Title: | Estimating Hierarchical Linear Models for Single-Case Designs |
---|---|
Description: | Provides a set of tools for estimating hierarchical linear models and effect sizes based on data from single-case designs. Functions are provided for calculating standardized mean difference effect sizes that are directly comparable to standardized mean differences estimated from between-subjects randomized experiments, as described in Hedges, Pustejovsky, and Shadish (2012) <DOI:10.1002/jrsm.1052>; Hedges, Pustejovsky, and Shadish (2013) <DOI:10.1002/jrsm.1086>; Pustejovsky, Hedges, and Shadish (2014) <DOI:10.3102/1076998614547577>; and Chen, Pustejovsky, Klingbeil, and Van Norman (2023) <DOI:10.1016/j.jsp.2023.02.002>. Includes an interactive web interface. |
Authors: | James Pustejovsky [aut, cre], Man Chen [aut], Bethany Hamilton [aut] |
Maintainer: | James Pustejovsky <[email protected]> |
License: | GPL-3 |
Version: | 0.7.3 |
Built: | 2025-02-19 03:59:49 UTC |
Source: | https://github.com/jepusto/scdhlm |
Data from a multiple baseline design conducted by Alber-Morgan, Ramp, Anderson, & Martin (2007). The variables are as follows:
case
Participant identifier
condition
Factor identifying
the phase of the design (baseline or treatment)
session
Measurement occasion
outcome
Number of words read correctly per
minute
A data frame with 119 rows and 4 variables
Alber-Morgan, S. R., Ramp, E. M., Anderson, L. L., & Martin, C. M. (2007). Effects of repeated readings, error correction, and performance feedback on the fluency and comprehension of middle school students with behavior problems. Journal of Special Education, 41(1), 17-30. doi:10.1177/00224669070410010201
Data from an ABAB design conducted by Anglesea, Hoch, & Taylor (2008). The variables are as follows:
case
Case identifier.
condition
Factor indicating baseline or treatment condition
phase
Study phase (including both control and treatment condition)
session
Measurement occasion
outcome
Total seconds of eating time
A data frame with 55 rows and 5 variables
Anglesea, M. M., Hoch, H., & Taylor, B. A. (2008). Reducing rapid eating in teenagers with autism: Use of a pager prompt. Journal of Applied Behavior Analysis, 41(1), 107-111. doi:10.1901/jaba.2008.41-107
Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2012). A standardized mean difference effect size for single case designs. Research Synthesis Methods, 3, 224-239. doi:10.1002/jrsm.1052
Data from a multiple baseline design conducted by Barton-Arwood, Wehby, and Falk (2005). The variables are as follows:
case
Participant identifier
condition
Factor identifying
the phase of the design (A or B)
session
Measurement occasion
outcome
Oral reading fluency score (words per minute)
A data frame with 143 rows and 4 variables
Barton-Arwood, S. M., Wehby, J. H., & Falk, K. B. (2005). Reading instruction for elementary-age students with emotional and behavioral disorders: Academic and behavioral outcomes. Exceptional Children, 72(1), 7-27. doi:10.1177/001440290507200101
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", A = NULL, B = NULL, D = NULL, cover = 95, bound = 35, symmetric = TRUE, ... )
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", A = NULL, B = NULL, D = NULL, cover = 95, bound = 35, symmetric = TRUE, ... )
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 ( |
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 |
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 |
series |
(Optional) variable name (unquoted) that identifies the unique
data series for |
center |
Numeric value for the centering value for session. Default is 0. |
round_session |
Logical indicating whether to round |
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 |
RE_base |
Vector of integers specifying which random effect terms to
include in the baseline phase. Setting |
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 |
FE_trt |
Vector of integers specifying which fixed effect terms to
include in the treatment phase. Setting |
RE_trt |
Vector of integers specifying which random effect terms to
include in the treatment phase. Setting |
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 |
corStruct |
(Optional) character string indicating the correlation
structure of session-level errors. Options are |
varStruct |
(Optional) character string indicating the
heteroscedasticity structure of session-level errors. Options are
|
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
|
cover |
Confidence level. |
bound |
Numerical tolerance for non-centrality parameter in
|
symmetric |
If |
... |
further arguments. |
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).
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))
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))
Data from a clustered multiple baseline across participants design conducted by Bryant et al. (2018). The variables are as follows:
Study_ID
. Study identifier.
school
. School identifier.
group
. Group identifier.
case
. Student identifier.
treatment
. Indicator for treatment phase.
session
. Measurement occasion.
session_trt
. Measurement occasion times treatment phase.
outcome
. Texas Early Mathematics Inventory (TEMI-Aim Check) scores.
session_c
. Measurement occasion centered at the follow-up time.
A data frame with 536 rows and 8 variables
Bryant, D. R., Bryant, B. R., Sorelle-Miner, D. A., Falcomata, T. S. & Nozari, M. (2018). Tier 3 intensified intervention for second grade students with severe mathematics difficulties. Archives of Psychology, 2(11), 1-24. doi:10.31296/aop.v2i11.86
In one call, 1) clean single-case design data for treatment reversal and multiple baseline designs, 2) fit a multi-level model using restricted maximum likelihood estimation, and 3) estimate a standardized mean difference effect size.
calc_BCSMD( design, 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", A = NULL, B = NULL, D = NULL, cover = 95, bound = 35, symmetric = TRUE, summary = TRUE, data = NULL, ... )
calc_BCSMD( design, 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", A = NULL, B = NULL, D = NULL, cover = 95, bound = 35, symmetric = TRUE, summary = TRUE, data = NULL, ... )
design |
Character string to specify whether data comes from a treatment
reversal ( |
case |
vector of case indicators or name of a character or factor vector
within |
phase |
vector of treatment indicators or name of a character or factor
vector within |
session |
vector of measurement occasions or name of numeric vector
within |
outcome |
vector of outcome data or name of numeric vector of outcome
data within |
cluster |
(Optional) vector of cluster indicators or name of a character
or factor vector within |
series |
(Optional) vector of series indicators or name of a character
or factor vector within |
center |
Numeric value for the centering value for session. Default is 0. |
round_session |
Logical indicating whether to round |
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 |
RE_base |
Vector of integers specifying which random effect terms to
include in the baseline phase. Setting |
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 |
FE_trt |
Vector of integers specifying which fixed effect terms to
include in the treatment phase. Setting |
RE_trt |
Vector of integers specifying which random effect terms to
include in the treatment phase. Setting |
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 |
corStruct |
(Optional) character string indicating the correlation
structure of session-level errors. Options are |
varStruct |
(Optional) character string indicating the
heteroscedasticity structure of session-level errors. Options are
|
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
|
cover |
Confidence level. |
bound |
Numerical tolerance for non-centrality parameter in
|
symmetric |
If |
summary |
Logical indicating whether to return a data frame with effect
size estimates and other information. If |
data |
(Optional) dataset to use for analysis. Must be a
|
... |
further arguments. |
If summary == TRUE
, a data frame containing the
design-comparable effect size estimate, standard error, confidence
interval, and other information. If summary == FALSE
, a list
containing all elements of a 'g_mlm()' object, plus the fitted 'lme()'
model.
data(Laski) # Change-in-levels model with fixed treatment effect calc_BCSMD(design = "MBP", case = case, phase = treatment, session = time, outcome = outcome, FE_base = 0, RE_base = 0, FE_trt = 0, data = Laski) # Model with linear time trends in baseline and treatment phases, # random baseline slopes, fixed treatment effects calc_BCSMD(design = "MBP", case = case, phase = treatment, session = time, outcome = outcome, center = 4, FE_base = c(0,1), RE_base = c(0,1), FE_trt = c(0,1), data = Laski) data(Anglesea) calc_BCSMD(design = "TR", case = case, phase = condition, session = session, outcome = outcome, treatment_name = "treatment", FE_base = 0, RE_base = 0, FE_trt = 0, data = Anglesea) data(Thiemann2001) calc_BCSMD(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, data = Thiemann2001) data(Bryant2018) calc_BCSMD(design = "CMB", cluster = group, case = case, phase = treatment, session = session, outcome = outcome, center = 49, treatment_name = "treatment", FE_base = c(0,1), RE_base = 0, RE_base_2 = 0, FE_trt = c(0,1), RE_trt = NULL, RE_trt_2 = NULL, data = Bryant2018)
data(Laski) # Change-in-levels model with fixed treatment effect calc_BCSMD(design = "MBP", case = case, phase = treatment, session = time, outcome = outcome, FE_base = 0, RE_base = 0, FE_trt = 0, data = Laski) # Model with linear time trends in baseline and treatment phases, # random baseline slopes, fixed treatment effects calc_BCSMD(design = "MBP", case = case, phase = treatment, session = time, outcome = outcome, center = 4, FE_base = c(0,1), RE_base = c(0,1), FE_trt = c(0,1), data = Laski) data(Anglesea) calc_BCSMD(design = "TR", case = case, phase = condition, session = session, outcome = outcome, treatment_name = "treatment", FE_base = 0, RE_base = 0, FE_trt = 0, data = Anglesea) data(Thiemann2001) calc_BCSMD(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, data = Thiemann2001) data(Bryant2018) calc_BCSMD(design = "CMB", cluster = group, case = case, phase = treatment, session = session, outcome = outcome, center = 49, treatment_name = "treatment", FE_base = c(0,1), RE_base = 0, RE_base_2 = 0, FE_trt = c(0,1), RE_trt = NULL, RE_trt_2 = NULL, data = Bryant2018)
Data from a BAB design conducted by Carson, Gast, & Ayres (2008). The variables are as follows:
case
Participant identifier
treatment
Factor describing the treatment condition
phase
Numeric describing the phase of the study design for each case
outcome
Outcome scores
time
Measurement occasion
A data frame with 47 rows and 5 variables
Carson, K. D., Gast, D. L., & Ayres, K. M. (2008). Effects of a photo activity schedule book on independent task changes by students with intellectual disabilities in community and school job sites. European Journal of Special Needs Education, 23, 269-279.
Data from a multiple baseline design conducted by Case, Harris, and Graham (1992). The variables are as follows:
case
.
Participant identifier.
session
. Measurement occasion.
condition
. Factor identifying the phase of the design (baseline or
treatment).
outcome
. Number of subtraction equations and answers
correct on each word problem probe.
A data frame with 56 rows and 4 variables
Case, L. P., Harris, K. R., & Graham, S. (1992). Improving the mathematical problem-solving skills of students with learning disabilities: Self-regulated strategy development. The Journal of Special Education, 26(1), 1-19. doi:10.1177/002246699202600101
Calculates a confidence interval given a g_REML
, a
g_HPS
, or a g_mlm
object using either a central t
distribution (for a symmetric interval) or a non-central t distribution
(for an asymmetric interval).
g |
an estimated effect size object of class |
cover |
confidence level |
bound |
numerical tolerance for non-centrality parameter in
|
symmetric |
If |
A vector of upper and lower confidence bounds.
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) Laski_g_REML <- suppressWarnings( g_REML(Laski_RML, p_const = c(0,1), r_const = c(1,0,1), returnModel = FALSE) ) CI_g(Laski_g_REML, symmetric = TRUE) CI_g(Laski_g_REML, symmetric = FALSE) Laski_HPS <- with(Laski, effect_size_MB(outcome, treatment, case, time)) CI_g(Laski_HPS, symmetric = FALSE) Laski_g_mlm <- g_mlm(mod = Laski_RML, p_const = c(0,1), r_const = c(1,0,1)) CI_g(Laski_g_mlm, symmetric = FALSE)
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) Laski_g_REML <- suppressWarnings( g_REML(Laski_RML, p_const = c(0,1), r_const = c(1,0,1), returnModel = FALSE) ) CI_g(Laski_g_REML, symmetric = TRUE) CI_g(Laski_g_REML, symmetric = FALSE) Laski_HPS <- with(Laski, effect_size_MB(outcome, treatment, case, time)) CI_g(Laski_HPS, symmetric = FALSE) Laski_g_mlm <- g_mlm(mod = Laski_RML, p_const = c(0,1), r_const = c(1,0,1)) CI_g(Laski_g_mlm, symmetric = FALSE)
Simulates data from a simple linear mixed effects model, then calculates REML and HPS effect size estimators as described in Pustejovsky, Hedges, & Shadish (2014).
compare_RML_HPS(iterations, beta, rho, phi, design, m, n, MB = TRUE)
compare_RML_HPS(iterations, beta, rho, phi, design, m, n, MB = TRUE)
iterations |
number of independent iterations of the simulation |
beta |
vector of fixed effect parameters |
rho |
intra-class correlation parameter |
phi |
autocorrelation parameter |
design |
design matrix. If not specified, it will be calculated based on |
m |
number of cases. Not used if |
n |
number of measurement occasions. Not used if |
MB |
If true, a multiple baseline design will be used; otherwise, an AB design will be used. Not used if |
A matrix reporting the mean and variance of the effect size estimates and various associated statistics.
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
compare_RML_HPS(iterations=10, beta = c(0,1,0,0), rho = 0.3, phi = 0.5, design=design_matrix(m=3,n=8))
compare_RML_HPS(iterations=10, beta = c(0,1,0,0), rho = 0.3, phi = 0.5, design=design_matrix(m=3,n=8))
Data from a multiple baseline design conducted by Datchuk (2016). The variables are as follows:
case
. Participant
identifier.
session
. Measurement occasion.
condition
. Factor identifying the phase of the design (baseline or
treatment).
outcome
. Correct word sequences per minute.
A data frame with 74 rows and 4 variables
Datchuk, S. M. (2016). Writing simple sentences and descriptive paragraphs: Effects of an intervention on adolescents with writing difficulties. Journal of Behavioral Education, 25(2), 166-188. doi:10.1007/s10864-015-9236-x
Calculate the default initial treatment time and follow-up time that are used to define and estimate the between-case standardized mean differences for multiple baseline designs and variations.
default_times( design, case, phase, session, cluster = NULL, series = NULL, treatment_name = NULL, data = NULL )
default_times( design, case, phase, session, cluster = NULL, series = NULL, treatment_name = NULL, data = NULL )
design |
Character string to specify whether data comes from a treatment
reversal ( |
case |
vector of case indicators or name of a character or factor vector
within |
phase |
vector of treatment indicators or name of a character or factor
vector within |
session |
vector of measurement occasions or name of numeric vector
within |
cluster |
(Optional) vector of cluster indicators or name of a character
or factor vector within |
series |
(Optional) vector of series indicators or name of a character
or factor vector within |
treatment_name |
(Optional) character string corresponding to the name of the treatment phase. |
data |
(Optional) dataset to use for analysis. Must be a
|
A list of time range, default initial treatment time, and default follow-up time.
If treatment_name is left null, it will choose the second level of the phase variable to be the treatment phase.
data(Laski) default_times(design = "MBP", case = case, phase = treatment, session = time, data = Laski) data(Thiemann2001) default_times(design = "RMBB", case = case, series = series, phase = treatment, session = time, data = Thiemann2001) data(Bryant2018) default_times(design = "CMB", cluster = group, case = case, phase = treatment, session = session, data = Bryant2018)
data(Laski) default_times(design = "MBP", case = case, phase = treatment, session = time, data = Laski) data(Thiemann2001) default_times(design = "RMBB", case = case, series = series, phase = treatment, session = time, data = Thiemann2001) data(Bryant2018) default_times(design = "CMB", cluster = group, case = case, phase = treatment, session = session, data = Bryant2018)
Create a design matrix containing a linear trend, a treatment effect, and a
trend-by-treatment interaction for a single-case design with m
cases and n
measurement occasions.
design_matrix(m, n, treat_times = n/2 + 1, center = 0)
design_matrix(m, n, treat_times = n/2 + 1, center = 0)
m |
number of cases |
n |
number of time points |
treat_times |
(Optional) vector of length |
center |
centering point for time trend. |
A design matrix
design_matrix(3, 16, c(5,9,13))
design_matrix(3, 16, c(5,9,13))
Calculates the HPS effect size estimator based on data from an (AB)^k design, as described in Hedges, Pustejovsky, & Shadish (2012). Note that the data must contain one row per measurement occasion per subject.
effect_size_ABk( outcome, treatment, id, phase, time, data = NULL, phi = NULL, rho = NULL )
effect_size_ABk( outcome, treatment, id, phase, time, data = NULL, phi = NULL, rho = NULL )
outcome |
vector of outcome data or name of variable within |
treatment |
vector of treatment indicators or name of variable within |
id |
factor vector indicating unique cases or name of variable within |
phase |
factor vector indicating unique phases (each containing one contiguous control
condition and one contiguous treatment condition) or name of variable within |
time |
vector of measurement occasion times or name of variable within |
data |
(Optional) dataset to use for analysis. Must be data.frame. |
phi |
(Optional) value of the auto-correlation nuisance parameter, to be used in calculating the small-sample adjusted effect size |
rho |
(Optional) value of the intra-class correlation nuisance parameter, to be used in calculating the small-sample adjusted effect size |
A list with the following components
M_a |
Matrix reporting the total number of time points with data for all ids, by phase and treatment condition |
M_dot |
Total number of time points used to calculate the total variance (the sum of M_a ) |
D_bar |
numerator of effect size estimate |
S_sq |
sample variance, pooled across time points and treatment groups |
delta_hat_unadj |
unadjusted effect size estimate |
phi |
corrected estimate of first-order auto-correlation |
sigma_sq_w |
corrected estimate of within-case variance |
rho |
estimated intra-class correlation |
theta |
estimated scalar constant |
nu |
estimated degrees of freedom |
delta_hat |
corrected effect size estimate |
V_delta_hat |
estimated variance of the effect size |
If phi or rho is left unspecified (or both), estimates for the nuisance parameters will be calculated.
Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2012). A standardized mean difference effect size for single case designs. Research Synthesis Methods, 3, 224-239. doi:10.1002/jrsm.1052
data(Lambert) effect_size_ABk(outcome = outcome, treatment = treatment, id = case, phase = phase, time = time, data = Lambert) data(Anglesea) effect_size_ABk(outcome = outcome, treatment = condition, id = case, phase = phase, time = session, data = Anglesea)
data(Lambert) effect_size_ABk(outcome = outcome, treatment = treatment, id = case, phase = phase, time = time, data = Lambert) data(Anglesea) effect_size_ABk(outcome = outcome, treatment = condition, id = case, phase = phase, time = session, data = Anglesea)
Calculates the HPS effect size estimator based on data from a multiple baseline design, as described in Hedges, Pustejovsky, & Shadish (2013). Note that the data must contain one row per measurement occasion per subject.
effect_size_MB( outcome, treatment, id, time, data = NULL, phi = NULL, rho = NULL )
effect_size_MB( outcome, treatment, id, time, data = NULL, phi = NULL, rho = NULL )
outcome |
vector of outcome data or name of variable within |
treatment |
vector of treatment indicators or name of variable within |
id |
factor vector indicating unique cases or name of variable within |
time |
vector of measurement occasion times or name of variable within |
data |
(Optional) dataset to use for analysis. Must be data.frame. |
phi |
(Optional) value of the auto-correlation nuisance parameter, to be used in calculating the small-sample adjusted effect size |
rho |
(Optional) value of the intra-class correlation nuisance parameter, to be used in calculating the small-sample adjusted effect size |
A list with the following components
g_dotdot |
total number of non-missing observations |
K |
number of time-by-treatment groups containing at least one observation |
D_bar |
numerator of effect size estimate |
S_sq |
sample variance, pooled across time points and treatment groups |
delta_hat_unadj |
unadjusted effect size estimate |
phi |
corrected estimate of first-order auto-correlation |
sigma_sq_w |
corrected estimate of within-case variance |
rho |
estimated intra-class correlation |
theta |
estimated scalar constant |
nu |
estimated degrees of freedom |
delta_hat |
corrected effect size estimate |
V_delta_hat |
estimated variance of delta_hat
|
If phi or rho is left unspecified (or both), estimates for the nuisance parameters will be calculated.
Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2013). A standardized mean difference effect size for multiple baseline designs across individuals. Research Synthesis Methods, 4(4), 324-341. doi:10.1002/jrsm.1086
data(Saddler) effect_size_MB(outcome = outcome, treatment = treatment, id = case, time = time, data = subset(Saddler, measure=="writing quality")) data(Laski) effect_size_MB(outcome = outcome, treatment = treatment, id = case, time = time, data = Laski)
data(Saddler) effect_size_MB(outcome = outcome, treatment = treatment, id = case, time = time, data = subset(Saddler, measure=="writing quality")) data(Laski) effect_size_MB(outcome = outcome, treatment = treatment, id = case, time = time, data = Laski)
Estimates a design-comparable standardized mean difference effect size based on data from a multiple baseline design, using adjusted REML method as described in Pustejovsky, Hedges, & Shadish (2014). Note that the data must contain one row per measurement occasion per case.
g_REML( m_fit, p_const, r_const, X_design = model.matrix(m_fit, data = m_fit$data), Z_design = model.matrix(m_fit$modelStruct$reStruct, data = m_fit$data), block = nlme::getGroups(m_fit), times = attr(m_fit$modelStruct$corStruct, "covariate"), returnModel = TRUE )
g_REML( m_fit, p_const, r_const, X_design = model.matrix(m_fit, data = m_fit$data), Z_design = model.matrix(m_fit$modelStruct$reStruct, data = m_fit$data), block = nlme::getGroups(m_fit), times = attr(m_fit$modelStruct$corStruct, "covariate"), returnModel = TRUE )
m_fit |
Fitted model of class lme, with AR(1) correlation structure at level 1. |
p_const |
Vector of constants for calculating numerator of effect size.
Must be the same length as fixed effects in |
r_const |
Vector of constants for calculating denominator of effect size.
Must be the same length as the number of variance component parameters in |
X_design |
(Optional) Design matrix for fixed effects. Will be extracted from |
Z_design |
(Optional) Design matrix for random effects. Will be extracted from |
block |
(Optional) Factor variable describing the blocking structure. Will be extracted from |
times |
(Optional) list of times used to describe AR(1) structure. Will be extracted from |
returnModel |
(Optional) If true, the fitted input model is included in the return. |
A list with the following components
p_beta |
Numerator of effect size |
r_theta |
Squared denominator of effect size |
delta_AB |
Unadjusted (REML) effect size estimate |
nu |
Estimated denominator degrees of freedom |
kappa |
Scaled standard error of numerator |
g_AB |
Corrected effect size estimate |
V_g_AB |
Approximate variance estimate |
cnvg_warn |
Indicator that model did not converge |
sigma_sq |
Estimated level-1 variance |
phi |
Estimated autocorrelation |
Tau |
Vector of level-2 variance components |
I_E_inv |
Expected information matrix |
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) summary(Laski_RML) g_REML(Laski_RML, p_const = c(0,1), r_const = c(1,0,1), returnModel=FALSE) data(Schutte) Schutte$trt.week <- with(Schutte, unlist(tapply((treatment=="treatment") * week, list(treatment,case), function(x) x - min(x))) + (treatment=="treatment")) Schutte$week <- Schutte$week - 9 Schutte_RML <- lme(fixed = fatigue ~ week + treatment + trt.week, random = ~ week | case, correlation = corAR1(0, ~ week | case), data = subset(Schutte, case != 4)) summary(Schutte_RML) Schutte_g <- g_REML(Schutte_RML, p_const = c(0,0,1,7), r_const = c(1,0,1,0,0)) summary(Schutte_g)
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) summary(Laski_RML) g_REML(Laski_RML, p_const = c(0,1), r_const = c(1,0,1), returnModel=FALSE) data(Schutte) Schutte$trt.week <- with(Schutte, unlist(tapply((treatment=="treatment") * week, list(treatment,case), function(x) x - min(x))) + (treatment=="treatment")) Schutte$week <- Schutte$week - 9 Schutte_RML <- lme(fixed = fatigue ~ week + treatment + trt.week, random = ~ week | case, correlation = corAR1(0, ~ week | case), data = subset(Schutte, case != 4)) summary(Schutte_RML) Schutte_g <- g_REML(Schutte_RML, p_const = c(0,0,1,7), r_const = c(1,0,1,0,0)) summary(Schutte_g)
Graphs single case design data for treatment reversal and multiple baseline designs.
graph_SCD( design, case, phase, session, outcome, cluster = NULL, series = NULL, treatment_name = NULL, model_fit = NULL, data = NULL, newdata = NULL )
graph_SCD( design, case, phase, session, outcome, cluster = NULL, series = NULL, treatment_name = NULL, model_fit = NULL, data = NULL, newdata = NULL )
design |
Character string to specify whether data comes from a treatment
reversal ( |
case |
vector of case indicators or name of a character or factor vector
within |
phase |
vector of treatment indicators or name of a character or factor
vector within |
session |
vector of measurement occasions or name of numeric vector
within |
outcome |
vector of outcome data or name of numeric vector of outcome
data within |
cluster |
(Optional) vector of cluster indicators or name of a character
or factor vector within |
series |
(Optional) vector of series indicators or name of a character
or factor vector within |
treatment_name |
(Optional) character string corresponding to the name of the treatment phase. |
model_fit |
(Optional) lme fitted model that adds predicted values to graph |
data |
(Optional) dataset to use for analysis. Must be a
|
newdata |
(Optional) dataset to use for calculating predicted values
based on |
A ggplot graph
If treatment_name is left null it will choose the second level of the phase variable to be the treatment phase.
if (requireNamespace("ggplot2", quietly = TRUE)) { data(Anglesea) graph_SCD(design="TR", case=case, phase=condition, session=session, outcome=outcome, treatment_name = "treatment", data=Anglesea) data(BartonArwood) graph_SCD(design="MBP", case=case, phase=condition, session=session, outcome=outcome, treatment_name = "B", data=BartonArwood) data(Thiemann2001) graph_SCD(design="RMBB", case=case, series = series, phase=treatment, session=time, outcome=outcome, treatment_name = "treatment", data=Thiemann2001) data(Bryant2018) graph_SCD(design="CMB", cluster=group, case=case, phase=treatment, session=session, outcome=outcome, treatment_name = "treatment", data=Bryant2018) }
if (requireNamespace("ggplot2", quietly = TRUE)) { data(Anglesea) graph_SCD(design="TR", case=case, phase=condition, session=session, outcome=outcome, treatment_name = "treatment", data=Anglesea) data(BartonArwood) graph_SCD(design="MBP", case=case, phase=condition, session=session, outcome=outcome, treatment_name = "B", data=BartonArwood) data(Thiemann2001) graph_SCD(design="RMBB", case=case, series = series, phase=treatment, session=time, outcome=outcome, treatment_name = "treatment", data=Thiemann2001) data(Bryant2018) graph_SCD(design="CMB", cluster=group, case=case, phase=treatment, session=session, outcome=outcome, treatment_name = "treatment", data=Bryant2018) }
Data from a multiple baseline design conducted by Gunning & Espie (2003). The variables are as follows:
case
. Participant identifier.
session
. Measurement occasion.
condition
. Factor identifying the phase of the design (baseline or treatment).
outcome
. Sleep onset latency in minutes.
A data frame with 301 rows and 4 variables
Gunning, M. J., & Espie, C.A. (2003). Psychological treatment of reported sleep disorder in adults with intellectual disability using a multiple baseline design. Journal of Intellectual Disability Research, 47(3), 191-202. doi:10.1046/j.1365-2788.2003.00461.x
Calculates the expected information matrix from a fitted linear mixed effects model with AR(1) correlation structure in the level-1 errors.
Info_Expected_lmeAR1(m_fit)
Info_Expected_lmeAR1(m_fit)
m_fit |
Fitted model of class lme, with AR(1) correlation structure at level 1. |
Expected Information matrix corresponding to variance components of m_fit
.
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) Info_Expected_lmeAR1(Laski_RML)
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) Info_Expected_lmeAR1(Laski_RML)
Data from an ABAB design conducted by Lambert, Cartledge, Heward, & Lo (2008). The variables are as follows:
measure
. Outcome measure description (disruptive behavior or academic response).
case
. Student identifier.
treatment
. Factor indicating treatment or control condition.
SSR = single-subject responding. RC = response cards.
phase
. Study phase (including both control and treatment condition)
time
. Measurement occasion.
outcome
. Outcome scores.
A data frame with 461 rows and 6 variables
Lambert, M. C., Cartledge, G., Heward, W. L., & Lo, Y. (2006). Effects of response cards on disruptive behavior and academic responding during math lessons by fourth-grade urban students. Journal of Positive Behavior Interventions, 8(2), 88-99. doi:10.1177/10983007060080020701
Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2012). A standardized mean difference effect size for single case designs. Research Synthesis Methods, 3, 224-239. doi:10.1002/jrsm.1052
Data from a multiple baseline design conducted by Laski, Charlop, & Schreibman (1988). The variables are as follows:
case
. Child identifier.
outcome
. Frequency of child vocalization, as measured by
a partial interval recording procedure with 60 ten-second intervals per session.
time
. Measurement occasion.
treatment
. Indicator for treatment phase.
A data frame with 128 rows and 4 variables
Laski, K. E., Charlop, M. H., & Schreibman, L. (1988). Training parents to use the natural language paradigm to increase their autistic children's speech. Journal of Applied Behavior Analysis, 21(4), 391-400. doi:10.1901/jaba.1988.21-391
Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2013). A standardized mean difference effect size for multiple baseline designs across individuals. Research Synthesis Methods, 4(4), 324-341. doi:10.1002/jrsm.1086
Simulation results for model MB1 from Pustejovsky, Hedges, & Shadish (2014).
A data frame
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
Simulation results for model MB2 from Pustejovsky, Hedges, & Shadish (2014).
A data frame
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
Simulation results for model MB4 from Pustejovsky, Hedges, & Shadish (2014).
A data frame
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
Data from a multiple baseline design conducted by Musser, Bray, Kehle, and Jenson (2001). The variables are as follows:
student
Participant identifier
session
Measurement occasion
outcome
Percentage of disruptive intervals
treatment
Factor indicating baseline, treatment, or follow-up phase
A data frame with 136 rows and 4 variables
Musser, E. H., Bray, M. A., Kehle, T. J., & Jenson, W. R. (2001). Reducing disruptive behaviors in students with serious emotional disturbance. School Psychology Review, 30(2), 294-304.
Data from a multiple baseline design conducted by Peltier, Sinclair, Pulos, & Suk (2020). The variables are as follows:
case
.
Participant identifier.
session
. Measurement occasion.
condition
. Factor identifying the phase of the design (baseline or
treatment).
outcome
. Mathematical problem-solving performance
(percentage).
A data frame with 232 rows and 4 variables
Peltier, C., Sinclair, T. E., Pulos, J. M., & Suk, A. (2020). Effects of schema-based instruction on immediate, generalized, and combined structured word problems. The Journal of Special Education, 54(2), 101-112. doi:10.1177/0022466919883397
Calculate phase-pairs based on phases and session numbering.
phase_pairs(phase, session = seq_along(phase))
phase_pairs(phase, session = seq_along(phase))
phase |
vector of treatment indicators or a character or factor vector indicating unique treatment phases. |
session |
numeric vector of measurement occasions. |
phases <- rep(c("A","B","A","B"), each = 4) sessions <- 1:length(phases) phase_pairs(phases, sessions) phases <- rep(c("A","B","C","A","B","C","D"), each = 4) phase_pairs(phases) phases <- rep(c("B","A","C","B","A","B","C","A"), each = 4) phase_pairs(phases)
phases <- rep(c("A","B","A","B"), each = 4) sessions <- 1:length(phases) phase_pairs(phases, sessions) phases <- rep(c("A","B","C","A","B","C","D"), each = 4) phase_pairs(phases) phases <- rep(c("B","A","C","B","A","B","C","A"), each = 4) phase_pairs(phases)
Clean single case design data for treatment reversal and multiple baseline designs.
preprocess_SCD( design, case, phase, session, outcome, cluster = NULL, series = NULL, center = 0, round_session = TRUE, treatment_name = NULL, data = NULL )
preprocess_SCD( design, case, phase, session, outcome, cluster = NULL, series = NULL, center = 0, round_session = TRUE, treatment_name = NULL, data = NULL )
design |
Character string to specify whether data comes from a treatment
reversal ( |
case |
vector of case indicators or name of a character or factor vector
within |
phase |
vector of treatment indicators or name of a character or factor
vector within |
session |
vector of measurement occasions or name of numeric vector
within |
outcome |
vector of outcome data or name of numeric vector of outcome
data within |
cluster |
(Optional) vector of cluster indicators or name of a character
or factor vector within |
series |
(Optional) vector of series indicators or name of a character
or factor vector within |
center |
Numeric value for the centering value for session. Default is 0. |
round_session |
Logical indicating whether to round |
treatment_name |
(Optional) character string corresponding to the name of the treatment phase. |
data |
(Optional) dataset to use for analysis. Must be a
|
A cleaned SCD dataset that can be used for model fitting and effect size calculation.
If treatment_name is left null it will choose the second level of the phase variable to be the treatment phase.
data(Laski) preprocess_SCD(design = "MBP", case = case, phase = treatment, session = time, outcome = outcome, center = 4, data = Laski) data(Anglesea) preprocess_SCD(design="TR", case=case, phase=condition, session=session, outcome=outcome, treatment_name = "treatment", data=Anglesea) data(Thiemann2001) preprocess_SCD(design = "RMBB", case = case, series = series, phase = treatment, session = time, outcome = outcome, data = Thiemann2001)
data(Laski) preprocess_SCD(design = "MBP", case = case, phase = treatment, session = time, outcome = outcome, center = 4, data = Laski) data(Anglesea) preprocess_SCD(design="TR", case=case, phase=condition, session=session, outcome=outcome, treatment_name = "treatment", data=Anglesea) data(Thiemann2001) preprocess_SCD(design = "RMBB", case = case, series = series, phase = treatment, session = time, outcome = outcome, data = Thiemann2001)
Data from a multiple baseline design conducted by Rodgers, Datchuk, & Rila (2021). The variables are as follows:
case
.
Participant identifier.
session
. Measurement occasion.
condition
. Factor identifying the phase of the design (baseline or
treatment).
outcome
. The number of correct writing sequences in
1 minute.
A data frame with 83 rows and 4 variables
Rodgers, D. B., Datchuk, S. M., & Rila, A. L. (2021). Effects of a text-writing fluency intervention for postsecondary students with intellectual and developmental disabilities. Exceptionality, 29(4), 310-325. doi:10.1080/09362835.2020.1850451
Data from a multiple baseline design conducted by Rodriguez and Anderson (2014). The variables are as follows:
case
Participant identifier
condition
Factor identifying the phase of the design (A or B)
session
Measurement occasion
outcome
Percentage of intervals with problem behavior
A data frame with 148 rows and 4 variables
Rodriguez, B. J., & Anderson, C. M. (2014). Integrating a social behavior intervention during small group academic instruction using a total group criterion intervention. Journal of Positive Behavior Interventions, 16(4), 234-245. doi:10.1177/1098300713492858
Data from a treatment reversal design conducted by Romaniuk and colleagues (2002). The variables are as follows:
case
Participant identifier
phase
Factor identifying the phase of the design
condition
Factor identifying the treatment condition
session
Measurement occasion
outcome
Problem behavior
measurement
Character string describing how problem behavior was measured
A data frame with 148 rows and 4 variables
Romaniuk, C., Miltenberger, R., Conyers, C., Jenner, N., Jurgens, M., & Ringenberg, C. (2002). The influence of activity choice on problem behaviors maintained by escape versus attention. Journal of Applied Behavior Analysis, 35(4), 349-62. doi:10.1901/jaba.2002.35-349
Data from a multiple baseline design conducted by Ruiz, Luciano, Florez, Suarez-Falcon, & Cardona-Betancourt (2020). The variables are as follows:
case
. Participant identifier.
measure
. Outcome measure description (AAQ-II, ANXIETY, CFQ, DASS-TOTAL, DEPRESSION, PSWQ, PTQ, STRESS, VQ-OBSTRUCTION, or VQ-PROGRESS).
treatment
Factor indicating baseline, treatment, post, or follow-up phase.
time
. Measurement occasion.
outcome
. Outcome scores.
A data frame with 840 rows and 5 variables
Ruiz, F., Luciano, C., Florez, C., Suarez-Falcon, J., & Cardona-Betancourt, V. (2020). A Multiple-Baseline Evaluation of Acceptance and Commitment Therapy Focused on Repetitive Negative Thinking for Comorbid Generalized Anxiety Disorder and Depression. Frontiers in Psychology, 11. doi:10.3389/fpsyg.2020.00356
Data from a multiple baseline design conducted by Saddler, Behforooz, & Asaro, (2008). The variables are as follows:
case
Student identifier
measure
Factor indicating the outcome measure (writing quality, T-unit length, number of constructions)
outcome
Value of outcome measure.
time
. Measurement occasion.
treatment
. Factor indicating the treatment phase.
A data frame with 124 rows and 5 variables
Saddler, B., Behforooz, B., & Asaro, K. (2008). The effects of sentence-combining instruction on the writing of fourth-grade students with writing difficulties. The Journal of Special Education, 42(2), 79-90. doi:10.1177/0022466907310371
Hedges, L. V., Pustejovsky, J. E., & Shadish, W. R. (2013). A standardized mean difference effect size for multiple baseline designs across individuals. Research Synthesis Methods, 4(4), 324-341. doi:10.1002/jrsm.1086
Data from a multiple baseline design conducted by Salazar, Ruiz, Ramírez1, & Cardona-Betancourt (2020). The variables are as follows:
case
. Participant identifier.
measure
. Outcome measure description (AFQ-Y, PTQ-C, or GPQ-C).
treatment
Factor indicating baseline, treatment, post, or follow-up phase.
time
. Measurement occasion.
outcome
. Outcome scores.
A data frame with 324 rows and 5 variables
Salazar, D., Ruiz, F., Ramírez, E., & Cardona-Betancourt, V. (2020). Acceptance and Commitment Therapy Focused on Repetitive Negative Thinking for Child Depression: A Randomized Multiple-Baseline Evaluation. The Psychological Record. doi:10.1007/s40732-019-00362-5
Data from a multiple baseline design conducted by Schutte, Malouff, & Brown (2008). Case 4 is excluded because nearly all of these measurements are at the upper extreme of the scale. The variables are as follows:
case
. Participant identifier.
week
. Measurement occasion.
treatment
. Factor indicating baseline or treatment phase.
fatigue
. Fatigue severity scale scores.
A data frame with 136 rows and 4 variables
Schutte, N. S., Malouff, J. M., & Brown, R. F. (2008). Efficacy of an emotion-focused treatment for prolonged fatigue. Behavior Modification, 32(5), 699-713. doi:10.1177/0145445508317133
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
Calculate session-by-treatment interactions based on phases and session numbering.
session_by_treatment(phase, session, trt_phase)
session_by_treatment(phase, session, trt_phase)
phase |
vector of treatment indicators or a character or factor vector indicating unique treatment phases. |
session |
numeric vector of measurement occasions. |
trt_phase |
character string indicating the phase value corresponding to the treatment condition. |
An interactive shiny interface for estimating design-comparable standardized mean difference effect sizes from single-case designs. Estimation methods for multiple baseline and treatment reversal designs are available.
shine_scd(dataset = NULL, ...)
shine_scd(dataset = NULL, ...)
dataset |
Optionally, a data.frame or path to a file from which to read
data. If specified, the app will open with the data loaded. Default is
NULL. If |
... |
Further arguments passed to |
## Not run: shine_scd() data(Laski) shine_scd(dataset = Laski) shine_scd(dataset = "SCD_data.xlsx", sheet = "Laski") shine_scd(dataset = "Laski.csv") ## End(Not run)
## Not run: shine_scd() data(Laski) shine_scd(dataset = Laski) shine_scd(dataset = "SCD_data.xlsx", sheet = "Laski") shine_scd(dataset = "Laski.csv") ## End(Not run)
Simulates data from a linear mixed effects model, then calculates REML effect size estimator as described in Pustejovsky, Hedges, & Shadish (2014).
simulate_MB2( iterations, beta, rho, phi, tau1_ratio, tau_corr, design, m, n, MB = TRUE )
simulate_MB2( iterations, beta, rho, phi, tau1_ratio, tau_corr, design, m, n, MB = TRUE )
iterations |
number of independent iterations of the simulation |
beta |
vector of fixed effect parameters |
rho |
intra-class correlation parameter |
phi |
autocorrelation parameter |
tau1_ratio |
ratio of treatment effect variance to intercept variance |
tau_corr |
correlation between case-specific treatment effects and intercepts |
design |
design matrix. If not specified, it will be calculated based on |
m |
number of cases. Not used if |
n |
number of measurement occasions. Not used if |
MB |
If true, a multiple baseline design will be used; otherwise, an AB design will be used. Not used if |
A matrix reporting the mean and variance of the effect size estimates and various associated statistics.
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
set.seed(8) simulate_MB2(iterations = 5, beta = c(0,1,0,0), rho = 0.4, phi = 0.5, tau1_ratio = 0.5, tau_corr = -0.4, design = design_matrix(m=3, n=8)) set.seed(8) simulate_MB2(iterations = 5, beta = c(0,1,0,0), rho = 0.4, phi = 0.5, tau1_ratio = 0.5, tau_corr = -0.4, m = 3, n = 8, MB = FALSE)
set.seed(8) simulate_MB2(iterations = 5, beta = c(0,1,0,0), rho = 0.4, phi = 0.5, tau1_ratio = 0.5, tau_corr = -0.4, design = design_matrix(m=3, n=8)) set.seed(8) simulate_MB2(iterations = 5, beta = c(0,1,0,0), rho = 0.4, phi = 0.5, tau1_ratio = 0.5, tau_corr = -0.4, m = 3, n = 8, MB = FALSE)
Simulates data from a linear mixed effects model, then calculates REML effect size estimator as described in Pustejovsky, Hedges, & Shadish (2014).
simulate_MB4( iterations, beta, rho, phi, tau2_ratio, tau_corr, p_const, r_const, design, m, n, MB = TRUE )
simulate_MB4( iterations, beta, rho, phi, tau2_ratio, tau_corr, p_const, r_const, design, m, n, MB = TRUE )
iterations |
number of independent iterations of the simulation |
beta |
vector of fixed effect parameters |
rho |
intra-class correlation parameter |
phi |
autocorrelation parameter |
tau2_ratio |
ratio of trend variance to intercept variance |
tau_corr |
correlation between case-specific trends and intercepts |
p_const |
vector of constants for calculating numerator of effect size |
r_const |
vector of constants for calculating denominator of effect size |
design |
design matrix. If not specified, it will be calculated based on |
m |
number of cases. Not used if |
n |
number of measurement occasions. Not used if |
MB |
If true, a multiple baseline design will be used; otherwise, an AB design will be used. Not used if |
A matrix reporting the mean and variance of the effect size estimates and various associated statistics.
Pustejovsky, J. E., Hedges, L. V., & Shadish, W. R. (2014). Design-comparable effect sizes in multiple baseline designs: A general modeling framework. Journal of Educational and Behavioral Statistics, 39(4), 211-227. doi:10.3102/1076998614547577
simulate_MB4(iterations = 5, beta = c(0,1,0,0), rho = 0.8, phi = 0.5, tau2_ratio = 0.5, tau_corr = 0, p_const = c(0,1,0,7), r_const = c(1,0,1,0,0), design = design_matrix(3, 16, treat_times=c(5,9,13), center = 12)) simulate_MB4(iterations = 5, beta = c(0,1,0,0), rho = 0.8, phi = 0.5, tau2_ratio = 0.5, tau_corr = 0, m = 6, n = 8)
simulate_MB4(iterations = 5, beta = c(0,1,0,0), rho = 0.8, phi = 0.5, tau2_ratio = 0.5, tau_corr = 0, p_const = c(0,1,0,7), r_const = c(1,0,1,0,0), design = design_matrix(3, 16, treat_times=c(5,9,13), center = 12)) simulate_MB4(iterations = 5, beta = c(0,1,0,0), rho = 0.8, phi = 0.5, tau2_ratio = 0.5, tau_corr = 0, m = 6, n = 8)
g_REML
objectSimulates data from the linear mixed effects model used to estimate the specified standardized mean difference effect size. Suitable for parametric bootstrapping.
## S3 method for class 'g_REML' simulate(object, nsim = 1, seed = NULL, parallel = FALSE, ...)
## S3 method for class 'g_REML' simulate(object, nsim = 1, seed = NULL, parallel = FALSE, ...)
object |
a |
nsim |
number of models to simulate |
seed |
seed value. See documentation for |
parallel |
if |
... |
additional optional arguments |
A matrix with one row per simulation, with columns corresponding to the output
of g_REML
.
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) suppressWarnings( Laski_g <- g_REML(Laski_RML, p_const = c(0,1), r_const = c(1,0,1)) ) if (requireNamespace("plyr", quietly = TRUE)) { simulate(Laski_g, nsim = 5) }
data(Laski) Laski_RML <- lme(fixed = outcome ~ treatment, random = ~ 1 | case, correlation = corAR1(0, ~ time | case), data = Laski) suppressWarnings( Laski_g <- g_REML(Laski_RML, p_const = c(0,1), r_const = c(1,0,1)) ) if (requireNamespace("plyr", quietly = TRUE)) { simulate(Laski_g, nsim = 5) }
Data from a multiple baseline across behaviors design conducted by Thiemann & Goldstein (2001). The variables are as follows:
Study_ID
. Study identifier.
case
. Student identifier.
series
. Series identifier.
outcome
. Frequency of coded social communication skills, as measured by
a direct observation coding system with 15-second intervals recording for the occurrence
of any of the four social measures: contingent responses, securing attention, initiating
comments, and initiating requests.
time
. Measurement occasion.
treatment
. Indicator for treatment phase.
trt_time
. Measurement occasion times treatment phase.
time_c
. Measurement occasion centered at the follow-up time.
A data frame with 363 rows and 8 variables
Thiemann, K.S., & Goldstein, H. (2001). Social stories, written text cues, and video feedback: effects on social communication of children with Autism. Journal of Applied Behavior Analysis, 34(4), 425-446. doi:10.1901/jaba.2001.34-425
Data from a multiple baseline across behaviors design conducted by Thiemann & Goldstein (2004). The variables are as follows:
Study_ID
. Study identifier.
case
. Student identifier.
series
. Series identifier.
outcome
. Frequency of unprompted targeted social communication skills,
as measured by a direct observation, paper and pencil coding system during the 10-minute
social activity for each behavior for all sessions.
time
. Measurement occasion.
treatment
. Indicator for treatment phase.
trt_time
. Measurement occasion times treatment phase.
time_c
. Measurement occasion centered at the follow-up time.
A data frame with 408 rows and 8 variables
Thiemann, K.S., & Goldstein, H. (2004). Effects of peer training and written text cueing on social communication of school-age children with pervasive developmental disorder. Journal of Speech Language and Hearing Research, 47(1), 126-144. doi:10.1044/1092-4388(2004/012)
Data from an ABAB design conducted by Thorne and Kamps (2008). The variables are as follows:
case
. Participant identifier.
measure
. Outcome measure description (academic engagement or inappropriate verbalizations).
session
. Measurement occasion.
phase_id
. Categorical variable describing the phase of the study design for each case.
condition
Categorical variable describing whether each phase is a baseline (A) phase or intervention (B) phase.
phase_indicator
. Indicator variable equal to 1 during intervention phases.
outcome
. Outcome scores
A data frame with 776 rows and 7 variables
Thorne, S., & Kamps, D. (2008). The effects of a group contingency intervention on academic engagement and problem behavior of at-risk students. Behavior Analysis in Practice, 1(2), 12-18. doi:10.1007/BF03391723