tidyLPA: Functionality to carry out Latent Profile Analysis in R

Description

Latent Profile Analysis (LPA) is a statistical modeling approach for estimating distinct profiles, or groups, of variables. In the social sciences and in educational research, these profiles could represent, for example, how different youth experience dimensions of being engaged (i.e., cognitively, behaviorally, and affectively) at the same time.

Details

tidyLPA provides the functionality to carry out LPA in R. In particular, tidyLPA provides functionality to specify different models that determine whether and how different parameters (i.e., means, variances, and covariances) are estimated and to specify (and compare solutions for) the number of profiles to estimate.

Author(s)

Maintainer: Joshua M Rosenberg jmrosenberg@utk.edu

Authors:

• Caspar van Lissa c.j.vanlissa@uu.nl

Other contributors:

• Jennifer A Schmidt jaschmid@msu.edu [contributor]

• Patrick N Beymer beymerpa@msu.edu [contributor]

• Daniel Anderson daniela@uoregon.edu [contributor]

• Matthew J. Schell schellma@msu.edu [contributor]

See Also

Useful links:

• https://data-edu.github.io/tidyLPA/

• Report bugs at https://github.com/data-edu/tidyLPA/issues

Pipe

Description

tidyLPA suggests using the pipe operator, %>%, from the magrittr package (imported here from the dplyr package).

Arguments

Examples

# Instead of
subset(iris, select = c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width"))
# you can write
iris %>%
  subset(select = c("Sepal.Length", "Sepal.Width", "Petal.Length", "Petal.Width"))

Select best model using analytic hyrarchy process

Description

Integrates information from several fit indices, and selects the best model.

Usage

AHP(
  fitindices,
  relative_importance = c(AIC = 0.2323, AWE = 0.1129, BIC = 0.2525, CLC = 0.0922, KIC =
    0.3101)
)

Arguments

Details

Many fit indices are available for model selection. Following the procedure developed by Akogul and Erisoglu (2017), this function integrates information from several fit indices, and selects the best model, using Saaty's (1990) Analytic Hierarchy Process (AHP). Conceptually, the process consists of the following steps:

1. For each fit index, calculate the amount of support provided for each model, relative to the other models.

2. From these comparisons, obtain a "priority vector" of the amount of support for each model.

3. Compute a weighted average of the priority vectors for all fit indeces, with weights based on a simulation study examining each fit index' ability to recover the correct number of clusters (Akogul & Erisoglu, 2016).

4. Select the model with the highest weighted average priority.

Value

Numeric.

Author(s)

Caspar J. van Lissa

Examples

iris[,1:4] %>%
  estimate_profiles(1:4) %>%
  get_fit() %>%
  AHP()

Convert Mplus output to object of class 'tidyLPA'

Description

Takes a list of Mplus output files of class modelList, containing only mixture models with a single categorical latent variable, and converts it to an object of class tidyLPA.

Usage

as.tidyLPA(modelList)

Arguments

Value

A list of class tidyLPA.

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
library(MplusAutomation)
createMixtures(classes = 1:4, filename_stem = "cars",
               model_overall = "wt ON drat;",
               model_class_specific = "wt;  qsec;",
               rdata = mtcars,
               usevariables = c("wt", "qsec", "drat"),
               OUTPUT = "standardized")
runModels(replaceOutfile = "modifiedDate")
cars_results <- readModels(filefilter = "cars")
results_tidyLPA <- as.tidyLPA(cars_results)
results_tidyLPA
plot(results_tidyLPA)
plot_profiles(results_tidyLPA) # Throws error; missing column 'Classes'

## End(Not run)

Lo-Mendell-Rubin likelihood ratio test

Description

Implements the ad-hoc adjusted likelihood ratio test (LRT) described in Formula 15 of Lo, Mendell, & Rubin (2001), or LMR LRT.

Usage

calc_lrt(n, null_ll, null_param, null_classes, alt_ll, alt_param, alt_classes)

Arguments

Value

A numeric vector containing the likelihood ratio LR, the ad-hoc corrected LMR, degrees of freedom, and the LMR p-value.

References

Lo Y, Mendell NR, Rubin DB. Testing the number of components in a normal mixture. Biometrika. 2001;88(3):767–778. doi:10.1093/biomet/88.3.767

Examples

calc_lrt(150L, -741.02, 8, 1, -488.91, 13, 2)

Compare latent profile models

Description

Takes an object of class 'tidyLPA', containing multiple latent profile models with different number of classes or model specifications, and helps select the optimal number of classes and model specification.

Usage

compare_solutions(x, statistics = "BIC")

Arguments

Value

An object of class 'bestLPA' and 'list', containing a tibble of fits 'fits', a named vector 'best', indicating which model fit best according to each fit index, a numeric vector 'AHP' indicating the best model according to the AHP, an object 'plot' of class 'ggplot', and a numeric vector 'statistics' corresponding to argument of the same name.

Author(s)

Caspar J. van Lissa

Examples

iris_subset <- sample(nrow(iris), 20) # so examples execute quickly
results <- iris %>%
  subset(select = c("Sepal.Length", "Sepal.Width",
    "Petal.Length", "Petal.Width")) %>%
  estimate_profiles(1:3) %>%
  compare_solutions()

Simulated MAC data

Description

This simulated dataset, based on Curry et al., 2019, contains data on moral relevance and judgment across the seven domains of the Morality As Cooperation scale.

Usage

data(curry_mac)

Format

A data.frame with 1392 rows and 42 variables.

Details

References

Curry, O. S., Jones Chesters, M., & Van Lissa, C. J. (2019). Mapping morality with a compass: Testing the theory of ‘morality-as-cooperation’ with a new questionnaire. Journal of Research in Personality, 78, 106–124. doi:10.1016/j.jrp.2018.10.008

Simulated empathy data

Description

This simulated dataset, based on Van Lissa et al., 2014, contains six annual assessments of adolescents' mean scores on the empathic concern and perspective taking subscales of the Interpersonal Reactivity Index (Davis, 1983). The first measurement wave occurred when adolescents were, on average, 13 years old, and the last one when they were 18 years old.

Usage

data(empathy)

Format

A data frame with 467 rows and 13 variables.

Details

References

Van Lissa, C. J., Hawk, S. T., Branje, S. J., Koot, H. M., Van Lier, P. A., & Meeus, W. H. (2014). Divergence Between Adolescent and Parental Perceptions of Conflict in Relationship to Adolescent Empathy Development. Journal of Youth and Adolescence, (Journal Article), 1–14. doi:10.1007/s10964-014-0152-5

Estimate latent profiles

Description

Estimates latent profiles (finite mixture models) using either the open source package mclust or [OpenMx:mxModel]{OpenMx}, or the commercial program Mplus (using the R-interface of MplusAutomation).

Usage

estimate_profiles(
  df,
  n_profiles,
  models = NULL,
  variances = "equal",
  covariances = "zero",
  package = "mclust",
  select_vars = NULL,
  ...
)

Arguments

Details

Six models are currently available in tidyLPA, corresponding to the most common requirements. All models estimate the observed variable means for each class. The remaining parameters are:

1. Equal variances across classes; no covariances between observed variables

2. Varying variances across classes; no covariances between observed variables

3. Equal variances and equal covariances across classes

4. Varying variances and equal covariances (not available for package = 'mclust')

5. Equal variances and varying covariances (not available for package = 'mclust')

6. Varying variances and varying covariances

Two interfaces are available to estimate these models; specify their numbers in the models argument (e.g., models = 1, or models = c(1, 2, 3)), or specify the variances/covariances to be estimated (e.g.,: variances = c("equal", "varying"), covariances = c("zero", "equal")). Note that when package = 'mclust' is used, models = c(4, 5) are not available. Use package = 'OpenMx' or package = 'Mplus' to estimate these models.

Value

A list of class 'tidyLPA'.

Examples

# to make example run more quickly
iris_sample <- iris[c(1:10, 51:60, 101:114), ]

# Example 1:
iris_sample %>%
  subset(select = c("Sepal.Length", "Sepal.Width",
    "Petal.Length")) %>%
  estimate_profiles(3)


# Example 2:
iris %>%
  subset(select = c("Sepal.Length", "Sepal.Width",
    "Petal.Length")) %>%
  estimate_profiles(n_profiles = 1:4, models = 1:3)

# Example 3:
iris_sample %>%
  subset(select = c("Sepal.Length", "Sepal.Width",
    "Petal.Length")) %>%
  estimate_profiles(n_profiles = 1:4, variances = c("equal", "varying"),
                    covariances = c("zero", "zero"))



if(requireNamespace("OpenMx", quietly = TRUE)){
# to make example run more quickly
iris_sample <- iris[c(1:10, 51:60, 101:114), ]

# Example 1:
library(OpenMx)
iris_rename <- iris_sample
names(iris_sample) <- letters[seq_along(names(iris_sample))]
iris_sample %>%
  subset(select = c("a", "b", "c")) %>%
  estimate_profiles(3, package = "OpenMx") -> res
}

Estimate latent profiles using mclust

Description

Estimates latent profiles (finite mixture models) using the open source package mclust.

Usage

estimate_profiles_mclust(df, n_profiles, model_numbers, select_vars, ...)

Arguments

Value

An object of class 'tidyLPA' and 'list'

Author(s)

Caspar J. van Lissa

Estimate latent profiles using Mplus

Description

Estimates latent profiles (finite mixture models) using the commercial program Mplus, through the R-interface of MplusAutomation.

Usage

estimate_profiles_mplus2(
  df,
  n_profiles,
  model_numbers,
  select_vars,
  ...,
  keepfiles = FALSE
)

Arguments

Value

An object of class 'tidyLPA' and 'list'

Author(s)

Caspar J. van Lissa

Estimate latent profiles using OpenMx

Description

Estimates latent profiles using the R-package 'OpenMx'. Note that this requires installing 'OpenMx' and running 'library(OpenMx)'.

Usage

estimate_profiles_openmx(df, n_profiles, model_numbers, select_vars, ...)

Arguments

Value

An object of class 'tidyLPA' and 'list'

Author(s)

Caspar J. van Lissa

Get data from objects generated by tidyLPA

Description

Get data from objects generated by tidyLPA.

Usage

get_data(x, ...)

## S3 method for class 'tidyLPA'
get_data(x, ...)

## S3 method for class 'tidyProfile'
get_data(x, ...)

Arguments

Value

If one model is fit, the data is returned in wide format as a tibble. If more than one model is fit, the data is returned in long form. See the examples.

Methods (by class)

• get_data(tidyLPA): Get data for a latent profile analysis with multiple numbers of classes and models, of class 'tidyLPA'.

• get_data(tidyProfile): Get data for a single latent profile analysis object, of class 'tidyProfile'.

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
if(interactive()){
 library(dplyr)
 # the data is returned in wide form
 results <- iris %>%
   select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>%
   estimate_profiles(3)
 get_data(results)

 # note that if more than one model is fit, the data is returned in long form
 results1 <- iris %>%
   select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>%
   estimate_profiles(c(3, 4))
 get_data(results1)
 }

## End(Not run)

Get estimates from objects generated by tidyLPA

Description

Get estimates from objects generated by tidyLPA.

Usage

get_estimates(x, ...)

## S3 method for class 'tidyLPA'
get_estimates(x, ...)

## S3 method for class 'tidyProfile'
get_estimates(x, ...)

Arguments

Value

A tibble.

Methods (by class)

• get_estimates(tidyLPA): Get estimates for a latent profile analysis with multiple numbers of classes and models, of class 'tidyLPA'.

• get_estimates(tidyProfile): Get estimates for a single latent profile analysis object, of class 'tidyProfile'.

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
if(interactive()){
 results <- iris %>%
   select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>%
   estimate_profiles(3)
 get_estimates(results)
 get_estimates(results[[1]])
 }

## End(Not run)

Get fit indices from objects generated by tidyLPA

Description

Get fit indices from objects generated by tidyLPA.

Usage

get_fit(x, ...)

## S3 method for class 'tidyLPA'
get_fit(x, ...)

## S3 method for class 'tidyProfile'
get_fit(x, ...)

Arguments

Value

A tibble. Learn more at https://data-edu.github.io/tidyLPA/articles/Introduction_to_tidyLPA.html#getting-fit-statistics

Methods (by class)

• get_fit(tidyLPA): Get fit indices for a latent profile analysis with multiple numbers of classes and models, of class 'tidyLPA'.

• get_fit(tidyProfile): Get fit indices for a single latent profile analysis object, of class 'tidyProfile'.

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
if(interactive()){
 results <- iris %>%
   select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>%
   estimate_profiles(3)
 get_fit(results)
 get_fit(results[[1]])
 }

## End(Not run)

Simulated identity data

Description

This simulated dataset, based on Crochetti et al., 2014, contains five annual assessments of adolescents' mean scores on the commitment, exploration (in depth), and reconsideration subscales of the Utrecht-Management of Identity Commitments Scale (Crocetti et al., 2008). The scores reported here reflect the educational identity subscales of this instrument. The first measurement wave occurred when adolescents were, on average, 14 years old, and the last one when they were 18 years old.

Usage

data(id_edu)

Format

A data frame with 443 rows and 16 variables.

Details

References

Crocetti, E., Klimstra, T. A., Hale, W. W., Koot, H. M., & Meeus, W. (2013). Impact of early adolescent externalizing problem behaviors on identity development in middle to late adolescence: A prospective 7-year longitudinal study. Journal of Youth and Adolescence, 42(11), 1745-1758. doi:10.1007/s10964-013-9924-6

student questionnaire data with four variables from the 2015 PISA for students in the United States

Description

student questionnaire data with four variables from the 2015 PISA for students in the United States

Usage

pisaUSA15

Format

Data frame with columns #'

broad_interest

composite measure of students' self reported broad interest

enjoyment

composite measure of students' self reported enjoyment

instrumental_mot

composite measure of students' self reported instrumental motivation

self_efficacy

composite measure of students' self reported self efficacy

...

Source

http://www.oecd.org/pisa/data/

Apply POMS-coding to data

Description

Takes in a data.frame, and applies POMS (proportion of of maximum)-coding to the numeric columns.

Usage

poms(data)

Arguments

Value

A data.frame.

Author(s)

Caspar J. van Lissa

Examples

data <- data.frame(a = c(1, 2, 2, 4, 1, 6),
                   b = c(6, 6, 3, 5, 3, 4),
                   c = c("a", "b", "b", "t", "f", "g"))
poms(data)

Print tidyLPA

Description

S3 method 'print' for class 'tidyLPA'.

Usage

## S3 method for class 'tidyLPA'
print(
  x,
  stats = c("AIC", "BIC", "Entropy", "prob_min", "prob_max", "n_min", "n_max", "BLRT_p"),
  digits = 2,
  na.print = "",
  ...
)

Arguments

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
if(interactive()){
 iris %>%
   select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>%
   estimate_profiles(3)
 }

## End(Not run)

Print tidyProfile

Description

S3 method 'print' for class 'tidyProfile'.

Usage

## S3 method for class 'tidyProfile'
print(x, digits = 2, na.print = "", ...)

Arguments

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
if(interactive()){
 tmp <- iris %>%
   select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>%
   estimate_profiles(3)
 tmp[[2]]
 }

## End(Not run)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

tidySEM

plot_bivariate, plot_density, plot_profiles

Apply single imputation to data

Description

This function accommodates several methods for single imputation of data. Currently, the following methods are defined:

imputeData

Applies the mclust native imputation function imputeData.

missForest

Applies non-parametric, random-forest based data imputation using missForest. Random forests can accommodate any complex interactions and non-linear relations in the data. Simulation studies indicate that this method is preferable to mclust's imputeData (see examples).

Usage

single_imputation(x, method = "imputeData")

Arguments

Value

A data.frame

Author(s)

Caspar J. van Lissa

Examples

## Not run: 
library(ggplot2)
library(missForest)
library(mclust)

dm <- 2
k <- 3
n <- 100
V <- 4

# Example of one simulation
class <- sample.int(k, n, replace = TRUE)
dat <- matrix(rnorm(n*V, mean = (rep(class, each = V)-1)*dm), nrow  = n,
              ncol = V, byrow = TRUE)
results <- estimate_profiles(data.frame(dat), 1:5)
plot_profiles(results)
compare_solutions(results)

# Simulation for parametric data (i.e., all assumptions of latent profile
# analysis met)
simulation <- replicate(100, {
    class <- sample.int(k, n, replace = TRUE)
    dat <- matrix(rnorm(n*V, mean = (rep(class, each = V)-1)*dm), nrow  = n,
                  ncol = V, byrow = TRUE)

    d <- prodNA(dat)

    d_mf <- missForest(d)$ximp
    m_mf <- Mclust(d_mf, G = 3, "EEI")
    d_im <- imputeData(d, verbose = FALSE)
    m_im <- Mclust(d_im, G = 3, "EEI")

    class_tabl_mf <- sort(prop.table(table(class, m_mf$classification)),
                          decreasing = TRUE)[1:3]
    class_tabl_im <- sort(prop.table(table(class, m_im$classification)),
                          decreasing = TRUE)[1:3]
    c(sum(class_tabl_mf), sum(class_tabl_im))
})
# Performance on average
rowMeans(simulation)
# Performance SD
colSD(t(simulation))
# Plot shows slight advantage for missForest
plotdat <- data.frame(accuracy = as.vector(simulation), model =
                      rep(c("mf", "im"), n))
ggplot(plotdat, aes(x = accuracy, colour = model))+geom_density()

# Simulation for real data (i.e., unknown whether assumptions are met)
simulation <- replicate(100, {
    d <- prodNA(iris[,1:4])

    d_mf <- missForest(d)$ximp
    m_mf <- Mclust(d_mf, G = 3, "EEI")
    d_im <- imputeData(d, verbose = FALSE)
    m_im <- Mclust(d_im, G = 3, "EEI")

    class_tabl_mf <- sort(prop.table(table(iris$Species,
                          m_mf$classification)), decreasing = TRUE)[1:3]
    class_tabl_im <- sort(prop.table(table(iris$Species,
                          m_im$classification)), decreasing = TRUE)[1:3]
    c(sum(class_tabl_mf), sum(class_tabl_im))
})

# Performance on average
rowMeans(simulation)
# Performance SD
colSD(t(simulation))
# Plot shows slight advantage for missForest
plotdat <- data.frame(accuracy = as.vector(tmp),
                      model = rep(c("mf", "im"), n))
ggplot(plotdat, aes(x = accuracy, colour = model))+geom_density()

## End(Not run)