misty (version 0.4.8)

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"),
                     check = TRUE, output = TRUE)

Value

Returns an object of class misty.object, which is a list with following entries: function call (call), type of analysis type, specification of function arguments (args), and list with results (result).

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.

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

See Also

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

Examples

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
mod2 <- 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 = matrix(c(0.931008649, 0.004110479, 0.004110479, 0.017068857), ncol = 2),
                     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)
}