multilevel.r2.manual: R-Squared Measures for Multilevel and Linear Mixed Effects Models by Rights and Sterba (2019), Manually Inputting Parameter Estimates

Description

This function computes R-squared measures by Rights and Sterba (2019) for multilevel and linear mixed effects models by manually inputting parameter estimates.

Usage

multilevel.r2.manual(data, within = NULL, between = NULL, random = NULL,
                     gamma.w = NULL, gamma.b = NULL, tau, sigma2,
                     intercept = TRUE, center = TRUE, digits = 3,
                     plot = FALSE, gray = FALSE, start = 0.15, end = 0.85,
                     color = c("#D55E00", "#0072B2", "#CC79A7", "#009E73", "#E69F00"),
                     write = NULL, append = TRUE, check = TRUE, output = TRUE)

Value

Returns an object of class misty.object, which is a list with following entries:

call: function call
type: type of analysis
data: matrix or data frame specified in data
plot: ggplot2 object for plotting the results
args: specification of function arguments
result: list with result tables, i.e., decomp for the decomposition, total for total R2 measures, within for the within-cluster R2 measures, and between

for the between-cluster R2 measures.

Arguments

data: a matrix or data frame with the level-1 and level-2 predictors and outcome variable used in the model.
within: a character vector with the variable names in data or numeric vector with numbers corresponding to the columns in data of the level-1 predictors used in the model. If none used, set to NULL.
between: a character vector with the variable names in data or numeric vector with numbers corresponding to the columns in data of the level-2 predictors used in the model. If none used, set to NULL.
random: a character vector with the variable names in data or numeric vector with numbers corresponding to the columns in data of the level-1 predictors that have random slopes in the model. If no random slopes specified, set to NULL.
gamma.w: a numeric vector of fixed slope estimates for all level-1 predictors, to be entered in the order of the predictors listed in the argument within.
gamma.b: a numeric vector of the intercept and fixed slope estimates for all level-2predictors, to be entered in the order of the predictors listed in the argument between. Note that the first element is the parameter estimate for the intercept if intercept = TRUE.
tau: a matrix indicating the random effects covariance matrix, the first row/column denotes the intercept variance and covariances (if intercept is fixed, set all to 0) and each subsequent row/column denotes a given random slope's variance and covariances (to be entered in the order listed in the argument random).
sigma2: a numeric value indicating the level-1 residual variance.
intercept: logical: if TRUE (default), the first element in the gamma.b is assumed to be the fixed intercept estimate; if set to FALSE, the first element in the argument gamma.b is assumed to be the first fixed level-2 predictor slope.
center: logical: if TRUE (default), all level-1 predictors are assumed to be cluster-mean-centered and the function will output all decompositions; if set to FALSE, function will output only the total decomposition.
digits: an integer value indicating the number of decimal places to be used.
plot: logical: if TRUE, bar chart showing the decomposition of scaled total, within-cluster, and between-cluster outcome variance into five (total), three (within-cluster), and two (between-cluster) proportions is drawn. Note that the ggplot2 package is required to draw the bar chart.
gray: logical: if TRUE, graphical parameter to draw the bar chart in gray scale.
start: a numeric value between 0 and 1, graphical parameter to specify the gray value at the low end of the palette.
end: a numeric value between 0 and 1, graphical parameter to specify the gray value at the high end of the palette.
color: a character vector, graphical parameter indicating the color of bars in the bar chart in the following order: Fixed slopes (Within), Fixed slopes (Between), Slope variation (Within), Intercept variation (Between), and Residual (Within). By default, colors from the colorblind-friendly palettes are used.
write: a character string naming a text file with file extension ".txt" (e.g., "Output.txt") for writing the output into a text file.
append: logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check: logical: if TRUE (default), argument specification is checked.
output: logical: if TRUE (default), output is shown on the console.

Author

Jason D. Rights, Sonya K. Sterba, Jessica K. Flake, and Takuya Yanagida

Details

A number of R-squared measures for multilevel and linear mixed effects models have been developed in the methodological literature (see Rights & Sterba, 2018). R-squared measures by Rights and Sterba (2019) provide an integrative framework of R-squared measures for multilevel and linear mixed effects models with random intercepts and/or slopes. Their measures are based on partitioning model implied variance from a single fitted model, but they provide a full partitioning of the total outcome variance to one of five specific sources. See the help page of the multilevel.r2 function for more details.

References

Rights, J. D., & Cole, D. A. (2018). Effect size measures for multilevel models in clinical child and adolescent research: New r-squared methods and recommendations. Journal of Clinical Child and Adolescent Psychology, 47, 863-873. https://doi.org/10.1080/15374416.2018.1528550

Rights, J. D., & Sterba, S. K. (2019). Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. Psychological Methods, 24, 309-338. https://doi.org/10.1037/met0000184

Examples

Run this code

if (FALSE) {
# Load misty, lme4, nlme, and ggplot2 package
library(misty)
library(lme4)

# Load data set "Demo.twolevel" in the lavaan package
data("Demo.twolevel", package = "lavaan")

#-------------------------------------------------------------------------------

# Cluster mean centering, center() from the misty package
Demo.twolevel$x2.c <- center(Demo.twolevel$x2, type = "CWC",
                             cluster = Demo.twolevel$cluster)

# Compute group means, cluster.scores() from the misty package
Demo.twolevel$x2.b <- cluster.scores(Demo.twolevel$x2,
                                     cluster = Demo.twolevel$cluster)

# Estimate random intercept model using the lme4 package
mod1 <- lmer(y1 ~ x2.c + x2.b + w1 + (1| cluster), data = Demo.twolevel,
             REML = FALSE, control = lmerControl(optimizer = "bobyqa"))

# Estimate random intercept and slope model using the lme4 package
mod2 <- lmer(y1 ~ x2.c + x2.b + w1 + (1 + x2.c | cluster), data = Demo.twolevel,
             REML = FALSE, control = lmerControl(optimizer = "bobyqa"))

#-------------------------------------------------------------------------------
# Example 1: Random intercept model

# Fixed slope estimates
fixef(mod1)

# Random effects variance-covariance matrix
as.data.frame(VarCorr(mod1))

# R-squared measures according to Rights and Sterba (2019)
multilevel.r2.manual(data = Demo.twolevel,
                     within = "x2.c", between = c("x2.b", "w1"),
                     gamma.w = 0.41127956,
                     gamma.b = c(0.01123245, -0.08269374, 0.17688507),
                     tau = 0.9297401,
                     sigma2 = 1.813245794)

#-------------------------------------------------------------------------------
# Example 2: Random intercept and slope model

# Fixed slope estimates
fixef(mod2)

# Random effects variance-covariance matrix
as.data.frame(VarCorr(mod2))

# R-squared measures according to Rights and Sterba (2019)
multilevel.r2.manual(data = Demo.twolevel,
                     within = "x2.c", between = c("x2.b", "w1"), random = "x2.c",
                     gamma.w = 0.41127956,
                     gamma.b = c(0.01123245, -0.08269374, 0.17688507),
                     tau = matrix(c(0.931008649, 0.004110479, 0.004110479, 0.017068857), ncol = 2),
                     sigma2 = 1.813245794)
}

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