Simulate Model MB4 from Pustejovsky, Hedges, & Shadish (2014)

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
)

Arguments

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, n, and MB.

m

number of cases. Not used if design is specified.

n

number of measurement occasions. Not used if design is specified.

MB

If true, a multiple baseline design will be used; otherwise, an AB design will be used. Not used if design is specified.

Value

A matrix reporting the mean and variance of the effect size estimates and various associated statistics.

References

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

Examples

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))
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#>                                 mean         var
#> p_beta                     0.8863860  0.63389224
#> r_theta                    0.7162655  0.28624419
#> delta_AB                   1.2470977  1.27198736
#> nu                         4.8449260 13.38419456
#> kappa                      0.5861962  0.04355094
#> g_AB                       0.9987941  0.89767369
#> V_g_AB                     1.1415435  0.43107846
#> cnvg_warn                  0.0000000  0.00000000
#> sigma_sq                   0.3768081  0.09044548
#> phi                        0.5899910  0.07151889
#> Tau.id.var(constant)       0.3394574  0.11066244
#> Tau.id.cov(trend,constant) 0.1457863  0.15162904
#> Tau.id.var(trend)          0.4760078  0.11156023
#> RML_coverage1              0.8000000  0.20000000
#> RML_coverage2              1.0000000  0.00000000
             
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)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#> Warning: nlminb problem, convergence error code = 1
#>   message = iteration limit reached without convergence (10)
#> Warning: 'g_REML()' is deprecated and may be removed in a later version of the package. Please use 'g_mlm()' instead.
#>                                 mean         var
#> p_beta                     1.0741215 0.088868814
#> r_theta                    0.5868042 0.066844240
#> delta_AB                   1.5775380 0.796114828
#> nu                         9.0893758 9.505430644
#> kappa                      0.4102940 0.005199201
#> g_AB                       1.4481733 0.754972872
#> V_g_AB                     0.3456622 0.028825886
#> cnvg_warn                  0.0000000 0.000000000
#> sigma_sq                   0.3801642 0.047102143
#> phi                        0.6270218 0.034673741
#> Tau.id.var(constant)       0.2066400 0.074931431
#> Tau.id.cov(trend,constant) 0.1248497 0.039708080
#> Tau.id.var(trend)          0.4089612 0.042225807
#> RML_coverage1              0.8000000 0.200000000
#> RML_coverage2              0.8000000 0.200000000