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: '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                     0.90837680  0.61101578
#> r_theta                    0.72147970  0.29740891
#> delta_AB                   1.26398428  1.23516332
#> nu                         4.79898794 13.67828487
#> kappa                      0.56663420  0.04460662
#> g_AB                       1.00608762  0.88375289
#> V_g_AB                     1.26455463  0.47705317
#> cnvg_warn                  0.00000000  0.00000000
#> sigma_sq                   0.26584306  0.04144766
#> phi                        0.54834218  0.04810402
#> Tau.id.var(constant)       0.45563664  0.30812460
#> Tau.id.cov(trend,constant) 0.05572171  0.15741017
#> Tau.id.var(trend)          0.52756257  0.07828586
#> RML_coverage1              0.80000000  0.20000000
#> RML_coverage2              1.00000000  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: '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                     1.0192931 0.0535067723
#> r_theta                    0.6543429 0.0258966787
#> delta_AB                   1.2628930 0.0525602672
#> nu                         7.6334267 0.5645641782
#> kappa                      0.3737198 0.0019078439
#> g_AB                       1.1326221 0.0399182952
#> V_g_AB                     0.2814817 0.0008025115
#> cnvg_warn                  0.0000000 0.0000000000
#> sigma_sq                   0.3761956 0.0491884499
#> phi                        0.6218518 0.0364802924
#> Tau.id.var(constant)       0.2781472 0.0691696359
#> Tau.id.cov(trend,constant) 0.1026264 0.0539395567
#> Tau.id.var(trend)          0.4106620 0.0415239349
#> RML_coverage1              1.0000000 0.0000000000
#> RML_coverage2              1.0000000 0.0000000000