In lebebr01/metaRmat: Synthesis of Correlation Matrices

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

We load the necessary packages as well as the data set for the example. Because for this example we are using only complete data we remove the the two studies with NA (i.e., Study 6 and Study 17).

library(metaRmat)
library(metafor)
library(corpcor)
library(Matrix)
library(matrixcalc)

becker09 <- na.omit(becker09) # ommiting studies with NA

Next, we create a list, which will be imputed in our other functions.

becker09_list <- df_to_corr(becker09, 
                            variables = c('Cognitive_Performance',
                                          'Somatic_Performance',
                                          'Selfconfidence_Performance', 
                                          'Somatic_Cognitive',
                                          'Selfconfidence_Cognitive',
                                          'Selfconfidence_Somatic'),
                            ID = 'ID')

Calculate OS

There are currently three options for the variance-covariance matrix of the correlation matrix (i.e, simple, average, and weighted) for this example we selected the weighted option.

#olkin_siotani(becker09_list, becker09$N, type = 'simple')
#olkin_siotani(becker09_list, becker09$N, type = 'average')
olkin_siotani(becker09_list, becker09$N, type = 'weighted')

Master Prep Data Function

The function below creates and organize elements that are then fitted internally into the metafor package. Below we fitted fixed and random-effects models and extracted some more detail information from objects that are not directly output by the functions. First, we see results under fixed-effect models.

input_metafor <- prep_data(becker09, becker09$N, type = 'weighted', missing = FALSE, 
                           variable_names = c('Cognitive_Performance', 'Somatic_Performance',
                                              'Selfconfidence_Performance', 
                                              'Somatic_Cognitive',
                                              'Selfconfidence_Cognitive',
                                              'Selfconfidence_Somatic'),
                           ID = 'ID')
fixed_model <- fit_model(data = input_metafor, effect_size = 'yi', 
                         var_cor = 'V', moderators = ~ -1 + factor(outcome), 
                         random_params = NULL)
# below the model_out_fixed will extract some of the info but I am also extracting some here
round(fixed_model$b, 3) # fixed effect estimates
round(fixed_model$vb, 5) # fixed effect COV
fixed_model # forthe Q and df 

Now we fit a random-effects model and extract some objects from this output.

random_model <- fit_model(data = input_metafor, effect_size = 'yi', 
                          var_cor = 'V', moderators = ~ -1 + factor(outcome), 
                          random_params = ~ factor(outcome) | factor(study))
# below the model_out_random will extract some of the info but I am also extracting some here
round(random_model$tau2, 3) # between studies variance 
round(random_model$b, 3) # random effect estimate
round(random_model$vb, 5) # random effect Cov

Extract model data

These are the results under random effect models. This is what the typical output for the mode extract_modelfunction for fixed-effect model looks like.

model_out_fixed <- extract_model(fixed_model, 
                                 variable_names = c('Cognitive_Performance',
                                                    'Somatic_Performance',
                                                    'Selfconfidence_Performance', 
                                                    'Somatic_Cognitive',
                                                    'Selfconfidence_Cognitive',
                                                    'Selfconfidence_Somatic'))
model_out_fixed 

For the random-effect, we extract several more objects from the extract_modelfunction. We can also build a correlation matrix of the $\hat{\tau}^2$ as well.

model_out_random <- extract_model(random_model, 
                                  variable_names = c('Cognitive_Performance',
                                                     'Somatic_Performance',
                                                     'Selfconfidence_Performance', 
                                                     'Somatic_Cognitive',
                                                     'Selfconfidence_Cognitive',
                                                     'Selfconfidence_Somatic'))
Rho <- model_out_random$rho 
Tau2 <- model_out_random$tau
#------------------
# tau matrix
#------------------
rho_t <-  vec2sm(Rho, diag = FALSE)
diag <- 1
diag(rho_t) <- diag
tdiag <- diag(sqrt(Tau2))
taumat <- tdiag %*% rho_t %*% tdiag
round(taumat, 3)
round(cov2cor(taumat),2)

Fit model with lavaan

Now, we are ready to input the average correlation matrix and its variance covariance matrix into the lavaan package and our own function to appropriate estimate SE via the multivariate delta method.

model <- "## Regression paths
Performance ~ Cognitive + Somatic + Selfconfidence
Selfconfidence ~ Cognitive + Somatic
"

path_output <- path_model(data = model_out_random, model = model, 
                          num_obs = sum(becker09$N))
summary(path_output)

Team

We now subset the data to obtain results only for the studies that reported on Team sports.

becker09_T <- subset(becker09, becker09$Team == "T")

becker09_list2 <- df_to_corr(becker09_T, 
                             variables = c('Cognitive_Performance',
                                           'Somatic_Performance',
                                           'Selfconfidence_Performance', 
                                           'Somatic_Cognitive',
                                           'Selfconfidence_Cognitive',
                                           'Selfconfidence_Somatic'),
                             ID = 'ID')

input_metafor2 <- prep_data(becker09_T, becker09_T$N, type = 'weighted', missing = FALSE, 
                            variable_names = c('Cognitive_Performance', 'Somatic_Performance',
                                               'Selfconfidence_Performance', 
                                               'Somatic_Cognitive',
                                               'Selfconfidence_Cognitive',
                                               'Selfconfidence_Somatic'),
                            ID = 'ID')

random_model2 <- fit_model(data = input_metafor2, effect_size = 'yi', 
                           var_cor = 'V', moderators = ~ -1 + factor(outcome), 
                           random_params = ~ factor(outcome) | factor(study))

Extract model data

model_out_random2 <- extract_model(random_model2, 
                                   variable_names = c('Cognitive_Performance',
                                                      'Somatic_Performance',
                                                      'Selfconfidence_Performance', 
                                                      'Somatic_Cognitive',
                                                      'Selfconfidence_Cognitive',
                                                      'Selfconfidence_Somatic'))

Fit model with lavaan

model <- "## Regression paths
Performance ~ Cognitive + Somatic + Selfconfidence
Selfconfidence ~ Cognitive + Somatic
"

path_output2 <- path_model(data = model_out_random2, model = model, 
                             num_obs = sum(becker09_T$N))
summary(path_output2)

Individual

Similarly, we now subset the data to obtain results only for the studies that reported on Individual sports.

becker09_I <- subset(becker09, becker09$Team == "I")

becker09_list3 <- df_to_corr(becker09_I, 
                             variables = c('Cognitive_Performance',
                                           'Somatic_Performance',
                                           'Selfconfidence_Performance', 
                                           'Somatic_Cognitive',
                                           'Selfconfidence_Cognitive',
                                           'Selfconfidence_Somatic'),
                             ID = 'ID')

input_metafor3 <- prep_data(becker09_I, becker09_I$N, type = 'weighted', missing = FALSE,
                            variable_names = c('Cognitive_Performance', 'Somatic_Performance',
                                               'Selfconfidence_Performance', 
                                               'Somatic_Cognitive',
                                               'Selfconfidence_Cognitive',
                                               'Selfconfidence_Somatic'),
                            ID = 'ID')

random_model3 <- fit_model(data = input_metafor3, effect_size = 'yi', 
                           var_cor = 'V', moderators = ~ -1 + factor(outcome), 
                           random_params = ~ factor(outcome) | factor(study))

Extract model data

model_out_random3 <- extract_model(random_model3, 
                                   variable_names = c('Cognitive_Performance',
                                                      'Somatic_Performance',
                                                      'Selfconfidence_Performance', 
                                                      'Somatic_Cognitive',
                                                      'Selfconfidence_Cognitive',
                                                      'Selfconfidence_Somatic'))

Fit model with lavaan

model <- "## Regression paths
Performance ~ Cognitive + Somatic + Selfconfidence
Selfconfidence ~ Cognitive + Somatic"

path_output3 <- path_model(data = model_out_random3, model = model, 
                           num_obs = sum(becker09_I$N))
lavaan::summary(path_output3)

Partial correlation matrix

Here we compute the synthetic partial correlation from the average correlation matrix.

# partial corr matrix
round(cor2pcor(model_out_random$beta_matrix),3)

# var-cov matrix of partials
Psy <- random_model$vb
round(var_path(model_out_random$beta_matrix, Psy, type = 'pcor'), 4)

Partial from uni approach

Here we work with partial correlation for each study and then synthesize that information.

#---------------------------------------------------------------------
# Create a data set with 8 complete studies
#---------------------------------------------------------------------
R <-  becker09_list
R$"6" <- NULL
R$"17" <- NULL
n <- becker09$N[c(-3, -5)]
#------------------------------------------------------------------
# first replace NA by zeros
RR <- R                           # redifine list

PR <- lapply(RR, cor2pcor)
pr <- unlist(lapply(PR, '[[', 4))
var_pr <- (1-pr^2)^2 / (n - 3 -1)

rma.uni(pr, var_pr)

lebebr01/metaRmat documentation built on Feb. 24, 2024, 10:44 a.m.