Package 'regtomean' reference manual

Title:	Regression Toward the Mean
Description:	In repeated measures studies with extreme large or small values it is common that the subjects measurements on average are closer to the mean of the basic population. Interpreting possible changes in the mean in such situations can lead to biased results since the values were not randomly selected, they come from truncated sampling. This method allows to estimate the range of means where treatment effects are likely to occur when regression toward the mean is present. Ostermann, T., Willich, Stefan N. & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.<doi:10.1186/1471-2288-8-52>. Acknowledgments: We would like to acknowledge "Lena Roth" and "Nico Steckhan" for the package's initial updates (Q3 2024) and continued supervision and guidance. Both have contributed to discussing and integrating these methods into the package, ensuring they are up-to-date and contextually relevant.
Authors:	Daniela Recchia [aut, cre], Thomas Ostermann [ctb], Julian Stein [ctb]
Maintainer:	Daniela Recchia <[email protected]>
License:	MIT + file LICENSE
Version:	1.2
Built:	2025-02-15 05:41:30 UTC
Source:	https://github.com/cran/regtomean

Correlation and Cohen's d effect sizes.

Description

This function calculates the correlation for the data and Cohen's d effect sizes, both based on pooled and on treatment standard deviations. It can optionally display the results in an HTML widget.

Usage

cordata(Before, After, within = TRUE, data = NULL)cordata(Before, After, within = TRUE, data = NULL)

Arguments

`Before`	a numeric vector giving the data values for the first (before) measure.
`After`	a numeric vector giving the data values for the second (after) measure.
`within`	A logical indicating whether the effect sizes should be computed based on paired samples (`TRUE`, default) or independent samples (`FALSE`).
`data`	an optional data frame containing the variables in the formula. By `default` the variables are taken from `environment (formula)`.

Details

This function computes the correlation between two measures and calculates Cohen's d effect sizes using both pooled and treatment standard deviations.

- If within = TRUE, the effect sizes are computed assuming paired samples. - If within = FALSE, the effect sizes are computed assuming independent samples.

The results are returned as a data frame and also displayed in an HTML widget in the RStudio Viewer or default web browser.

Value

Return a table containing the correlation, effect size pooled and effect size based on treatment.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York:Academic Press.

Examples

cordata("Before","After",data=language_test)cordata("Before","After",data=language_test)

Language Test in High School

Description

A dataset with scores from 8 students who failed a high school test and could not get their diploma. They repeated the exam and got new scores.

Usage

data("language_test")data("language_test")

Format

A data frame with 8 observations on the following 9 variables.

Student: a numeric vector
Before: a numeric vector
After: a numeric vector
‘⁠Total N⁠’: a numeric vector
Cross: a numeric vector
‘⁠Pre-treatment Mean⁠’: a numeric vector
‘⁠Pre-treatment Std⁠’: a numeric vector
‘⁠Post-treatment Mean⁠’: a numeric vector
‘⁠Post-treatment Std⁠’: a numeric vector

Author(s)

Daniela Recchia, Thomas Ostermann.

Source

McClave, J.T; Dietrich, F.H.:"Statistics";New York, Dellen Publishing; 1988.

Examples

data(language_test)
## maybe str(language_test) ; plot(language_test) ...
data(language_test)
## maybe str(language_test) ; plot(language_test) ...

Calculates and plots treatment and regression effects as also its p-values.

Description

This function calculates and plots treatment and regression effects of both before and after measures as also its p-values.

Usage

meechua_eff.CI(x,n,se_after)meechua_eff.CI(x,n,se_after)

Arguments

`x`	a data frame containing the results from `meechua_reg`. It is stored as `mod_coef`.
`n`	the original sample size (number of observations) from data.
`se_after`	the estimated standard error from `meechua_reg`. It is stored as `se_after`.

Details

After performing the meechua_reg the model coefficients mod_coef as also its global variable se_after are used as input in this function to estimate treatment and regression effects.

Value

Two plots are performed, the first "Treatment Effect and p-value" and the second "Confidence Intervals" for mu.

Author(s)

Daniela Recchia, Thomas Ostermann

References

Ostermann, T., Willich, Stefan N. & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Examples

# Initialize environment explicitly
#regtomean_env <- new.env(parent = emptyenv())

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
mee_chua <- replicate_data(0, 100, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]

# Perform regression analysis and store results
results <- meechua_reg(mee_chua)
mod_coef <- results$mod_coef
se_after <- results$se_after

# Call meechua_eff.CI
meechua_eff.CI(mod_coef, 100, se_after)# Initialize environment explicitly
#regtomean_env <- new.env(parent = emptyenv())

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
mee_chua <- replicate_data(0, 100, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]

# Perform regression analysis and store results
results <- meechua_reg(mee_chua)
mod_coef <- results$mod_coef
se_after <- results$se_after

# Call meechua_eff.CI
meechua_eff.CI(mod_coef, 100, se_after)

Plot models from `meechua_reg`

Description

This functions plots all 4 diagnostics plots for each linear regression model: "Residuals vs Fitted", "Normal Q-Q", "Scale-Location" and "Residuals vs Leverage".

Usage

meechua_plot(models = NULL, env = regtomean_env)meechua_plot(models = NULL, env = regtomean_env)

Arguments

`models`	A list containing the estimated linear models, typically the output of `meechua_reg`. If `models` is `NULL`, the function attempts to retrieve the models from the specified environment (`env`).
`env`	An environment where the models are stored. The default is `regtomean_env`. This argument is used only if `models` is not explicitly provided.

Details

For each model from models 4 diagnostic plots are performed. For the first model the numbers 1 to 4 should be given, for the second model numbers from to 8 to 12, and so on.

Value

Diagnostics plots for the set of models from meechua_reg.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Examples

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
mee_chua <- replicate_data(50, 60, "Before", "After", data = language_test)
mee_chua_sort <- mee_chua[order(mee_chua$mu), ]

# Perform regression analysis
results <- meechua_reg(mee_chua_sort)

# Plot models
meechua_plot(results$models)# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
mee_chua <- replicate_data(50, 60, "Before", "After", data = language_test)
mee_chua_sort <- mee_chua[order(mee_chua$mu), ]

# Perform regression analysis
results <- meechua_reg(mee_chua_sort)

# Plot models
meechua_plot(results$models)

Fit linear models on the (replication) data.

Description

This function fit linear models for a subset of data frames.

Usage

meechua_reg(x)meechua_reg(x)

Arguments

`x`	Data to be used in the regression.

Details

The data used for the regression must be sorted by mu.

A set of linear models will be estimated and model coefficients are saved and stored in mod_coef.

The estimated standard errror for the after measure is also stored in se_after to be used further in other functions.

Value

A table containing the estimations for each mu. The variables models, mod_coef, se_after are stored globally for further analysis if to_global is set to TRUE. In any case the values will be returned. The models are saved in an object called mee_chua, which is not automatically printed but is saved in the environment.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Examples

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
replicate_data <- function(start, end, Before, After, data) {
  mu <- seq(start * 100, end * 100, by = (end - start))
  mu <- rep(mu, each = nrow(data))
  
  before <- data[[Before]] - mu / 100
  after <- data[[After]]
  
  mee_chua <- data.frame(mu = mu, before = before, after = after)
  return(mee_chua)
}

mee_chua <- replicate_data(0, 1, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]  # Sortieren nach 'mu'

# Regression ausführen und Ergebnisse erhalten
reg_results <- meechua_reg(mee_chua)

# Zugriff auf Ergebnisse
mod_coef <- reg_results$mod_coef
se_after <- reg_results$se_after

# Anzeigen der Ergebnisse
print(mod_coef)
print(se_after)
# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

# Replicate data
replicate_data <- function(start, end, Before, After, data) {
  mu <- seq(start * 100, end * 100, by = (end - start))
  mu <- rep(mu, each = nrow(data))
  
  before <- data[[Before]] - mu / 100
  after <- data[[After]]
  
  mee_chua <- data.frame(mu = mu, before = before, after = after)
  return(mee_chua)
}

mee_chua <- replicate_data(0, 1, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]  # Sortieren nach 'mu'

# Regression ausführen und Ergebnisse erhalten
reg_results <- meechua_reg(mee_chua)

# Zugriff auf Ergebnisse
mod_coef <- reg_results$mod_coef
se_after <- reg_results$se_after

# Anzeigen der Ergebnisse
print(mod_coef)
print(se_after)

Plot t-Statistics and p-Values for Intervention Impact

Description

Based on the data before and after the intervention and the regression models from the function meechua_reg, this function plots the t-statistics and p-values for a given range of $\mu$ to assess whether the intervention has a significant impact on the measurements, accounting for regression to the mean.

Usage

plot_mu(x, n, se_after, lower = F, alpha = 0.05)
plot_mu(x, n, se_after, lower = F, alpha = 0.05)

Arguments

`x`	A data frame containing the results from `meechua_reg`. Specifically, this should be the `mod_coef` data frame obtained from `meechua_reg`.
`n`	The original sample size (number of observations) of the data.
`se_after`	The estimated standard error from `meechua_reg`. This should be the `se_after` vector obtained from `meechua_reg`.
`lower`	A boolean value specifying the direction of the one-sided tests. For `lower = FALSE` (the default), it tests whether the intervention is increasing the measurements. For `lower = TRUE`, it tests whether the second measurements are lower than expected.
`alpha`	Specifies the significance threshold for the p-values of the corresponding one-sided tests. The default is `alpha = 0.05`.

Value

A list containing the most significant $\mu$ , t-statistic, p-value, and the range of $\mu$ for which the treatment impact is significant.

Author(s)

Julian Stein

References

Ostermann, T., Willich, S. N., & Luedtke, R. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Examples

# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

mee_chua <- replicate_data(0, 1, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]  # Sortieren nach 'mu'

# Regression ausführen und Ergebnisse erhalten
reg_results <- meechua_reg(mee_chua)

# Zugriff auf Ergebnisse
mod_coef <- reg_results$mod_coef
se_after <- reg_results$se_after

# mod_coef and se_after are stored in the environment.
plot_mu(mod_coef, 8, se_after)
# Generate example data
language_test <- data.frame(
  Before = rnorm(100, mean = 50, sd = 10),
  After = rnorm(100, mean = 55, sd = 10)
)

mee_chua <- replicate_data(0, 1, "Before", "After", data = language_test)
mee_chua <- mee_chua[order(mee_chua$mu), ]  # Sortieren nach 'mu'

# Regression ausführen und Ergebnisse erhalten
reg_results <- meechua_reg(mee_chua)

# Zugriff auf Ergebnisse
mod_coef <- reg_results$mod_coef
se_after <- reg_results$se_after

# mod_coef and se_after are stored in the environment.
plot_mu(mod_coef, 8, se_after)

Plot Results for p-values and t-values

Description

This function plots the t-statistics and p-values for a range of $\mu$ values, based on the provided data and regression models. It helps visualize whether the intervention has a significant impact on the measurements, accounting for regression to the mean.

Usage

plot_t(
  mu_start,
  mu_end,
  n,
  y1_mean,
  y2_mean,
  y1_std,
  y2_std,
  cov,
  lower = F,
  alpha = 0.05,
  r_insteadof_cov = F
)
plot_t(
  mu_start,
  mu_end,
  n,
  y1_mean,
  y2_mean,
  y1_std,
  y2_std,
  cov,
  lower = F,
  alpha = 0.05,
  r_insteadof_cov = F
)

Arguments

`mu_start`	Numeric. The starting value of $\mu$ for the range of values to be plotted.
`mu_end`	Numeric. The ending value of $\mu$ for the range of values to be plotted.
`n`	Numeric. The original sample size (number of observations) of the data.
`y1_mean`	Numeric. The mean of the first measurement.
`y2_mean`	Numeric. The mean of the second measurement.
`y1_std`	Numeric. The standard deviation of the first measurement.
`y2_std`	Numeric. The standard deviation of the second measurement.
`cov`	Numeric. The covariance between the two measurements, or if `r_insteadof_cov` is `TRUE`, the correlation coefficient.
`lower`	Logical. If `TRUE`, the function tests whether the second measurements are lower than expected. If `FALSE` (the default), it tests whether the intervention is increasing the measurements.
`alpha`	Numeric. The significance threshold for the p-values of the one-sided tests. The default is `0.05`.
`r_insteadof_cov`	Logical. If `TRUE`, `cov` is interpreted as the correlation coefficient instead of the covariance. Default is `FALSE`.

Value

A ggplot2 plot with two y-axes: one showing p-values and the other showing t-statistics. The function also prints key values including the most significant $\mu$ , the minimal p-value, and the range of $\mu$ where the treatment effect is significant.

Author(s)

Julian Stein

References

Ostermann, T., Willich, S. N., & Luedtke, R. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Examples

# Example usage of the plot_t function
plot_t(
  mu_start = 0, mu_end = 10, n = 50, y1_mean = 5, 
  y2_mean = 5, y1_std = 2, y2_std = 2, cov = 0.5
)

plot_t(
  mu_start = 0, mu_end = 10, n = 50, y1_mean = 5, 
  y2_mean = 5, y1_std = 2, y2_std = 2, cov = 0.5, 
  lower = TRUE, alpha = 0.1
)

# Example usage of the plot_t function
plot_t(
  mu_start = 0, mu_end = 10, n = 50, y1_mean = 5, 
  y2_mean = 5, y1_std = 2, y2_std = 2, cov = 0.5
)

plot_t(
  mu_start = 0, mu_end = 10, n = 50, y1_mean = 5, 
  y2_mean = 5, y1_std = 2, y2_std = 2, cov = 0.5, 
  lower = TRUE, alpha = 0.1
)

Replicates before and after values 100 times.

Description

This function replicates 100 times the "before" and "after" values, given a start and end reference for the population mean (mu).

Usage

replicate_data(start, end, Before, After, data)
replicate_data(start, end, Before, After, data)

Arguments

`start`	A numeric value specifying the start value for `mu`.
`end`	A numeric value specifying the end value for `mu`.
`Before`	A numeric vector giving the data values for the first ("before") measurement.
`After`	A numeric vector giving the data values for the second ("after") measurement.
`data`	An optional data frame containing the `Before` and `After` variables. If not provided, the `Before` and `After` vectors must be supplied directly.

Details

To overcome the limitations of Mee and Chua's test regarding the population mean (mu), this function performs a replication of the data over a specified range of values.

The replicated data is used for systematically estimating the unknown population mean (mu). Further analyses are based on this new dataset.

Value

A data frame containing the replicated dataset, which includes the columns mu, before, and after.

Author(s)

Daniela Recchia, Thomas Ostermann.

References

Ostermann, T., Willich, Stefan N., & Luedtke, Rainer. (2008). Regression toward the mean - a detection method for unknown population mean based on Mee and Chua's algorithm. BMC Medical Research Methodology.

Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute (15: 246-263).

Examples

# Example usage of replicate_data
replicate_data(0, 100, "Before", "After", data = language_test)
# Example usage of replicate_data
replicate_data(0, 100, "Before", "After", data = language_test)

Package 'regtomean'

Help Index

Correlation and Cohen's d effect sizes.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Language Test in High School

Description

Usage

Format

Author(s)

Source

Examples

Calculates and plots treatment and regression effects as also its p-values.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plot models from meechua_reg

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Fit linear models on the (replication) data.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plot t-Statistics and p-Values for Intervention Impact

Description

Usage

Arguments

Value

Author(s)

References

Examples

Plot Results for p-values and t-values

Description

Usage

Arguments

Value

Author(s)

References

Examples

Replicates before and after values 100 times.

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Plot models from `meechua_reg`