rwg.lindell: Lindell, Brandt and Whitney (1999) r*wg(j) Within-Group Agreement Index for Multi-Item Scales

Description

This function computes r*wg(j) within-group agreement index for multi-item scales as described in Lindell, Brandt and Whitney (1999).

Usage

rwg.lindell(..., data = NULL, cluster, A = NULL, ranvar = NULL, z = TRUE,
            expand = TRUE, na.omit = FALSE, append = TRUE, name = "rwg",
            as.na = NULL, check = TRUE)

Value

Returns a numeric vector containing r*wg(j) agreement index for multi-item scales with the same length as group if expand = TRUE or a data frame with following entries if expand = FALSE:

cluster: cluster identifier
n: cluster size
rwg.lindell: r*wg(j) estimate for each group
z.rwg.lindell: Fisher z-transformed r*wg(j) estimate for each cluster

Arguments

...: a numeric vector or data frame. Alternatively, an expression indicating the variable names in data e.g., rwg.lindell(x1, x2, x3, data = dat). Note that the operators ., +, -, ~, :, ::, and ! can also be used to select variables, see 'Details' in the df.subset function.
data: a data frame when specifying one or more variables in the argument .... Note that the argument is NULL when specifying a numeric vector or data frame for the argument ....
cluster: either a character string indicating the variable name of the cluster variable in ... or data, or a vector representing the nested grouping structure (i.e., group or cluster variable).
A: a numeric value indicating the number of discrete response options of the items from which the random variance is computed based on \((A^2 - 1) / 12\). Note that either the argument j or the argumentranvar is specified.
ranvar: a numeric value indicating the random variance to which the mean of the item variance is divided. Note that either the argument j or the argumentranvar is specified.
z: logical: if TRUE (default), Fisher z-transformation based on the formula \(z = 0.5*log((1 + r) / (1 - r))\) is applied to the vector of r*wg(j) estimates.
expand: logical: if TRUE (default), vector of r*wg(j) estimates is expanded to match the input vector x.
na.omit: logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion).
append: logical: if TRUE (default), a variable with the r*wg(j) within-group agreement index are appended to the data frame specified in the argument data.
name: a character string indicating the name of the variable appended to the data frame specified in the argument data when append = TRUE. By default, the variable is named rwg.
as.na: a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis. Note that as.na() function is only applied to x, but not to cluster.
check: logical: if TRUE (default), argument specification is checked.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

Details

The r*wg(j) index is calculated by dividing the mean of the item variance by the expected random variance (i.e., null distribution). The default null distribution in most research is the rectangular or uniform distribution calculated with \(\sigma^2_eu = (A^2 - 1) / 12\), where \(A\) is the number of discrete response options of the items. However, what constitutes a reasonable standard for random variance is highly debated. Note that the r*wg(j) allows that the mean of the item variances to be larger than the expected random variances, i.e., r*wg(j) values can be negative.

Note that the rwg.j.lindell() function in the multilevel package uses listwise deletion by default, while the rwg.lindell() function uses all available information to compute the r*wg(j) agreement index by default. In order to obtain equivalent results in the presence of missing values, listwise deletion (na.omit = TRUE) needs to be applied.

Examples for the application of r*wg(j) within-group agreement index for multi-item scales can be found in Bardach, Yanagida, Schober and Lueftenegger (2018), Bardach, Lueftenegger, Yanagida, Schober and Spiel (2018), and Bardach, Lueftenegger, Yanagida, Spiel and Schober (2019).

References

Bardach, L., Lueftenegger, M., Yanagida, T., & Schober, B. (2019). Achievement or agreement - Which comes first? Clarifying the temporal ordering of achievement and within-class consensus on classroom goal structures. Learning and Instruction, 61, 72-83. https://doi.org/10.1016/j.learninstruc.2019.01.003

Bardach, L., Lueftenegger, M., Yanagida, T., Schober, B. & Spiel, C. (2019). The role of within-class consensus on mastery goal structures in predicting socio-emotional outcomes. British Journal of Educational Psychology, 89, 239-258. https://doi.org/10.1111/bjep.12237

Bardach, L., Yanagida, T., Schober, B. & Lueftenegger, M. (2018). Within-class consensus on classroom goal structures: Relations to achievement and achievement goals in mathematics and language classes. Learning and Individual Differences, 67, 78-90. https://doi.org/10.1016/j.lindif.2018.07.002

Lindell, M. K., Brandt, C. J., & Whitney, D. J. (1999). A revised index of interrater agreement for multi-item ratings of a single target. Applied Psychological Measurement, 23, 127-135. https://doi.org/10.1177/01466219922031257

O'Neill, T. A. (2017). An overview of interrater agreement on Likert scales for researchers and practitioners. Frontiers in Psychology, 8, Article 777. https://doi.org/10.3389/fpsyg.2017.00777

Examples

Run this code

dat <- data.frame(id = c(1, 2, 3, 4, 5, 6, 7, 8, 9),
                  cluster = c(1, 1, 1, 2, 2, 2, 3, 3, 3),
                  x1 = c(2, 3, 2, 1, 1, 2, 4, 3, 5),
                  x2 = c(3, 2, 2, 1, 2, 1, 3, 2, 5),
                  x3 = c(3, 1, 1, 2, 3, 3, 5, 5, 4))

# Example 1a: Compute Fisher z-transformed r*wg(j) for a multi-item scale
# with A = 5 response options
rwg.lindell(dat[, c("x1", "x2", "x3")], cluster = dat$cluster, A = 5)

# Example 1b: Alternative specification using the 'data' argument,
rwg.lindell(x1:x3, data = dat, cluster = "cluster", A = 5)
# Example 2: Compute Fisher z-transformed r*wg(j) for a multi-item scale with a random variance of 2
rwg.lindell(dat[, c("x1", "x2", "x3")], cluster = dat$cluster, ranvar = 2)

# Example 3: Compute r*wg(j) for a multi-item scale with A = 5 response options
rwg.lindell(dat[, c("x1", "x2", "x3")], cluster = dat$cluster, A = 5, z = FALSE)

# Example 4: Compute Fisher z-transformed r*wg(j) for a multi-item scale
# with A = 5 response options, do not expand the vector
rwg.lindell(dat[, c("x1", "x2", "x3")], cluster = dat$cluster, A = 5, expand = FALSE)

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