="modified", ...)

Arguments

Details

This function plots the frequency vector along with its AJUS classification and skew. See ajus for a description of the AJUS system and the different parameters. In contrast to the ajus function, ajusPlot can deal with missing values. Missing values are removed when calculating the AJUS type (because AJUS does not handle missing values), but they are considered in the plot. This makes ajusPlot useful for classifying time series where missing values may occur. Additional arguments can be passed to the underlying plot function.

Author(s)

Didier Ruedin

See Also

ajus

Censor helper function

Description

Helper function to censor frequency vectors

Usage

censor(V, left=0, right=100)

Arguments

Details

Helper function to censor frequency vectors

Value

censored frequency vector

Author(s)

Clem Aeppli

See Also

truncate

Reduces a vector to a frequency vector

Description

Takes a vector and reduces it to a frequency vector.

Usage

collapse(D,pos=FALSE, na.rm=TRUE)

Arguments

Details

This function reduces a vector to a frequency vector. This function is very similar to the way table summarizes vectors, but this function can deal with categories of frequency 0 if the argument pos is specified. Here we assume a vector with an entry for each individual (the order of the values is ignored). Each entry states the position of an individual. When the number of positions is naturally limited, such as when categorical positions are used, frequency vectors can summarize this information: how many individuals have position 1, how many individuals have position 2, etc. A frequency vector has an entry for each position in the population (sorted in ascending order). Each entry states the number of individuals in the population with this position.

The argument pos is required if certain positions do not occur in the population (or if there is a chance that they do not occur in a specific sub-population). For example, if we have positions on a 7-point scale, and position 3 never occurs in the population, the argument pos must be specified. In this case, the argument may be pos=1:7. We can also use categories more generally, as in c(-3, -1, 0, 0.5, 1, 2, 5). Specifying the positions of categories when all positions occur in the population has no side-effects. See the example for an illustration.

By default, missing values (NA) are removed with as.numeric(na.omit()). This helps with some vectors that include NA that fail otherwise. If NA are maintained with na.rm=FALSE, they are included as the last category. The argument pos cannot include NA as a position; NA are removed if the argument pos is used.

Value

A frequency vector

Author(s)

Didier Ruedin

See Also

expand

Examples

V = c(1,1,1,1,1,1,3,3,3,3,4,5,5,5,5)
# summarize using table()
table(V)
# summarize using collapse()
collapse(V)
# assuming possible values (1,2,3,4,5), we get that zero times 2 included:
collapse(V, pos=c(1,2,3,4,5))

Compare agreement A with and without simulated coding error

Description

Calculate agreement in ordered rating scales, and compares this to agreement with simulated coding error.

Usage

compareAgreement(V, n=500, e=0.01, N=500, pos=FALSE)

Arguments

Details

This function calculates agreement on a vector, and compares the value with agreement with simulated coding error. It runs the function agreementError N times. The other arguments (n, e, pos) are passed down to the agreementError function.

Value

The function returns a list with agreement A without simulated coding errors, the mean of agreement with simulated coding error, and the standard deviation of agreement with simulated coding error.

Author(s)

Didier Ruedin

See Also

agreement, agreementError

Examples

# Sample data:
V <- c(1,1,1,1,2,3,3,3,3,4,4,4,4,4,4)
compareAgreement(V)

Compares two values

Description

This is a helper function to compare two values.

Usage

compareValues(A,B,tolerance=0.1)

Arguments

Details

This is a helper function compare two values. Two values are more or less the same, or one of the two is bigger.

Value

The function returns number to describe the relationship: -1 if A is bigger, 1 if B is bigger, and 0 if the two are more or less the same.

Author(s)

Didier Ruedin

Measures concentration

Description

This function measures concentration in a frequency vector

Usage

concentration(V, metric=2)

Arguments

Details

This function measures concentration in a frequency vector in city blocks. The default metric is 2.

Value

measure of concentration

Author(s)

Clem Aeppli

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
concentration(V)

Calculate Tastle and Wierman's measure of consensus

Description

Calculate consensus in ordered rating scales. This function implements Tastle and Wierman's (2007) measure of consensus (ordinal dispersion), which can be used to describe agreement, consensus, dispersion, or polarization among respondents.

Usage

consensus(V)

Arguments

Details

This function calculates consensus following Tastle and Wierman (2007). The measure of consensus is based on the Shannon entropy. A frequency vector describes the number of observations in a given category. For example, the vector [10,20,30,15,4] describes 10 observations with position 1, 20 observations with position 2, 30 observations with position 3, 15 observations with position 4, and 4 observations with position 5.

If you come across an error that the vector supplied does not contain whole numbers, try round(V,0) to remove any detritus from calculating the frequency vector.

Value

The function returns the measure of consensus. It is 1 if there is perfect uniformity; it is 0 if there is perfect bimodality (=lack of agreement)

Author(s)

Didier Ruedin

References

Tastle, W., and M. Wierman. 2007. Consensus and dissention: A measure of ordinal dispersion. International Journal of Approximate Reasoning 45(3): 531-545.

See Also

agreement

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
# Calculate consensus
consensus(V)
# The degree of consensus is given as 0.7256876

Approximate variance of consensus

Description

Calculate approximate variance of Blair and Lacy's consensus Cns

Usage

consensus.variance(V)

Arguments

Details

Helper function to calculate approximate variance of Blair and Lacy's (2000) consensus Cns.

Value

Approximate variance of Blair and Lacy's consensus Cns

Author(s)

Clem Aeppli

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

consensus

Measures distance

Description

This function measures distance between two frequency vectors

Usage

disper(A, B, metric=2)

Arguments

Details

Calculates the distance between two frequency vectors.

Value

measure of distance

Author(s)

Clem Aeppli

See Also

concentration

Measures dispersion

Description

This function measures dispersion in a frequency vector

Usage

dispersion(V, metric=2)

Arguments

Details

dispersion is 1-concentration

Value

measure of dispersion

Author(s)

Clem Aeppli

See Also

concentration

Calculate d-squared

Description

Calculate Blair and Lacy's d-squared.

Usage

dsquared(V)

Arguments

Details

This function calculates Blair and Lacy's d-squared, a measure of concentration based on squared Euclidean distances. This function follows the presentation by Blair and Lacy 2000. The measure l-squared normalizes the values and is implemented as lsquared.

Value

The function returns the d-squared.

Author(s)

Didier Ruedin

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

lsquared, BlairLacy

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
dsquared(V)

Calculate Shannon entropy

Description

Calculate Shannon entropy, following Tastle and Wierman.

Usage

entropy(V)

Arguments

Details

This function calculates the Shannon entropy following Tastle and Wierman (2007). A frequency vector describes the number of observations in a given category. For example, the vector [10,20,30,15,4] describes 10 observations with position 1, 20 observations with position 2, 30 observations with position 3, 15 observations with position 4, and 4 observations with position 5.

This function follows Tastle and Wierman and ignores categories with zero observations. This does not follow the formula indicated.

See consensus for a function that considers the order of categories.

Value

The function returns the Shannon entropy.

Author(s)

Didier Ruedin

References

Tastle, W., and M. Wierman. 2007. Consensus and dissention: A measure of ordinal dispersion. International Journal of Approximate Reasoning 45 (3): 531-545.

See Also

consensus

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
# Calculate entropy
entropy(V)

Expands a frequency vector to a vector

Description

This function expands a frequency vector to a vector.

Usage

expand(F)

Arguments

Details

This function takes a frequency vector and expands it to a longer vector with one entr for each observation. It is reverses the collapse function. A frequency vector has an entry for each position in the population. Each entry states the number of individuals in the population with this position. Here we create a vector with an entry for each individual.

Value

A vector

Author(s)

Didier Ruedin

See Also

collapse

Classify changes over time

Description

Classify changes over time using the ISD-system introduced by Galtung (1969).

Usage

isd(V, tolerance=0.1)

Arguments

Details

This function implements the ISD-system introduced by Galtung (1969). The input is a vector of length 3. Each value stands for a different point in time. The ISD-system examines the two transition points, and classifies the changes over time.

Value

The function returns a list. The type returns a number corresponding to the pattern described by Galtung. The description returns a string where the two transitions are spelled out (increase, flat, decrease).

Author(s)

Didier Ruedin

References

Galtung, J. (1969) Theory and Methods of Social Research. Oslo: Universitetsforlaget.

See Also

ajus

Approximate variance of Blair and Lacy's l

Description

Calculate approximate variance of Blair and Lacy's (2000) l

Usage

l.variance(V)

Arguments

Details

Helper function to calculate approximate variance of Blair and Lacy's (2000) l.

Value

Approximate variance of Blair and Lacy's l

Author(s)

Clem Aeppli

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

BlairLacy

Calculate l-squared

Description

Calculate Blair and Lacy's l-squared.

Usage

lsquared(V)

Arguments

Details

This function calculates Blair and Lacy's l-squared, a measure of concentration based on squared Euclidean distances. This function follows the presentation by Blair and Lacy 2000. The measure ‘l’ by Blair and Lacy is implemented as BlairLacy.

Value

The function returns the l-squared.

Author(s)

Didier Ruedin

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

BerryMielke, BlairLacy

Examples

# Sample data
V <- c(30,40,210,130,530,50,10)
lsquared(V)

Approximate variance of Blair and Lacy's lsquared

Description

Calculate approximate variance of Blair and Lacy's (2000) lsquared

Usage

lsquared.variance(V)

Arguments

Details

Helper function to calculate approximate variance of Blair and Lacy's (2000) lsquared.

Value

Approximate variance of Blair and Lacy's lsquared

Author(s)

Clem Aeppli

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

BlairLacy

Non-zero minimum

Description

Helper function to calculate the smallest value of the vector except for 0 (non-zero minimum).

Usage

minnz(V)

Arguments

Details

This is a helper function to calculate the non-zero minimum of a vector. The result is the smallest value of the vector, but cannot be zero.

Value

The function returns the non-zero minimum

Author(s)

Didier Ruedin

Identify multiple modes

Description

Identifies (multiple) modes in a frequency vector.

Usage

modes(V, pos=FALSE, tolerance=0.1)

Arguments

Details

This function identifies which positions of a frequency vector correspond to the mode. If there are multiple modes of the same value, all matching positions will be reported. Use the function collapse to create frequency vectors if necessary.

Value

The function returns a list. The at returns the categories of the frequency vector. Either these categories were specified using the argument pos, or we assume it to be 1:k (with k the number of categories in the frequency vector). If the length of the pos argument does not match the length of the frequency vector, a warning is shown, and the pos argument is ignored. The frequencies returns the frequency vector. The mode returns the value of the mode(s). If there are multiple modes, they are listed. Similar frequencies are counted as equal, using the tolerance argument. To prevent similar frequencies to be considered the same, set tolerance to 0. The positions returns the positions of the vector that correspond to the mode. This will differ from the mode if pos is provided.The contiguous returns TRUE of all modes are contiguous, and FALSE if there are different values in between. If there is only one mode, it is defined as contiguous (i.e. TRUE).

Author(s)

Didier Ruedin

See Also

secondModes

Examples

# Example 1: finding the mode
V1 <- c(30,40,210,130,530,50,10)
modes(V1) # will find position 5
# Example 2:
V2 <- c(3,0,4,1)
modes(V2) # will find position 3
# Example 3: providing categories
modes(V2,pos=-1:2) # will still find position 3, but give the value of 1 as mode
# Example 4: similar values
V3 <- c(30,40,500,130,530,50,10) 
modes(V3, tolerance=30) # will find positions 3 and 5 (500 and 530 are nearly the same)

Calculates patterns agreement

Description

Helper function to calculate agreement A from a pattern vector.

Usage

patternAgreement(P, old=FALSE)

Arguments

Details

This is a helper function to calculate agreement A from a pattern vector.

Value

The function returns the measure of agreement A

Author(s)

Didier Ruedin

See Also

agreement

Creates pattern vector

Description

Helper function to create a pattern vector from a frequency vector.

Usage

patternVector(V)

Arguments

Details

This is a helper function to create a pattern vector from a frequency vector. A pattern vector reduced all values greater or equal to 1 to 1, and values of 0 remain 0. A frequency vector (0,0,18,59,0,34,2) is turned into a pattern vector (0,0,1,1,0,1,1).

Value

The function returns a pattern vector.

Author(s)

Didier Ruedin

See Also

agreement

Calculate polarization

Description

Calculates polarization, based on measure of agreement A

Usage

polarization(V, old = FALSE)

Arguments

Details

This function calculates polarization by re-scaling agreement A introduced by Cees van der Eijk. Whereas agreement A ranges from -1 to 1, polarization ranges from 0 to 1. If all observations are in the same category, polarization is 0. With half the observations in one category, and half the observations in a different (non-neighbouring) category, polarization is 1. Polarization is 0.5 for a uniform distribution over all categories.

Value

The function returns a polarization score

Author(s)

Didier Ruedin

See Also

agreement

Examples

V <- c(30,40,210,130,530,50,10)
# Calculate polarization
polarization(V)
# The rate of polarization is given as 0.1943333

Remove zeros and repeated values

Description

This is a helper function to remove all zeros and repeated values from a vector.

Usage

reduceVector(X)

Arguments

Details

This is a helper function to strip all zeros and repeated values from a vector.

Value

The function returns vector

Author(s)

Didier Ruedin

See Also

agreement

Approximate variance of the categorical standard deviation

Description

Calculate approximate variance of the categorical standard deviation

Usage

sd.variance(V)

Arguments

Details

Helper function to calculate approximate variance of the categorical standard deviation.

Value

Approximate variance of the categorical standard deviation

Author(s)

Clem Aeppli

See Also

truncate

Most common and second most common values

Description

Identifies the most common (multiple) modes for frequency vectors as well as the second most common values.

Usage

secondModes(V, pos=FALSE, tolerance=0.1)

Arguments

Details

This function identifies which positions of a frequency vector correspond to the mode(s) as implemented in the modes function. It also reports the second most common position in the same manner.

Value

The function returns a list for the most common and the second most common value(s). The output corresponds to that of the modes function.

Author(s)

Didier Ruedin

See Also

modes

Truncate helper function

Description

Helper function to truncate frequency vectors

Usage

truncatevector(V, left=0, right=100)

Arguments

Details

Helper function to truncate frequency vectors

Value

truncated frequency vector

Author(s)

Clem Aeppli

See Also

censor

Approximate variance of the consensus (Cns) estimator

Description

Calculate approximate variance of the consensus (Cns) estimator

Usage

var.variance(V)

Arguments

Details

Helper function to calculate approximate variance of the Consensus (Cns) estimator.

Value

Approximate variance of Blair and Lacy's l

Author(s)

Clem Aeppli

References

Blair, J., and M. Lacy. 2000. Statistics of Ordinal Variation. Sociological Methods & Research 28 (3): 251-280.

See Also

consensus