A convenience function for calculating multiple design-comparable effect sizes from a dataset that compiles data from multiple single-case design studies

Calculates standardized mean difference effect sizes for a data set including one or multiple single-case design studies using the same design (treatment reversal, multiple baseline/probe across participants, replicated multiple baseline across behaviors, or clustered multiple baseline across participants).

batch_calc_BCSMD(
  data,
  design,
  grouping,
  case,
  phase,
  session,
  outcome,
  cluster = NULL,
  series = NULL,
  center = 0,
  round_session = TRUE,
  treatment_name = NULL,
  FE_base = 0,
  RE_base = 0,
  RE_base_2 = NULL,
  FE_trt = 0,
  RE_trt = NULL,
  RE_trt_2 = NULL,
  corStruct = "AR1",
  varStruct = "hom",
  Bayesian = FALSE,
  prior = NULL,
  chains = 4,
  iter = 2000,
  warmup = iter/2,
  thin = 10,
  cores = 1,
  seed = NA,
  A = NULL,
  B = NULL,
  D = NULL,
  cover = 95,
  bound = 35,
  symmetric = TRUE,
  summary = TRUE,
  ...
)

Arguments

data

A data frame containing SCD data for which design-comparable effect sizes will be calculated.

design

Character string to specify whether data comes from a treatment reversal ("TR"), multiple baseline across participants ("MBP"), replicated multiple baseline across behaviors ("RMBB"), or clustered multiple baseline across participants ("CMB").

grouping

A variable name or list of (unquoted) variable names that uniquely identify each study.

case

A variable name (unquoted) that identifies unique cases within each grouping variable.

phase

A variable name (unquoted) that identifies unique treatment phases.

session

A variable name (unquoted) that contains the measurement times for each data series.

outcome

A variable name (unquoted) that contains the outcome measurements for each data series.

cluster

(Optional) variable name (unquoted) that identifies the unique clusters of cases for CMB designs.

series

(Optional) variable name (unquoted) that identifies the unique data series for RMBB designs.

center

Numeric value for the centering value for session. Default is 0.

round_session

Logical indicating whether to round session to the nearest integer. Defaults to TRUE.

treatment_name

(Optional) character string corresponding to the name of the treatment phase.

FE_base

Vector of integers specifying which fixed effect terms to include in the baseline phase. Setting FE_base = 0 includes only a level. Setting FE_base = c(0,1) includes a level and a linear time trend.

RE_base

Vector of integers specifying which random effect terms to include in the baseline phase. Setting RE_base = 0 includes only levels (i.e., random intercepts). Setting RE_base = c(0,1) includes random levels and random linear trends.

RE_base_2

Vector of integers specifying which random effect terms to include in the baseline phase for the cluster level in clustered multiple baseline design across participants or for the case level in replicated multiple baseline across behaviors. Setting RE_base_2 = 0 includes only levels (i.e., random intercepts). Setting RE_base_2 = c(0,1) includes random levels and random linear trends.

FE_trt

Vector of integers specifying which fixed effect terms to include in the treatment phase. Setting FE_trt = 0 includes only a change in level. Setting FE_trt = c(0,1) includes a change in level and a treatment-by-linear time trend.

RE_trt

Vector of integers specifying which random effect terms to include in the treatment phase. Setting RE_trt = 0 includes only random changes in level. Setting RE_trt = c(0,1) includes random changes in level and random treatment-by-linear time trends.

RE_trt_2

Vector of integers specifying which random effect terms to include in the treatment phase for the cluster level in clustered multiple baseline design across participants or for the case level in replicated multiple baseline across behaviors. Setting RE_trt_2 = 0 includes only random changes in level. Setting RE_trt_2 = c(0,1) includes random changes in level and random treatment-by-linear time trends.

corStruct

(Optional) character string indicating the correlation structure of session-level errors. Options are "AR1" (default), "MA1", or "IID".

varStruct

(Optional) character string indicating the heteroscedasticity structure of session-level errors. Options are "hom" (default) or "het", which allows for the session-level error variances to differ by phase.

Bayesian

Logical indicating whether to apply Bayesian estimation methods. If FALSE (default), apply restricted maximum likelihood estimation. If TRUE, apply Bayesian estimation methods (i.e., Markov Chain Monte Carlo) to the parameters of the specified hierarchical linear model.

prior

(Optional) One or more brmsprior objects created by "set_prior" in the "brms" R package. Default is prior = NULL when flat priors will be applied for Bayesian estimation. Ignored if Bayesian = FALSE.

chains

Number of Markov chains to use for Bayesian estimation. Default is chains = 4. Ignored if Bayesian = FALSE.

iter

Number of iterations per chain to use for Bayesian estimation. Default is iter = 2000. Ignored if Bayesian = FALSE.

warmup

Number of burn-in iterations to use for Bayesian estimation. Default is iter/2. Ignored if Bayesian = FALSE.

thin

Thinning rate to use for Bayesian estimation. Default is thin = 10. Ignored if Bayesian = FALSE.

cores

Number of cores to use for Bayesian estimation. Default is cores = 1. Ignored if Bayesian = FALSE.

seed

Random number generation seed to use for Bayesian estimation. Default is seed = NA, which will cause the seed to be set randomly. Ignored if Bayesian = FALSE.

A

The time point immediately before the start of treatment in the hypothetical between-group design.

B

The time point at which outcomes are measured in the hypothetical between-group design.

D

Numerical indicating the treatment duration across cases. Note that B = A + D and it is not allowed to specify both B and D.

cover

Confidence level.

bound

Numerical tolerance for non-centrality parameter in qt.

symmetric

If TRUE (the default), use a symmetric confidence interval. If FALSE, use a non-central t approximation to obtain an asymmetric confidence interval.

summary

Logical indicating whether to return a data frame with effect size estimates and other information. If TRUE (default), return a data.frame containing the effect size estimate, standard error, confidence interval (or credible interval if Bayesian == TRUE), and other information. If FALSE, return a list with effect size estimate, degrees of freedom, and other information.

...

further arguments passed to calc_BCSMD.

Value

A data frame containing the design-comparable effect size estimate, standard error, confidence interval, and other information, for each unique category of grouping variable(s).

Examples

data(Thiemann2001)
data(Thiemann2004)
datThiemann <- rbind(Thiemann2001, Thiemann2004)

# Change-in-levels model with a fixed treatment effect
batch_calc_BCSMD(data = datThiemann,
                 grouping = Study_ID,
                 design = "RMBB",
                 case = case, series = series, phase = treatment,
                 session = time, outcome = outcome,
                 FE_base = 0, RE_base = 0,
                 RE_base_2 = 0, FE_trt = 0)

# Models with linear time trends in baseline and treatment phase,
# random baseline slope at series level, fixed treatment effects
batch_calc_BCSMD(data = datThiemann,
                 grouping = Study_ID,
                 design = "RMBB",
                 case = case, series = series, phase = treatment,
                 session = time, outcome = outcome,
                 FE_base = c(0,1), RE_base = c(0,1),
                 RE_base_2 = 0, FE_trt = c(0,1))