Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Arguments

Value

The result of calling 'rhs(lhs)'.

Test for homoskedasticity at level one

Description

Based on Raudenbush and Bryk (2002) and Hoffman (2007). A statistically significant Chisq indicates heteroskedasticity. Output shows the H statistic, degrees of freedom, and p value.

Usage

Htest(newdata, fml, group)

Arguments

Value

Returns a data frame which contains:

References

Hoffman, L. (2007). Multilevel models for examining individual differences in within-person variation and covariation over time. Multivariate Behavioral Research, 42(4), 609–629. Raudenbush, S., & Bryk, A. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Sage.

Examples

set.seed(123)
x1 <- rnorm(400)
y <- x1 * .3 + rnorm(400)
gr <- rep(1:20, each = 20)
dat <- data.frame(x1, y, gr)
Htest(dat, y ~ x1, 'gr') #no violation
y <- x1 * .3 + rnorm(400, 0, sqrt(x1^2)) #add violation
dat <- data.frame(x1, y, gr)
Htest(dat, y ~ x1, 'gr')

Compute the inverse square root of a matrix

Description

From Imbens and Kolesar (2016).

Usage

MatSqrtInverse(A)

Arguments

Clustered dataset for centering example

Description

Dataset of 60 observations from 3 clusters.

Usage

cdata.ex

Format

A wide data frame of 60 observations. Used for discussing within and between group effects.

x

The predictor.

y

The outcome of interest.

Student engagement dataset (complete data).

Description

Example data used to investigate missing data (this is the complete dataset).

Usage

data(engage)

Format

A data frame with 528 observations from 40 groups and 7 variables:

eng

Student engagement.

mot

Student motivation.

gpa

Student grade point average.

grade

Student grade level (6-8; a factor).

rural

School level rural variable indicator; 1 = yes/0 = no.

frpm

Percent of students eligible for free or reduced price meals at the school.

school

School indicator (clustering variable).

Student engagement dataset (with missing data).

Description

Example data used to investigate missing data (this has missing data).

Usage

data(engage.miss)

Format

A data frame with 528 observations from 40 groups and 7 variables:

eng

Student engagement.

mot

Student motivation.

gpa

Student grade point average.

grade

Student grade level (6-8; a factor).

rural

School level rural variable indicator; 1 = yes/0 = no.

frpm

Percent of students eligible for free or reduced price meals at the school.

school

School indicator (clustering variable).

Glance at goodness-of-fit statistics

Description

Helper function used to obtain supporting fit statistics for multilevel models. The R2s are computed using the 'performance' package.

Usage

## S3 method for class 'CR2'
glance(x, ...)

Arguments

Value

glance returns one row with the columns:

Group-mean center a variable

Description

Also referred to as centering within cluster (or within context) or demeaning the variable. By default, uses na.rm = TRUE when computing group means.

Usage

group_center(x, grp)

Arguments

Value

A vector of group-mean centered variables.

Examples

data(mtcars)
#create a group centered variable
mtcars$mpg.gpc <- group_center(mtcars$mpg, mtcars$cyl)

Computes the group mean of a variable

Description

Computes the group means of a variable by a specified cluster/group. Can also be used with factors that have two levels.

Usage

group_mean(x, grp, lm = FALSE)

Arguments

Value

Outputs a vector of group means.

Examples

data(mtcars)
#create a group mean aggregated variable
mtcars$mpg.barj <- group_mean(mtcars$mpg, mtcars$cyl)

Hospital, doctor, patient (hdp) dataset

Description

This dataset has a three-level, hierarchical structure with patients nested within doctors within hospitals. The simulation code can be found at <https://stats.idre.ucla.edu/r/codefragments/mesimulation/#setup>.

Usage

data(hdp)

Format

A data frame with 8,525 rows and 17 variables:

Age

Continuous in years but recorded at a higher degree of accuracy.

Married

Binary, married/living with partner or single.

FamilyHx

Binary (yes/no), does the patient have a family history (Hx) of cancer?

SmokingHx

Categorical with three levels, current smoker, former smoker, never smoked.

Sex

Binary (female/male).

CancerStage

Categorical with four levels, stages 1-4.

LengthofStay

Count number of days patients stayed in the hospital after surgery.

WBC

Continuous, white blood count. Roughly 3,000 is low, 10,000 is middle, and 30,000 per microliter is high.

RBC

Continuous, red blood count.

BMI

Body mass index given by the formula (kg / meters^2).

IL6

Continuous, interleukin 6, a proinflammatory cytokine commonly examined as an indicator of inflammation, cannot be lower than zero.

CRP

Continuous, C-reactive protein, a protein in the blood also used as an indicator of inflammation. It is also impacted by BMI.

HID

Hospital identifier.

DID

Doctor identifier

Experience

Years as a doctor.

School

Whether the school doctor trained at was high quality or not.

remission

Cancer in remission? 1 = yes, 0 = no.

Source

https://stats.oarc.ucla.edu/r/codefragments/mesimulation/

Likelihood Ratio Test with Model Results Using Plausible Values

Description

Compares two nested models (a full and a reduced model). Results in an F statistic (not the traditional chi-square) with a p-value (see Huang, 2024). The full model must come first. Statistically significant results indicate that the full model fits better than the reduced model. Uses computations shown by Li et al. (1991).

Usage

lrtPV(mf, mr)

Arguments

References

Huang, F. (2024). Using plausible values when fitting multilevel models with large-scale assessment data using R. Large-scale Assessments in Education, 12(7). (link)

Li, K. H., Meng, X.L., Raghunathan, T. E., & Rubin, D. B. (1991). Significance levels from repeated p-values with multiply imputed data. Statistica Sinica, 65–92.

Examples

## Not run: 
data(pisa2012, package = 'MLMusingR')
reduced <- mixPV(pv1math + pv2math + pv3math + pv4math + pv5math ~
 escs + (1|schoolid), data = pisa2012,
 weights = c('w_fstuwt', 'w_fschwt'))
full <- mixPV(pv1math + pv2math + pv3math + pv4math + pv5math ~
 escs + (escs|schoolid), data = pisa2012,
 weights = c('w_fstuwt', 'w_fschwt'))
lrtPV(full, reduced)

## End(Not run)

Fit Weighted Multilevel Models Using Plausible Values

Description

Helper function to fit multilevel models with plausible values using weights at different levels using the mix function from the WeMix package (Bailey et al., 2023): see https://cran.r-project.org/web/packages/WeMix/WeMix.pdf.

Usage

mixPV(fml, data = NULL, mc = FALSE, silent = FALSE, ...)

Arguments

Value

A list object of mix results. Results are pooled using the summary function.

Author(s)

Francis Huang, huangf@missouri.edu

References

Huang, F. (2024). Using plausible values when fitting multilevel models with large-scale assessment data using R. Large-scale Assessments in Education, 12(7). (link)

Examples

## Not run: 
data(pisa2012, package = 'MLMusingR')
m1 <- mixPV(pv1math + pv2math + pv3math + pv4math + pv5math ~ escs + (1|schoolid),
weights = c('w_fstuwt', 'w_fschwt'), data = pisa2012)
summary(m1)

## End(Not run)

Amount of missing data per variable

Description

Amount of missing data per variable

Usage

nmiss(dat)

Arguments

Value

By default, this function will print the following items to the console

• The percent of missing data per variable.

• The percent of complete cases (range: 0 to 1).

• Suggested number of datasets to impute when using multiple imputation.

Examples

data(mtcars)
mtcars[c(2:3), 4] <- NA #create NAs
nmiss(mtcars)

USA data from PISA 2012

Description

Example data for mixPV.

Usage

data(pisa2012)

Format

A data frame with 3136 rows and 14 variables:

pv1math

Plausible value #1 for mathematics

pv2math

Plausible value #2 for mathematics

pv3math

Plausible value #3 for mathematics

pv4math

Plausible value #4 for mathematics

pv5math

Plausible value #5 for mathematics

escs

Index of economic, social, and cultural status.

schoolid

School identifier

st29q03

Maths interest- Look forward to lessons.

st04q01

Student gender.

w_fstuwt

Final student weight (total).

w_fschwt

School weight.

sc14q02

Shortage- Maths teachers

pwt1

Student weight (conditional).

noise1

Random noise.

Source

https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2014028

Pool plausible values using Rubin's rules

Description

Pool plausible values using Rubin's rules

Usage

pool_pv(Bs, SEs, ns2, dfadj = TRUE)

Arguments

Sample dataset 1 for testing the likelihood ratio test

Description

Example data for testing the need for a random intercept. Illustrates the need to adjust the p values for a modified LRT.

Usage

data(ri_test1)

Format

A data frame with 900 observations from 30 groups and 4 variables:

y

The outcome variable.

w1

A level-2 predictor.

x1

A level-1 predictor

group

The cluster identifier

Sample dataset 2 for testing the likelihood ratio test (LRT)

Description

Example data for testing the need for a random intercept. LRT results show that a random slope is not warranted.

Usage

data(ri_test2)

Format

A data frame with 3,000 observations from 30 groups and 4 variables:

y

The outcome variable.

w1

A level-2 predictor.

x1

A level-1 predictor

group

The cluster identifier

Cluster robust standard errors with degrees of freedom adjustments for lmerMod/lme objects

Description

Function to compute the CR2/CR0 cluster robust standard errors (SE) with Bell and McCaffrey (2002) degrees of freedom (dof) adjustments. Suitable even with a low number of clusters. The model based (mb) and cluster robust standard errors are shown for comparison purposes.

Usage

robust_mixed(m1, digits = 3, type = "CR2", satt = TRUE, Gname = NULL)

Arguments

Value

A data frame (results) with the cluster robust adjustments with p-values.

Author(s)

Francis Huang, huangf@missouri.edu

Bixi Zhang, bixizhang@missouri.edu

References

Bell, R., & McCaffrey, D. (2002). Bias reduction in standard errors for linear regression with multi-stage samples. Survey Methodology, 28, 169-182. (link)

Liang, K.Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13-22. (doi:10.1093/biomet/73.1.13)

Examples

require(lme4)
data(sch29, package = 'MLMusingR')
robust_mixed(lmer(math ~ male + minority + mses + mhmwk + (1|schid), data = sch29))

Compute Satterthwaite degrees of freedom

Description

Function to compute empirical degrees of freedom based on Bell and McCaffrey (2002).

Usage

satdf(m1, type = "none", Vinv2, Vm2, br2, Gname = NULL)

Arguments

Author(s)

Francis Huang, huangf@missouri.edu

Bixi Zhang, bixizhang@missouri.edu

Data from 29 schools (based on the NELS dataset) used for regression diagnostics

Description

For examining the association between amount homework done per week and math outcome.

Usage

data(sch29)

Format

A data frame with 648 rows and 8 variables:

schid

The school identifier (the grouping variable)

ses

Student-level socioeconomic status

byhomewk

Total amount of time the student spent on homework per week. 1 = None, 2 = Less than one hour, 3 = 1 hour, 4 = 2 hours, 5 = 3 hours, 6 = 4-6 hours, 7 = 7 - 9 hours, 8 = 10 or more

math

Mathematics score.

male

Dummy coded gender, 1 = male, 0 = female

minority

Dummy coded minority status, 1 = yes, 0 = no

mses

Aggregated socioeconomic status at the school level

mhmwk

Aggregated time spent on homework at the school level

Source

https://nces.ed.gov/pubs92/92030.pdf

Create summary output from the mixPV function

Description

Create summary output from the mixPV function

Usage

## S3 method for class 'mixPV'
summary(object, dfadj = TRUE, ...)

Arguments

Use the summary function on a saved list of mixPV results

Description

Use the summary function on a saved list of mixPV results

Usage

summary_all(x)

Arguments

Suspension data from Virginia

Description

Data from 8465 students from 100 schools in Virginia

Usage

data(suspend)

Format

Dataset:

school

School identifier

pminor

Percent minority enrollment at school

male

1 = male, 0 = female

sus

Whether the student was suspended (1 = yes) in the school year or not (0 = no). Self reported.

fight

If the student got into one or more fights (1 = yes) in the school year

gpa

Students self-reported GPA; 1 = D to 4 = A

Thai data from PISA

Description

Example data to be used for centering

Usage

data(thai)

Format

A data frame with 6606 rows and 18 variables:

pv1math

First plausible value in mathematics.

escs

Index of economic, social, and cultural status.

hisei

Highest parent occupational status.

sex

Student gender. 1 = Female, 2 = Male.

intmat

Mathematics interest.

matheff

Mathematics self-efficacy.

schoolid

School identifier

othl

Spoke another language at home other than Thai. 1 = yes, 0 = no.

books

How many books at home.

pared

Highest parental education in years.

w_fstuwt

Student weight.

pv1read

Plausible value #1 for reading.

pv2read

Plausible value #2 for reading.

pv3read

Plausible value #3 for reading.

pv4read

Plausible value #4 for reading.

pv5read

Plausible value #5 for reading.

private

Private school. 1 = yes, 0 = no.

schsize

Total school enrolment.

Source

https://gpseducation.oecd.org/CountryProfile?primaryCountry=THA

Thai data from PISA (reduced)

Description

Example data to be used for centering

Usage

data(thai)

Format

A data frame with 4271 rows and 7 variables:

math

First plausible value in mathematics.

escs

Index of economic, social, and cultural status.

intmat

Mathematics interest.

schoolid

School identifier

othl

Spoke another language at home other than Thai. 1 = yes, 0 = no.

private

Private school. 1 = yes, 0 = no.

schsize

Total school enrolment.

Source

https://gpseducation.oecd.org/CountryProfile?primaryCountry=THA

Tidy a CR2 object

Description

Tidy a CR2 object

Usage

## S3 method for class 'CR2'
tidy(x, conf.int = FALSE, conf.level = 0.95, ...)

Arguments

Value

A tidy [tibble::tibble()] summarizing component-level information about the model

Helper function to allow use with modelsummary

Description

Helper function to allow use with modelsummary

Usage

## S3 method for class 'mixPV'
tidy(x, dfadj = TRUE, ...)

Arguments

Wide dataset to be used for growth modeling

Description

A dataset containing 30 observations with reading scores taken in the fall kindergarten, spring kindergarten, and spring first grade

Usage

wide

Format

A wide data frame of 30 observations:

studentid

Factor indicating student identification

int

treatment or control

female

1 = female, 0 = male

fall_k

Reading scores in fall kindergarten

spring_k

Reading scores in spring kindergarten

spring_g1

Reading scores in spring first grade

Scale of Sampling Weights

Description

Uses the cluster and ecluster (cluster size and effective cluster size) options specified in Mplus. See note from the Mplus website. If there is no variation in weights within a cluster, the weights will scale to 1.

Usage

wscale(cluster, data, wt, type = "cluster")

Arguments

Examples

data(pisa2012, package = 'MLMusingR')
pisa2012$clustwt <- wscale('schoolid', pisa2012, 'w_fschwt')