multilevel.r2.manual: R-Squared Measures for Multilevel and Linear Mixed Effects...

In misty: Miscellaneous Functions 'T. Yanagida'

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"),
                     check = TRUE, output = TRUE)

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.
check	logical: if TRUE, argument specification is checked.
output	logical: if TRUE, output is shown on the console.

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.

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.

Note

This function is based on a copy of the function r2mlm_manual() in the r2mlm package by Mairead Shaw, Jason Rights, Sonya Sterba, and Jessica Flake.

Author(s)

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

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

See Also

multilevel.r2, multilevel.cor, multilevel.descript, multilevel.icc, multilevel.indirect

Examples

## Not run: 
# 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"))

#---------------------------
# 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)

#---------------------------
# 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)

## End(Not run)

misty documentation built on Nov. 15, 2023, 1:06 a.m.