| Title: | Informative Hypothesis Testing Web Applications |
|---|---|
| Description: | Offering enhanced statistical power compared to traditional hypothesis testing methods, informative hypothesis testing allows researchers to explicitly model their expectations regarding the relationships among parameters. An important software tool for this framework is 'restriktor'. The 'mmirestriktor' package provides 'shiny' web applications to implement some of the basic functionality of 'restriktor'. The mmirestriktor() function launches a 'shiny' application for fitting and analyzing models with constraints. The FbarCards() function launches a card game application which can help build intuition about informative hypothesis testing. The iht_interpreter() helps interpret informative hypothesis testing results based on guidelines in Vanbrabant and Rosseel (2020) <doi:10.4324/9780429273872-14>. |
| Authors: | Mackson Ncube [aut, cre], mightymetrika, LLC [cph, fnd] |
| Maintainer: | Mackson Ncube <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.3.1.9000 |
| Built: | 2025-01-29 03:22:58 UTC |
| Source: | https://github.com/mightymetrika/mmirestriktor |
This function calculates the equally spaced differences between means in a one-way ANOVA setup. It is based on the formula presented in Vanbrabant et al. (2015) for calculating differences between means, d.
d_eq_spaced(k, f)d_eq_spaced(k, f)
k |
An integer representing the number of groups (k = 3, ..., 8). |
f |
A numeric value representing the effect size (f = 0.10, 0.15, 0.20, 0.25, 0.30, 0.40). Typical values represent small (0.10), medium (0.25), and large (0.40) effects. |
A numeric value representing the equally spaced difference, d, based on the number of groups (k) and the effect size (f).
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
d_eq_spaced(4, 0.25) # For k = 4 and f = 0.25d_eq_spaced(4, 0.25) # For k = 4 and f = 0.25
This function deals n^2 cards from a specified or default deck to form an n x n grid. The remaining deck is also returned alongside the grid.
deal_cards_to_grid(deck = mmcards::shuffle_deck(), n)deal_cards_to_grid(deck = mmcards::shuffle_deck(), n)
deck |
A dataframe representing a deck of cards, with each row being a a card. The parameter is designed to take mmcards::shuffle_deck() or mmcards::i_deck() as input. |
n |
A single integer representing the number of rows and columns in the grid (i.e., the grid will be n x n). This parameter is required and does not have a default value. |
A list containing two elements:
cards_matrix: an n x n matrix where each element is a list
representing a card.
updated_deck: a list representing the remaining deck after n^2
cards have been dealt.
# Dealing cards to a 2x2 grid using the default shuffled deck deal_cards_to_grid(n = 2)# Dealing cards to a 2x2 grid using the default shuffled deck deal_cards_to_grid(n = 2)
Launches a 'shiny' app for the FbarCards game. In this game, a grid of cards is displayed and the objective is to reorder the cards in each row such that, when the rows are stacked, the columns of cards are in increasing order from left to right. Players can swap the positions of two cards in the same row before finalizing their choices and scoring the game. The game utilizes Informative Hypothesis Testing (IHT) to score the final grid of cards.
FbarCards()FbarCards()
This function launches a shiny app and does not return a value.
if (interactive()) { FbarCards() }if (interactive()) { FbarCards() }
This function generates a specified number of datasets for use in ANOVA simulations.Each dataset is generated based on a specified number of groups, effect size, and sample size per group. The data generation follows the model: yi = mu1xi1 + ... + mukxik + ei, as described in Vanbrabant, Van De Schoot, and Rosseel (2015).
generate_datasets(S, k, f, n)generate_datasets(S, k, f, n)
S |
Integer, the number of datasets to generate. |
k |
Integer, the number of groups (k = 3, ..., 8). |
f |
Numeric, the effect size (f = 0.10, 0.15, 0.20, 0.25, 0.30, 0.40). |
n |
Integer, the sample size per group. |
A list of data frames, each representing a dataset. Each data frame contains two columns: 'x', indicating group membership, and 'y', representing the dependent variable generated according to the model.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
generate_datasets(S = 2, k = 4, f = 0.25, n = 30)generate_datasets(S = 2, k = 4, f = 0.25, n = 30)
This function generates a specified number of datasets for regression analysis
simulations. Each dataset is generated using the sim_reg function, based on
given parameters like sample size, number of predictors, effect size, and
correlation coefficient.
generate_datasets_reg(S = 20000, n, p, f2, rho, beta = 0.1)generate_datasets_reg(S = 20000, n, p, f2, rho, beta = 0.1)
S |
The number of datasets to generate, default is 20000. |
n |
The number of observations in each dataset. |
p |
The number of predictors in the regression model for each dataset. |
f2 |
The effect size for each dataset, defined as (f^2 = R^2 / (1 - R^2)). |
rho |
The correlation coefficient between predictors in each dataset. |
beta |
The regression coefficients for the predictors in each dataset, either as a single value or a vector of length (p). |
The function uses sim_reg to simulate individual datasets, which
are then combined into a list. Each dataset is a data frame with named
columns for the response variable and predictors.
A list of data frames, each representing a simulated dataset for regression analysis. Each data frame contains columns for the response variable 'y' and predictors 'x1', 'x2', ..., 'xp'.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
datasets <- generate_datasets_reg(S = 2, n = 50, p = 3, f2 = 0.10, rho = 0.5)datasets <- generate_datasets_reg(S = 2, n = 50, p = 3, f2 = 0.10, rho = 0.5)
This function provides a human-readable explanation of the results of an informative hypothesis test. It interprets the p-values of both Type A and Type B tests and provides an overall conclusion.
iht_interpreter(iht_res, alpha = 0.05)iht_interpreter(iht_res, alpha = 0.05)
iht_res |
A 'conTest' object containing the results of an informative hypothesis test. |
alpha |
The significance level for interpreting the p-values. Default is 0.05. |
A character string providing a detailed interpretation of the hypothesis test results.
Vanbrabant, L., & Rosseel, Y. (2020). An Introduction to Restriktor: Evaluating informative hypotheses for linear models. In R. van de Schoot & M. Miocevic (Eds.), Small Sample Size Solutions: A Guide for Applied Researchers and Practitioners (1st ed., pp. 157 -172). Routledge.
model <- mmir_model(mpg ~ -1 + hp + wt, data = mtcars, engine = "lm", standardize = TRUE) iht_res <- restriktor::iht(model, constraints = 'hp < wt') iht_interpreter(iht_res) |> cat()model <- mmir_model(mpg ~ -1 + hp + wt, data = mtcars, engine = "lm", standardize = TRUE) iht_res <- restriktor::iht(model, constraints = 'hp < wt') iht_interpreter(iht_res) |> cat()
This function computes the power of hypothesis tests in a linear regression setting, considering constraints on the regression coefficients. It processes a list of data frames, each representing a different dataset, and calculates the power based on specified constraints.
lr_pow(df_list, constr = 0, standardize = TRUE, alpha = 0.05)lr_pow(df_list, constr = 0, standardize = TRUE, alpha = 0.05)
df_list |
A list of data frames, each representing a dataset for regression analysis. Each data frame should contain the response variable 'y' and the predictor variables 'x1', 'x2', ..., 'xp'. |
constr |
The number of inequality constraints imposed on the regression coefficients. It must be a non-negative integer less than or equal to the number of predictors (p). A value of 0 implies no constraints or equality constraints. |
standardize |
A logical value indicating whether the predictor variables should be standardized before fitting the model. Default is TRUE. |
alpha |
The significance level used in hypothesis testing, default is 0.05. |
The function validates the 'constr' parameter, optionally standardizes the predictor variables, constructs the necessary constraints, and calculates power by fitting a linear model to each dataset. It uses the 'iht' function from the 'restriktor' package to apply the constraints and evaluate the hypothesis tests.
A numeric value representing the calculated power, defined as the proportion of datasets meeting the hypothesis test criteria as defined by the constraints and significance level.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
generate_datasets_reg(S = 4, n = 30, p = 3, f2 = 0.20, rho = 0.5) |> lr_pow()generate_datasets_reg(S = 4, n = 30, p = 3, f2 = 0.20, rho = 0.5) |> lr_pow()
mmir_model() is a function for the 'mmirestriktor' package that fits a model to data using one of the specified engines ('lm', 'glm', or 'rlm'). It also provides an option to standardize numeric variables.
mmir_model(formula, data, engine = "lm", standardize = TRUE, ...)mmir_model(formula, data, engine = "lm", standardize = TRUE, ...)
formula |
An object of class 'formula' (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
A data frame containing the variables in the model. |
engine |
A character string indicating which engine to use for model fitting. Can be one of 'lm', 'glm', or 'rlm'. Default is 'lm'. |
standardize |
Logical. If TRUE, numeric predictor variables in 'data' are standardized before fitting the model. Default is TRUE. |
... |
Additional arguments to be passed to the model fitting function (lm, glm, or rlm). |
The mmir_model() function serves as a utility function for fitting models in the 'mmirestriktor' package. It supports different modeling engines and allows for variable standardization.
An object representing the fitted model, of class 'lm', 'glm', or 'rlm' depending on the engine used.
mod <- mmir_model(mpg ~ hp + wt, data = mtcars, engine = "lm") summary(mod)mod <- mmir_model(mpg ~ hp + wt, data = mtcars, engine = "lm") summary(mod)
This function launches a Shiny app which allows users to fit and analyze models with restrictions using the mmir_model(), restriktor::iht(), and restriktor::restriktor() functions. The app provides a user interface to upload a CSV file, specify a model formula, and define constraints for informative hypothesis testing.
mmirestriktor()mmirestriktor()
The app has the following functionalities:
Upload a CSV file to be used as the dataset for modeling.
View the variables available in the uploaded dataset.
Input a formula to define the model to be fit.
Choose a model fitting engine from "lm", "glm", and "rlm".
Specify extra arguments for the model fitting function.
View the terms available for defining constraints after fitting the model.
Define constraints for hypothesis testing.
Set a significance level (alpha) for hypothesis testing.
Choose the type of analysis to perform: Informative Hypothesis Test and/or Restricted Means.
View the results and interpretation of the hypothesis tests after running the analysis.
This function does not return a value; it launches a Shiny app in the user's default web browser.
if (interactive()){ mmirestriktor() }if (interactive()){ mmirestriktor() }
This function calculates the means of different groups in a one-way ANOVA setting. It uses the equally spaced difference calculated by 'd_eq_spaced' and follows the approach described in Vanbrabant et al. (2015).
mui(k, f)mui(k, f)
k |
An integer representing the number of groups (k = 3, ..., 8). |
f |
A numeric value representing the effect size (f = 0.10, 0.15, 0.20, 0.25, 0.30, 0.40).Typical values represent small (0.10), medium (0.25), and large (0.40) effects. |
A numeric vector containing the means of the groups. Each element of the vector corresponds to a group mean.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
mui(4, 0.25) # For k = 4 and f = 0.25mui(4, 0.25) # For k = 4 and f = 0.25
This function calculates the power for hypothesis tests in a constrained statistical inference setting, particularly in the context of ANOVA and regression as discussed in Vanbrabant et al. (2015). It is designed to work with a list of data frames, where each data frame represents a different dataset. The function accommodates both equality and inequality constraints.
pj_pow(df_list, constr = 0, alpha = 0.05)pj_pow(df_list, constr = 0, alpha = 0.05)
df_list |
A list of data frames, each representing a dataset. Designed to use results generated from the generate_datasets() function. |
constr |
An integer indicating the number of inequality constraints. A value of 0 indicates that all constraints are equality constraints. The value must be a non-negative integer less than the number of groups. |
alpha |
The significance level used in the hypothesis testing, with a default value of 0.05. It should be a numeric value between 0 and 1. |
The function first checks the validity of the 'constr' parameter and then constructs the constraint string based on the number of constraints. It runs the model for each dataset in the df_list using the mmir_model function and applies the constraints using the restriktor::iht function. The power is calculated based on the proportion of datasets that meet the hypothesis test criteria defined by the constraints and the significance level.
The function returns the calculated power as a numeric value, representing the proportion of p-values smaller than the predefined significance level alpha.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
generate_datasets(S = 2, k = 4, f = 0.25, n = 30) |> pj_pow(constr=1)generate_datasets(S = 2, k = 4, f = 0.25, n = 30) |> pj_pow(constr=1)
This function creates and launches a Shiny web application for running
simulations related to constrained statistical inference in ANOVA and regression
settings. The application allows users to set various parameters for
replext_t1_c1 and replext_t2_c1 functions and view the resulting simulation
data. The simulation is based on Vanbrabant et al. (2015).
replext()replext()
The Shiny application consists of a user interface for setting simulation parameters and a server logic to process the simulations. Users can select between different simulation settings (cell blocks), specify parameters, run the simulations, view the results in a table format, and download the results. The application also handles dynamic UI elements based on user selections and manages data downloads.
The app's UI includes:
A sidebar for input parameters and action buttons.
A main panel for displaying simulation results.
The server logic includes:
Rendering parameter input UI based on selected cell block.
Running simulations and storing results.
Rendering and exporting the results table.
A Shiny app object which can be run to start the application.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
# Launch the Replext Simulation Shiny application if(interactive()){ replext() }# Launch the Replext Simulation Shiny application if(interactive()){ replext() }
This function creates and launches a Shiny web application for running
simulations related to constrained statistical inference in ANOVA and regression
settings. The application allows users to set various parameters for
replext_t1_c1 and replext_t2_c1 functions and view the resulting simulation
data. The simulation is based on Vanbrabant et al. (2015). The app includes
functionality to interact with a PostgreSQL database. The app includes a user
interface for selecting simulation parameters and a server logic to process the
simulation and handle user interactions, including saving and retrieving data
from a database.
replext_pgsql(dbname, datatable, host, port, user, password)replext_pgsql(dbname, datatable, host, port, user, password)
dbname |
The name of the PostgreSQL database to connect to. |
datatable |
The name of the table in the database where the simulation results will be stored and retrieved. |
host |
The host address of the PostgreSQL database. |
port |
The port number for the PostgreSQL database connection. |
user |
The username for accessing the PostgreSQL database. |
password |
The password for the specified user to access the PostgreSQL database. |
The Shiny application consists of a user interface for setting simulation parameters and a server logic to process the simulations and save to PostgreSQL database. Users can select between different simulation settings (cell blocks), specify parameters, run the simulations, view the results in a table format, submit results to PostgreSQL database, and download the database table. The application also handles dynamic UI elements based on user selections and manages data downloads.
A Shiny app object which can be run to start the application.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
if (interactive()) { replext_pgsql( dbname = "your_db_name", datatable = "your_data_table", host = "localhost", port = 5432, user = "your_username", password = "your_password" ) }if (interactive()) { replext_pgsql( dbname = "your_db_name", datatable = "your_data_table", host = "localhost", port = 5432, user = "your_username", password = "your_password" ) }
This function performs repeated simulations for ANOVA to determine minimum sample sizes for given power and effect sizes, as well as calculating Type I error rates. It is designed to replicate and extend the results for Table 1 Cell 1 in Vanbrabant et al. (2015).
replext_t1_c1( S = 20000, k = 3, fs = c(0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4), n_start = 6, constrs = c(0, 1, 2), alpha = 0.05, pow = 0.8, nmax = 1000 )replext_t1_c1( S = 20000, k = 3, fs = c(0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4), n_start = 6, constrs = c(0, 1, 2), alpha = 0.05, pow = 0.8, nmax = 1000 )
S |
The number of datasets to generate for each simulation, default is 20000. |
k |
The number of groups in the ANOVA design. |
fs |
A vector of effect sizes to consider in the simulations. |
n_start |
The starting sample size for the simulations. |
constrs |
A vector of constraint types to be used in the simulations. |
alpha |
The significance level used in hypothesis testing, default is 0.05. |
pow |
The desired power for the statistical test, default is 0.80. |
nmax |
The maximum sample size to consider in the simulations. |
The function uses a nested approach, first determining minimum sample sizes for various combinations of effect size and constraints, and then calculating Type I error rates. It leverages the 'pj_pow' function for power calculation and integrates internal function 'find_min_sample_size' for determining the smallest sample size achieving the desired power.
A data frame containing the calculated Type I error rates and the minimum sample sizes required for each combination of effect size and constraint type.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
replext_t1_c1(S=5, fs = c(0.40), constrs = c(2))replext_t1_c1(S=5, fs = c(0.40), constrs = c(2))
This function generates replext tables for linear regression, similar to those in Table 2 Cell 1 of the referenced paper. It computes minimum sample sizes for various power and effect size combinations, and calculates Type I error rates.
replext_t2_c1( S = 20000, p = 3, f2s = c(0.02, 0.05, 0.08, 0.1, 0.15, 0.2, 0.25, 0.35), n_start = 6, constrs = c(0, 1, 2, 3), rho = 0, beta = 0.1, alpha = 0.05, pow = 0.8, standardize = TRUE, nmax = 1000 )replext_t2_c1( S = 20000, p = 3, f2s = c(0.02, 0.05, 0.08, 0.1, 0.15, 0.2, 0.25, 0.35), n_start = 6, constrs = c(0, 1, 2, 3), rho = 0, beta = 0.1, alpha = 0.05, pow = 0.8, standardize = TRUE, nmax = 1000 )
S |
The number of datasets to generate for each simulation, default is 20000. |
p |
The number of predictors in the regression model. |
f2s |
A vector of effect sizes to be used in the simulations. |
n_start |
The starting sample size for the simulations. |
constrs |
A vector of constraint types (number of inequality constraints) to be applied in the simulations. |
rho |
The correlation coefficient between predictors, default is 0.0. |
beta |
The regression coefficient for predictors, default is 0.1. |
alpha |
The significance level used in hypothesis testing, default is 0.05. |
pow |
The desired power for the statistical test, default is 0.80. |
standardize |
A logical flag to indicate whether to standardize the predictors in the datasets, default is TRUE. |
nmax |
The maximum sample size to consider in the simulations. |
The function uses a nested approach to first determine minimum sample
sizes for different combinations of effect size and constraints, and then
calculates Type I error rates. It leverages the lr_pow function for power
calculation and uses generate_datasets_reg for dataset generation.
A data frame containing Type I error rates and the minimum sample sizes required for each combination of effect size and constraint type.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
replext_t2_c1(S = 2, f2s = c(0.35), constrs = c(2))replext_t2_c1(S = 2, f2s = c(0.35), constrs = c(2))
This function provides a human-readable interpretation of the results of a restricted means analysis. It compares the original (unconstrained) and reduced (restricted) R-squared values to evaluate the imposed constraints. It also returns the Generalized Order-Restricted Information Criterion (GORIC) which can be used for model comparison.
rm_interpreter(rm_res)rm_interpreter(rm_res)
rm_res |
An object of class 'restriktor', typically the result of a call
to |
A character string with an interpretation of the analysis results, including the R-squared values, their reduction, and the Generalized Order-Restricted Information Criterion (GORIC) if available.
Vanbrabant, L., & Rosseel, Y. (2020). An Introduction to Restriktor: Evaluating informative hypotheses for linear models. In Small Sample Size Solutions (1st ed., p. 16). Routledge.
restriktor for generating 'restriktor' objects.
model <- mmir_model(mpg ~ -1 + hp + wt, data = mtcars, engine = "lm", standardize = TRUE) rm_res <- restriktor::restriktor(model, constraints = 'hp < wt') rm_interpreter(rm_res) |> cat()model <- mmir_model(mpg ~ -1 + hp + wt, data = mtcars, engine = "lm", standardize = TRUE) rm_res <- restriktor::restriktor(model, constraints = 'hp < wt') rm_interpreter(rm_res) |> cat()
This function simulates data for linear regression analysis, as described in the supplemental material of the referenced paper. It generates datasets with a specified number of predictors and sample size, effect size, and correlation coefficient, considering a linear model with fixed regression coefficients.
sim_reg(n, p, f2, rho, beta = 0.1)sim_reg(n, p, f2, rho, beta = 0.1)
n |
The total number of observations to generate. |
p |
The number of predictors (Beta) in the regression model. |
f2 |
The effect size, calculated as (f^2 = R^2 / (1 - R^2)), where ( R^2) is the coefficient of determination. |
rho |
The correlation coefficient between predictors, representing the off-diagonal elements in the covariance matrix. Should be a numeric value. |
beta |
The regression coefficients, either a single value replicated for each predictor or a vector of length equal to the number of predictors (p). |
The function validates the length of the beta vector, constructs a covariance matrix for the predictors, and calculates the variance of the error term. It then uses the multivariate normal distribution to generate predictor values and calculates the response variable based on the specified regression coefficients and effect size.
A list containing two elements: 'y', the simulated response variable, and 'X', the matrix of predictors.
Vanbrabant, Leonard; Van De Schoot, Rens; Rosseel, Yves (2015). Constrained statistical inference: sample-size tables for ANOVA and regression. Frontiers in Psychology, 5. DOI:10.3389/fpsyg.2014.01565. URL: https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01565
# Example usage: # Simulate data for a regression model with 100 observations, 3 predictors, # an effect size of 0.10, and a correlation coefficient of 0.5 sim_reg(n = 100, p = 3, f2 = 0.10, rho = 0.5)# Example usage: # Simulate data for a regression model with 100 observations, 3 predictors, # an effect size of 0.10, and a correlation coefficient of 0.5 sim_reg(n = 100, p = 3, f2 = 0.10, rho = 0.5)