Title: Meta Analysis and Research Synthesis
Version: 0.2.2
Description: Includes functions for conducting univariate and multivariate meta-analysis. This includes the estimation of the asymptotic variance-covariance matrix of effect sizes. For more details see Becker (1992) <doi:10.2307/1165128>, Cooper, Hedges, and Valentine (2019) <doi:10.7758/9781610448864>, and Schmid, Stijnen, and White (2020) <doi:10.1201/9781315119403>.
Depends: R (≥ 4.2)
Imports: Matrix, corpcor, matrixcalc
License: MIT + file LICENSE
Encoding: UTF-8
LazyData: true
Suggests: knitr, rmarkdown, dplyr, testthat (≥ 3.0.0)
VignetteBuilder: knitr
RoxygenNote: 7.3.2
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2025-03-26 16:11:16 UTC; blebeau
Author: Brandon LeBeau ORCID iD [aut, cre], Ariel M. Aloe [aut], Betsy Jane Becker [ctb], Seohee Park [ctb], Roberto C. Toro Rodriguez [ctb]
Maintainer: Brandon LeBeau <lebebr01+mars@gmail.com>
Repository: CRAN
Date/Publication: 2025-03-27 18:00:05 UTC

Mul R2

Description

Mul R2

Usage

Mul_R2(model_input, R)

Arguments

model_input

Model input as a character string. Multiple models need to be on their own line. Model syntax uses lavann like syntax, see details for more details about this syntax.

R

A correlation matrix, most likely this will be the average correlation matrix outputted from the metafor package.

Value

A vector of names

Olkin & Siotani 1976 variance-covariance numerator

Description

Computation for the numerator of the variance-covariance matrix.

Usage

OS(data)

Arguments

data

A correlation matrix.

Value

A matrix representing the variance-covariance matrix.

bcg Data

Description

This data ...

Usage

bcg

Format

A dataframe with 13 rows and 11 columns:

Trial

Trial ID

Examples

  bcg

Becker 2009 data

Description

This data contains data originally collected by Becker in 2009 on ...

Usage

becker09

Format

A dataframe with 10 rows and 9 columns:

ID

Study ID

N

Study sample size

Team

...

Cognitive_Performance

Correlation between Cognitive and Performance

Somatic_Performance

Correlation between Somatic and Performance

Selfconfidence_Performance

Correlation between Self Confidence and Performance

Somatic_Cognitive

Correlation between Somatic and Cognitive

Selfconfidence_Cognitive

Correlation between Self Confidence and Cognitive

Selfconfidence_Somatic

Correlation between Self Confidence and Somatic

Examples

  becker09

c mat ft

Description

c mat ft

Usage

c_mat_ft(model_input, R)

Arguments

model_input

Model input as a character string. Multiple models need to be on their own line. Model syntax uses lavann like syntax, see details for more details about this syntax.

R

A correlation matrix, most likely this will be the average correlation matrix outputted from the metafor package.

Value

A list.

Examples

Br <-  matrix(c(1.00000000, -0.09773331, -0.1755029,  0.3186775,
-0.09773331,  1.00000000,  0.5271873, -0.4175596,
-0.17550292,  0.5271872,  1.0000000, -0.4006848,
0.31867753, -0.41755963, -0.4006848,  1.0000000),
nrow = 4, byrow = TRUE)

colnames(Br) <- c("Performance",  "Self_confidence",  "Cognitive", "Somatic" )

rownames(Br) <- colnames(Br)

## Proposed path model
model <- "## Regression paths
Performance ~  Self_confidence  + Cognitive  + Somatic
Self_confidence ~ Cognitive + Somatic "

c_mat_ft(model, Br)

Helper function to read in data

Description

This function builds a list of correlation matrices from data that are in flat files where a correlation matrix is coded into a single row, a common format for coding correlation matrices.

Usage

df_to_corr(data, variables, ID = NULL)

Arguments

data

Data frame input used to convert to correlation matrices.

variables

A character vector of variable names representing the columns to convert to a pairwise correlation matrix. Variable names take the following format: "columnname_rowname" where the name prior to the underscore is the column name and the name after the underscore is the row name.

ID

A variable name, as a character string, to use as names for the list elements.

Value

A list of correlation matrices.

Examples

becker09 <- read.csv(paste0(system.file('raw_data', package = 'mars'),
   '/Becker09.csv'))
becker09_list <- df_to_corr(becker09,
   variables = c('Cognitive_Performance',
                 'Somatic_Performance',
                 'Selfconfidence_Performance',
                 'Somatic_Cognitive',
                 'Selfconfidence_Cognitive',
                 'Selfconfidence_Somatic'),
    ID = 'ID')

Master Estimation Function

Description

The primary estimation function for conducting the optimization. The function is typically called through the mars function, but can be called here directly.

Usage

estimation(
  formula = NULL,
  effect_name = NULL,
  studyID = NULL,
  effectID = NULL,
  variance = NULL,
  data,
  estimation_method = "REML",
  optim_method = "L-BFGS-B",
  structure = "UN",
  varcov_type,
  weights = NULL,
  intercept = FALSE,
  N = NULL,
  missing = "remove",
  robustID = NULL,
  multivariate_covs = NULL,
  tol = 1e-10,
  ...
)

Arguments

formula

The formula used for specifying the fixed and random structure. Used for univariate and multilevel structures.

effect_name

Character string representing the name of the effect size column in the data.

studyID

Character string representing the study ID

effectID

Character string representing the effect size ID

variance

Character string representing the name of the variance of the effect size in the data.

data

Data used for analysis

estimation_method

Type of estimation used, either "REML" or "MLE", REML is the default

optim_method

Optimization method that is passed to the optim function. Default is 'L-BFGS-B'.

structure

Between studies covariance structure, default is "UN" or unstructured. See details for more specifics.

varcov_type

Type of variance covariance matrix computed. Default is 'cor_weighted' for correlations or 'smd_outcome' for standardized mean differences.

weights

User specified matrix of weights.

intercept

Whether a model intercept should be specified, default is FALSE meaning no intercept. See details for more information.

N

Character string representing the sample size of the studies.

missing

What to do with missing data, default is 'remove'

robustID

A character vector specifying the cluster group to use for computing the robust standard errors.

multivariate_covs

A one-sided formula to specify the covariates used in a multivariate analysis.

tol

Tolerance for estimating, passed to optim

...

Additional arguments to pass to optim.

Value

Output is a named list; The output returns the estimated parameters, fit statistics, estimation inputs.

Estimate regression coefficients

Description

Estimate regression coefficients

Usage

find_B(model_input, R)

Arguments

model_input

Model input as a character string. Multiple models need to be on their own line. Model syntax uses lavann like syntax, see details for more details about this syntax.

R

A correlation matrix, most likely this will be the average correlation matrix outputted from the metafor package.

Details

Coming soon.

The output will be the same length as the number of regression equations specified in the model_input argument.

Value

A list of parameter estimates

Examples

Br <-  matrix(c(1.00000000, -0.09773331, -0.1755029,  0.3186775,
-0.09773331,  1.00000000,  0.5271873, -0.4175596,
-0.17550292,  0.5271872,  1.0000000, -0.4006848,
0.31867753, -0.41755963, -0.4006848,  1.0000000),
nrow = 4, byrow = TRUE)

colnames(Br) <- c("Performance",  "Self_confidence",  "Cognitive", "Somatic" )

rownames(Br) <- colnames(Br)

## Proposed path model
model <- "## Regression paths
Performance ~  Self_confidence  + Cognitive  + Somatic
Self_confidence ~ Cognitive + Somatic "

find_B(model, Br)

Find regression coefficients

Description

Find regression coefficients

Usage

find_reg_coef(model_input, R, ...)

Arguments

model_input

Model input as a character string. Multiple models need to be on their own line. See details for specification.

R

A correlation matrix, most likely this will be the average correlation matrix outputted from the metafor package.

...

Currently not used

Value

A vector of regression coefficient estimates.

Master mars function

Description

The primary function used for input and estimation. The function takes the data inputs and routes the estimation and structure type based on data structure. The function can handle univariate, multivariate, longitudinal, and multilevel meta-analytic models.

Usage

mars(
  data,
  studyID,
  effectID,
  sample_size,
  effectsize_type = NULL,
  formula = NULL,
  variable_names = NULL,
  effectsize_name = NULL,
  estimation_method = "REML",
  variance = NULL,
  varcov_type,
  weights = NULL,
  structure = "UN",
  intercept = FALSE,
  missing = "remove",
  optim_method = "L-BFGS-B",
  robustID = NULL,
  multivariate_covs = NULL,
  tol = 1e-10,
  ...
)

Arguments

data

Data used for analysis

studyID

Character string representing the study ID

effectID

Character string representing the effect size ID

sample_size

Character string representing the sample size of the studies.

effectsize_type

Type of effect size being analyzed

formula

The formula used for specifying the fixed and random structure. Used for univariate and multilevel structures.

variable_names

Vector of character strings representing the attributes with correlations. The attributes that are correlated should be separated by an underscore.

effectsize_name

Character string representing the name of the effect size column in the data.

estimation_method

Type of estimation used, either "REML" or "MLE", REML is the default

variance

Character string representing the name of the variance of the effect size in the data.

varcov_type

Type of variance covariance matrix computed. Default is 'cor_weighted' for correlations or 'smd_outcome' for standardized mean differences.

weights

User specified matrix of weights for analysis.

structure

Between studies covariance structure, default is "UN" or unstructured. See details for more specifics.

intercept

Whether a model intercept should be specified, default is FALSE meaning no intercept. See details for more information.

missing

Whether missing data should be removed, or kept. Default is removing.

optim_method

Optimization method that is passed to the optim function. Default is 'L-BFGS-B'.

robustID

A character vector specifying the cluster group to use for computing the robust standard errors.

multivariate_covs

A one-sided formula to specify the covariates used in a multivariate analysis.

tol

Tolerance of the optimization, default is 1E-10.

...

Not currently used.

Value

Returns a list of class mars; The returned object contains elements from the estimation.

Math Correlations Data

Description

This data contains correlations on math ...

Usage

math_correlations

Format

A nested list with correlations and sample size:

math_correlations

A list of math correlations

sample_size

Study sample size

Examples

  math_correlations

Model fitting function

Description

Model fitting function

Usage

model_fit(model_input, R, method_null = "sem", N)

Arguments

model_input

Model input as a character string. Multiple models need to be on their own line. See details for specification.

R

A correlation matrix, most likely this will be the average correlation matrix outputted from the metafor package.

method_null

Unsure

N

Sample size

Value

A list of fit indices.

Examples

Br <-  matrix(c(1.00000000, -0.09773331, -0.1755029,  0.3186775,
-0.09773331,  1.00000000,  0.5271873, -0.4175596,
-0.17550292,  0.5271872,  1.0000000, -0.4006848,
0.31867753, -0.41755963, -0.4006848,  1.0000000),
nrow = 4, byrow = TRUE)

colnames(Br) <- c("Performance",  "Self_confidence",  "Cognitive", "Somatic" )

rownames(Br) <- colnames(Br)

## Proposed path model
model <- "## Regression paths
Performance ~  Self_confidence  + Cognitive  + Somatic
Self_confidence ~ Cognitive + Somatic "

N <- 573
model_fit(model_input = model, R = Br,
         method_null = "sem", N)
model_fit(model_input = model, R = Br,
         method_null = "sem", N )

Olkin & Siotani variance-covariance matrix

Description

Computational function to compute the Olkin & Siotani (1976) variance-covariance matrix for correlation matrices. It allows the user to specify three different computations.

Usage

olkin_siotani(data, n, type = c("average", "weighted", "simple"))

Arguments

data

A correlation matrix or a list of correlation matrices.

n

Sample size

type

The type of Olkin and Siotani correction to make.

Details

The three possible computations that can be specified are:

Value

List of matrices, same length as the number of studies or number of correlation matrices.

References

Becker, B. J. (1992). Using results from replicated studies to estimate linear models. Journal of Educational Statistics, 17(4), 341-362. Olkin, I. (1976). Asymptotic distribution of functions of a correlation matrix. Essays in provability and statistics: A volume in honor of Professor Junjiro Ogawa.

Path Model Function

Description

This function fits the path model and returns adjusted standard errors.

Usage

path_model(
  mars_object,
  model,
  num_obs = NULL,
  adjust_se = TRUE,
  method_null = "sem",
  ...
)

Arguments

mars_object

The mars fitted object.

model

This is model syntax specified in the format by lavaan.

num_obs

Number of observations

adjust_se

Adjust the standard errors to reflect the ...

method_null

Unsure

...

Currently not used.

Details

The input is the coefficients and the variance covariance matrix returned from the mars function.

Value

List output with class path; The output is the parameter estimates from the fitted path model.

School Data

Description

This data ...

Usage

school

Format

A dataframe with 56 rows and 5 columns:

district

District ID

Examples

  school

SMD Simulated Data

Description

This data ...

Usage

smd_data

Format

A dataframe with 14 rows and 7 columns:

study

Study ID

Examples

  smd_data