meta_r function

Estimate meta-analytic Pearson's r across multiple studies with two continuous outcome variables.

meta_r is suitable for synthesizing across multiple studies that have measured a linear correlation (Pearson's r) from two continuous variables.

meta_r(
  data,
  rs,
  ns,
  labels = NULL,
  moderator = NULL,
  contrast = NULL,
  effect_label = "My effect",
  random_effects = TRUE,
  conf_level = 0.95
)

Arguments

• data: A dataframe or tibble
• rs: A collection of Pearson's r values, 1 per study, all between -1 and 1, inclusive
• ns: A collection of study sample sizes, all integers > 2
• labels: An optional collection of study labels
• moderator: An optional factor to analyze as a categorical moderator, must have k > 2 per groups
• contrast: An optional contrast to estimate between moderator levels; express as a vector of contrast weights with 1 weight per moderator level.
• effect_label: Optional character giving a human-friendly name of the effect being synthesized
• random_effects: TRUE for random effect model; FALSE for fixed effects
• conf_level: The confidence level for the confidence interval. Given in decimal form. Defaults to 0.95.

Returns

An esci-estimate object; a list of data frames and properties. Returned tables include:

• es_meta - A data frame of meta-analytic effect sizes. If a moderator was defined, there is an additional row for each level of the moderator.

  • effect_label - Study label
  • effect_size - Effect size
  • LL - Lower bound of conf_level% confidence interval
  • UL - Upper bound of conf_level% confidence interval
  • SE - Expected standard error
  • k - Number of studies
  • diamond_ratio - ratio of random to fixed effects meta-analytic effect sizes
  • diamond_ratio_LL - lower bound of conf_level% confidence interval for diamond ratio
  • diamond_ratio_UL - upper bound of conf_level% confidence interval for diamond ratio
  • I2 - I2 measure of heterogeneity
  • I2_LL - Lower bound of conf_level% confidence interval for I2
  • I2_UL - upper bound of conf_level% confidence interval for I2
  • PI_LL - lower bound of conf_level% of prediction interval
  • PI_UL - upper bound of conf_level% of prediction interval
  • p - p value for the meta-analytic effect size, based on null of exactly 0
  • *width - width of the effect-size confidence interval
  • FE_effect_size - effect size of the fixed-effects model (regardless of if fixed effects was selected
  • RE_effect_size - effect size of the random-effects model (regardless of if random effects was selected
  • FE_CI_width - width of the fixed-effects confidence interval, used to calculate diamond ratio
  • RE_CI_width - width of the fixed-effects confidence interval, used to calculate diamond ratio

• es_heterogeneity - A data frame of of heterogeneity values and conf_level% CIs for the meta-analytic effect size. If a moderator was defined also reports heterogeneity estimates for each level of the moderator.

  • effect_label - study label
  • moderator_variable_name - if moderator passed, gives name of the moderator
  • moderator_level - 'Overall' and each level of moderator, if passed
  • measure - Name of the measure of heterogeneity
  • estimate - Value of the heterogeneity estimate
  • LL - lower bound of conf_level% confidence interval
  • UL - upper bound of conf_level% confidence interval

• raw_data - A data from with one row for each study that was passed

  • label - study label
  • effect_size - effect size
  • weight - study weight in the meta analysis
  • sample_variance - expected level of sampling variation
  • SE - expected standard error
  • LL - lower bound of conf_level% confidence interval
  • UL - upper bound of conf_level% confidence interval
  • mean - used to calculate study p value; this is the d value entered for the study
  • sd - use to calculate study p value; set to 1 for each study
  • n - study sample size
  • p - p value for the study, based on null of exactly 0

Details

Once you generate an estimate with this function, you can visualize it with plot_meta().

The meta-analytic effect size, confidence interval and heterogeneity estimates all come from metafor::rma().

Examples

# Data: See Introduction to the New Statistics, first edition
esci_single_r <- data.frame(
  studies = c(
    'Violin, viola'     ,
    'Strings'   ,
    'Piano'     ,
    'Piano'     ,
    'Piano'     ,
    'Piano'     ,
    'Piano'     ,
    'Piano'     ,
    'Piano'     ,
    'All'       ,
    'Piano'     ,
    'Piano'     ,
    'Band'      ,
    'Music majors'      ,
    'Music majors'      ,
    'All'
  ),
  rvalues = c(
    .67,
    .51,
    .4,
    .46,
    .47,
    .228,
    -.224,
    .104,
    .322,
    .231,
    .67,
    .41,
    .34,
    .31,
    .54,
    .583
  ),
  sample_size = c(
    109,
    55,
    19,
    30,
    19,
    52,
    24,
    52,
    16,
    97,
    57,
    107,
    178,
    64,
    19,
    135
  ),
  subsets = as.factor(
    c(
      'Strings' ,
      'Strings' ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Piano'   ,
      'Strings' ,
      'Strings' ,
      'Strings' ,
      'Strings'
    )
 )
)

# Meta-analysis, random effects, no moderator
estimate <- esci::meta_r(
  esci_single_r,
  rvalues,
  sample_size,
  studies,
  random_effects = TRUE
)

# Forest plot
myplot_forest <- esci::plot_meta(estimate)

# Meta-analysis, random effects, moderator (subsets)
estimate_moderator <- esci::meta_r(
  esci_single_r,
  rvalues,
  sample_size,
  studies,
  subsets,
  random_effects = TRUE
)

# Forest plot
myplot_forest_moderator <- esci::plot_meta(estimate_moderator)