| Type: | Package |
| Title: | Regularized Bayesian Estimator for Two-Level Latent Variable Models |
| Version: | 0.0.2.0 |
| Author: | Valerii Dashuk [aut, cre], Binayak Timilsina [aut], Martin Hecht [aut], Steffen Zitzmann [aut] |
| Maintainer: | Valerii Dashuk <vadashuk@gmail.com> |
| Description: | Implements a regularized Bayesian estimator that optimizes the estimation of between-group coefficients for multilevel latent variable models by minimizing mean squared error (MSE) and balancing variance and bias. The package provides more reliable estimates in scenarios with limited data, offering a robust solution for accurate parameter estimation in two-level latent variable models. It is designed for researchers in psychology, education, and related fields who face challenges in estimating between-group effects under small sample sizes and low intraclass correlation coefficients. Dashuk et al. (2024) <doi:10.13140/RG.2.2.18148.39048> derived the optimal regularized Bayesian estimator; Dashuk et al. (2024) <doi:10.13140/RG.2.2.34350.01604> extended it to the multivariate case; and Luedtke et al. (2008) <doi:10.1037/a0012869> formalized the two-level latent variable framework. |
| Imports: | pracma |
| License: | GPL-3 |
| Depends: | R (≥ 4.1.0) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-07-11 21:33:27 UTC; valerii.dashuk |
| Repository: | CRAN |
| Date/Publication: | 2025-07-11 22:20:07 UTC |
Multi-Level Optimal Bayes Function (MLOB)
Description
Implements a regularized Bayesian approach that optimizes the estimation of between-group coefficients by minimizing Mean Squared Error (MSE), balancing both variance and bias. This method provides more reliable estimates in scenarios with limited data, offering a robust solution for accurate parameter estimation in multilevel models. The package is designed for researchers in psychology, education, and related fields who face challenges in estimating between-group effects in two-level latent variable models, particularly in scenarios with small sample sizes and low intraclass correlation coefficients.
Usage
mlob(
formula,
data,
group,
balancing.limit = 0.2,
conf.level = 0.05,
jackknife = FALSE,
punish.coeff = 2,
...
)
Arguments
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. Formula specifies the model (e.g., |
data |
a data frame (or object converted by as.data.frame to a data frame) containing the variables referenced in the formula. All variables used in the model, including the dependent variable, context variable, covariates, and grouping variable must be present in this data frame. |
group |
a name of the variable that defines the affiliation of an individual (row) to the specific group. |
balancing.limit |
a number that represents the threshold of the maximum relative part of the dataset that can be deleted to balance the data. Defaults to |
conf.level |
a numeric value representing the confidence level used to calculate confidence intervals for the estimators. Defaults to |
jackknife |
logical variable. If |
punish.coeff |
a multiplier that punishes the balancing procedure when deleting the whole group. If punish.coeff is equal to |
... |
additional arguments passed to the function. |
Details
This function also verifies whether the data is balanced (i.e., whether each group contains the same number of individuals). If the data is unbalanced, the balancing procedure comes into effect, and identifies the optimal number of items and groups to delete based on the punishment coefficient. If the amount of data deleted is more than defined by threshold (balancing.limit) then results should be interpreted with caution.
The summary() function produces output similar to:
Summary of Coefficients:
Estimate Std. Error Lower CI (99
beta_b 0.4279681 0.7544766 -1.5154349 2.371371 0.5672384 0.57055223
gamma_Petal.Length 0.4679522 0.2582579 -0.1972762 1.133181 1.8119567 0.06999289 .
For comparison, summary of coefficients from unoptimized analysis (ML):
Estimate Std. Error Lower CI (99
beta_b 0.6027440 5.424780e+15 -1.397331e+16 1.397331e+16 1.111094e-16 1.00000000
gamma_Petal.Length 0.4679522 2.582579e-01 -1.972762e-01 1.133181e+00 1.811957e+00 0.06999289 .
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Value
A list containing the results of the regularized Bayesian estimation, which includes the model formula,dependent and context variables,and other relevant details from the analysis.
Author(s)
Valerii Dashuk vadashuk@gmail.com, Binayak Timilsina binayak.timilsina001@gmail.com, Martin Hecht, and Steffen Zitzmann
References
Dashuk, V., Hecht, M., Luedtke, O., Robitzsch, A., & Zitzmann, S. (2024). doi:10.13140/RG.2.2.18148.39048
Dashuk, V., Hecht, M., Luedtke, O., Robitzsch, A., & Zitzmann, S. (2024). doi:10.13140/RG.2.2.34350.01604
Luedtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthen, B. (2008). doi:10.1037/a0012869
Examples
# Example 1: usage with the iris dataset
result_iris <- mlob(
Sepal.Length ~ Sepal.Width + Petal.Length,
data = iris, group = 'Species',
conf.level = 0.01,
jackknife = FALSE)
# View summary statistics (similar to summary of a linear model);
summary(result_iris)
# Example 2: usage with slightly unbalanced ChickWeight dataset
## Not run:
result_ChickWeight <- mlob(
weight ~ Diet,
data = ChickWeight,
group = 'Time',
punish.coeff = 1.5,
jackknife = FALSE)
# View the results
print(result_ChickWeight)
# View summary statistics
summary(result_ChickWeight)
## End(Not run)
# Example 3: usage with highly unbalanced mtcars dataset (adjusted balancing.limit)
result_mtcars <- mlob(
mpg ~ hp + wt + am + hp:wt + hp:am,
data = mtcars, group = 'cyl',
balancing.limit = 0.35)
# View summary statistics
summary(result_mtcars)