Computes ICC values for mixed-effects models

Description

Computes ICC values for lme4-fitted mixed-effects models.

Usage

ICCm(model, re_type = c("NA"))

Arguments

Value

If re_type is "NA", the proportion of variance at the random effect is computed.

If re_type = "nested", the likeness of y scores in the same level 3 unit (the proportion of variance at Level3_factor), the likeness of y scores in the same level 2 units in the same level 3 unit (proportion of variance at Level3_factor and Level2_factor), and the likeness of level 2 units in the same level 3 unit (proportion of Level2_factor variance at Level3_factor) are computed.

If re_type = "cc", the likeness of y scores in the same C1_factor unit (correlation between outcome values of units in same C1_factor but different C2_factor), the likeness of y scores in the same C2_factor (correlation between outcome values of units in the same C2_factor but different C2_factor), and the likeness of y scores in the same C1_factor and C2_factor combination (correlation between outcome values of units in the same C2_factor and C2_factor) are computed.

References

Snijders, T. A. B. & Bosker, R. J. (2012). Multilevel Analysis (2nd Ed.). Sage Publications Ltd. Goldstein, H., Browne, W., & Rasbash, J. (2002). Partitioning variation in multilevel models. Understanding statistics: statistical issues in psychology, education, and the social sciences, 1(4), 223-231.

Examples

# Gaussian
## Read in data
data(instruction)
## Create model
mod <- lme4::lmer(mathgain ~ (1 | classid), data = instruction)
## Estimate ICC
ICCm(mod)

# Logistic
## Read in data
data(reporting)
## Create model
mod <- lme4::glmer(mention.outliers ~ Basics + (1 | Journal), data = reporting, family = "binomial")
## Estimate ICC
ICCm(mod)

Plots Between Group Associations

Description

Plots the between-group associations between an outcome and predictor variable.

Usage

betweenPlot(
  x,
  y,
  grouping,
  dataset,
  xlab = x,
  ylab = y,
  between_title = "Between-Group Association Plot",
  point_color = "gray40",
  line_color = "black",
  se = FALSE,
  full_range = FALSE,
  lty = 1,
  size = 2
)

Arguments

Value

Produces a plot of the between-group associations between an outcome and predictor variable.

References

Chow, S., Gilmore, R. O., Hallquist, M., Ram, N., & Brinberg, M. (2019). Introduction to multilevel model and interactions. GitHub. https://github.com/psu-psychology/r-bootcamp-2019/blob/master/talks/RBootcamp_MLMInteractions_2019_0820_Final2.Rmd

Examples

# Read in data
data(instruction)
# Produce between plot
betweenPlot(x = "mathkind", y = "mathgain", grouping = "classid",
dataset = instruction, xlab = "Kindergarten Math Score",
ylab = "Gain in Math Score")

Caterpillar Plot

Description

Plots empirical Bayes both point prediction and prediction intervals for each random effect parameter across all groups.

Usage

caterpillarPlot(
  model,
  grouping,
  title = print(grouping),
  tall = TRUE,
  grey = FALSE
)

Arguments

Value

Produces a caterpillar plot.

References

Rabe-Hesketh S, Skrondal A (2012). Multilevel and Longitudinal Modeling Using Stata, Volumes I and II, Third Edition. 3 edition edition. Stata Press. ISBN 978-1-59718-108-2.

Examples

# Read in data
data(instruction)
# Create model
mod <- lme4::lmer(mathgain ~ (1 | classid), data = instruction)
# Produce caterpillar plot
caterpillarPlot(mod, title = "title", grouping = "classid", grey = TRUE)

Centers variables for mixed effects models

Description

Centers variables using the group-mean (person-mean) centering approach for mixed-effects models, and adds these variables to the data frame.

Usage

center(
  dataset,
  x,
  grouping,
  type = "mean",
  standardize = FALSE,
  centerResult = FALSE
)

Arguments

Value

Creates two new variables in the data frame - a mean of the desired variable computed for each unique value in the grouping variable and a deviation score for each observation within the grouping variable that is that observation's raw score subtracted from the group mean.

References

Enders, C. & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old problem. Psychological Methods, 12(2), 121–138

Examples

data(instruction)
#Center student level socioeconomic status, "ses", around class mean "ses"
### To repress output: use invisible()
center(dataset = instruction, x = "ses", grouping = "classid")
#Center class-level variable teacher's mathematic prepartion,
# mathprep, around school mean "mathprep"
center(dataset = instruction, x = "mathprep", grouping = "schoolid")

Instruction Data

Description

Data from a study on instructional improvement across 312 classrooms.

Usage

data(instruction)

Format

A data frame with 1190 observations on the following 8 variables.

female

Dummy variable for being female

mathkind

Math achievement score in the spring of kindergarten

mathgain

Gain in math achievement score from spring of kindergarten to spring of first grade

ses

Socioeconomic status

mathprep

First grade teacher's mathematic preparation (based on number of courses taken)

classid

Classroom identifier

schoolid

School identifier

childid

Student identifier

Source

Stata Press

References

Rabe-Hesketh, Sophia, and Brian Everitt. Handbook of statistical analyses using Stata. CRC Press, 2003.

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American educational research journal, 42(2), 371-406.

Examples

data(instruction)

Reports the output of testing all assumptions for a multilevel model

Description

Reports the results from testing all assumptions of a multilevel model and provides suggestions if an assumption is not passed

Usage

mlm_assumptions(model)

Arguments

Value

Tests the relevant assumptions of the specified multilevel model.

References

Glaser, R. E. (2006). Levene’s Robust Test of Homogeneity of Variances. Encyclopedia of Statistical Sciences. 6.

Examples

# Read in data
data(instruction)
# Create model
mod <- lme4::lmer(mathgain ~ mathkind + (1 | classid), data = instruction)
# Evaluate assumptions
mlm_assumptions(mod)

S3Methods for Printing

Description

Prints for mlmtools objects

Usage

## S3 method for class 'center'
print(x, ...)

## S3 method for class 'ICCm'
print(x, ...)

## S3 method for class 'rsqmlm'
print(x, ...)

## S3 method for class 'varCompare'
print(x, ...)

Arguments

Value

Prints mlmtools object

Reporting Data

Description

Data from a study on the reporting rates of outliers with data on 2235 experiments.

Usage

data(reporting)

Format

A data frame with 2235 observations on the following 18 variables.

Reference.Code

Bibtex reference code for the article

year

Year of publication

time.pulled

Year article was pulled for these data

Type

Type of psychological journal

Journal

Journal of publication

authors

Authors

article

Title of article

original.sample.size

Original sample size from the article

mention.outliers

Whether or not the article mentioned outliers

final.sample.size

Final sample size from the article

number.outliers

Number of outliers identified by the article

Basics

Whether or not they ran basic statistics (e.g., descriptive statistics, z scores, t tests, and correlations)

ANOVA

Whether or not they ran ANOVA

Regression

Whether or not they ran a regression

ChiSquare

Whether or not they ran a chi-squared test

Nonparametric

Whether or not they ran a nonparametric test

Modeling

Whether or not they used structural equation modeling

BayesOther

Whether or not they used Bayes or another form of analysis

Source

GitHub

References

Valentine, K. D., Buchanan, E. M., Cunningham, A., Hopke, T., Wikowsky, A., & Wilson, H. (2021). Have psychologists increased reporting of outliers in response to the reproducibility crisis?. Social and Personality Psychology Compass, 15(5), e12591.

Examples

data(reporting)

Calculates R-squared from lmer models

Description

Calculates variance explained by lme4-fitted mixed-effects models.

Usage

rsqmlm(model, by_cluster = FALSE)

Arguments

Value

Computes the percent variance explained by the model.

References

Nakagawa, S., Johnson, P. C., & Schielzeth, H. (2017). The coefficient of determination R 2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of the Royal Society Interface, 14(134), 20170213.

Examples

# Read in data
data(instruction)
# Center mathkind by classid
center(dataset = instruction, x = "mathkind", grouping = "classid")
# Create model
mod <- lme4::lmer(mathgain ~ classid_mathkind.cmn +
classid_mathkind.devcmn + (1 | classid), data = instruction)
# Calculate r-squared
### To repress output: use invisible()
rsq <- rsqmlm(mod)
rsq
rsq$marginal
rsq$conditional

Compares variance explained for two mixed effects models

Description

Compares variance explained by additional fixed effects for two lme4-fitted mixed-effects models.

Usage

varCompare(model1, model2)

Arguments

Details

Specifically, 1-(total variance for less parsimonious model/total variance for more parsimonious model).

Value

Computes the percent increase in variance explained by the less parsimonious (more complicated) model compared to the more parsimonious (less complicated) model.

References

Snijders, T. A. B. & Bosker, R. J. (2012). Multilevel Analysis (2nd Ed.). Sage Publications Ltd.

Examples

# Read in data
data(instruction)
# Create null model
mod0 <- lme4::lmer(mathgain ~ (1 | classid), data = instruction)
# Create model of interest
mod1 <- lme4::lmer(mathgain ~ mathkind + (1 | classid), data = instruction)
# Compare variance explained
### To repress output: use invisible()
varCompare(mod0, mod1)

Plots Within Group Associations

Description

Plots the within-group associations between an outcome and predictor variable.

Usage

withinPlot(
  x,
  y,
  grouping,
  dataset,
  xlab = x,
  ylab = y,
  within_title = "Within-Group Association Plot",
  point_color = "gray40",
  line_color = "black",
  se = FALSE,
  full_range = FALSE,
  lty = 1,
  size = 2
)

Arguments

Value

Produces a plot of the within-group associations between an outcome and predictor variable.

References

Chow, S., Gilmore, R. O., Hallquist, M., Ram, N., & Brinberg, M. (2019). Introduction to multilevel model and interactions. GitHub. https://github.com/psu-psychology/r-bootcamp-2019/blob/master/talks/RBootcamp_MLMInteractions_2019_0820_Final2.Rmd

Examples

# Read in data
data(instruction)
# Create within plot
mathkind_withinPlot <- withinPlot(x = "mathkind", y = "mathgain",
grouping = "classid", dataset = instruction,
xlab = "Kindergarten Math Score", ylab = "Gain in Math Score")