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

### Description

Simulates data from a linear mixed effects model, then calculates REML effect size estimator as described in Pustejovsky, Hedges, & Shadish (2014).

### Usage

1 2 | ```
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` |
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 |

### 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

1 2 3 4 5 6 | ```
simulate_MB4(iterations = 10, 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 = 10, beta = c(0,1,0,0), rho = 0.8, phi = 0.5,
tau2_ratio = 0.5, tau_corr = 0, m = 6, n = 8)
``` |