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Additional results from the simulations not included in the manuscript

Table of Contents

1 Performance metrics for \(\alpha=.01,.10\)

1.1 Between-items designs

  • \(\alpha\)=.01
    Type IType IPowerPowerC.PowerC.Power
    122412241224
    min-\(F'\).009.009.079.154.210.328
    LMEM, Maximal, \(\chi^2_{LR}\).017.013.118.185.223.342
    LMEM, Max-NRC, \(\chi^2_{LR}\).017.013.117.185.223.343
    \(F_1{\times}F_2\).014.019.106.222.224.337
    LMEM, Max-NWI \(\chi^2_{LR}\).021.015.135.202.223.342
    LMEM, Maximal, \(t\).029.017.162.214.222.343
    LMEM, Max-NRC, \(t\).029.017.162.214.223.343
    LMEM, Max-NWI, \(t\).037.021.186.234.222.342
    LMEM, RI-only, \(\chi^2_{LR}\).032.039.164.279.216.314
    LMEM, RI-only, \(t\).055.051.228.318.217.314
    LMEM, RI-only, MCMC.071.103.252.444.205.309
    \(F_1\).297.217.541.571.134.212
  • \(\alpha\)=.10
    Type IType IPowerPowerC.PowerC.Power
    122412241224
    min-\(F'\).092.093.311.444.210.328
    LMEM, Maximal, \(\chi^2_{LR}\).129.113.371.478.223.342
    LMEM, Max-NRC, \(\chi^2_{LR}\).128.112.370.477.223.343
    \(F_1{\times}F_2\).120.137.355.510.224.337
    LMEM, Max-NWI \(\chi^2_{LR}\).142.123.391.492.223.342
    LMEM, Maximal, \(t\).143.120.394.490.222.343
    LMEM, Max-NRC, \(t\).143.119.393.489.223.343
    LMEM, Max-NWI, \(t\).160.131.415.505.222.342
    LMEM, RI-only, \(\chi^2_{LR}\).171.177.419.548.216.314
    LMEM, RI-only, \(t\).193.189.447.563.217.314
    LMEM, RI-only, MCMC.255.294.524.680.205.309
    \(F_1\).497.420.732.767.134.212

1.2 Within-items designs

  • Note: corrected power for the LMEM, RI-only MCMC technique is estimated in the two tables below because the high Type I error rate along with the relatively small number of MCMC runs (10000) provided limited resolution.
  • \(\alpha\)=.01
    Type IType IPowerPowerC.PowerC.Power
    122412241224
    min-\(F'\).004.005.129.266.327.512
    LMEM, Maximal, \(\chi^2_{LR}\).013.012.240.382.433.591
    LMEM, Max-NRC, \(\chi^2_{LR}\).013.012.241.381.432.593
    \(F_1{\times}F_2\).012.018.212.410.416.578
    LMEM, Max-NWI \(\chi^2_{LR}\).012.012.215.363.416.579
    LMEM, Maximal, \(t\).022.016.306.425.434.592
    LMEM, Max-NRC, \(t\).023.016.308.425.432.593
    LMEM, Max-NWI, \(t\).022.018.287.416.416.580
    \(F_1\).083.059.455.538.345.506
    LMEM, RI-only, \(\chi^2_{LR}\).317.377.787.904.379.531
    LMEM, RI-only, \(t\).320.379.789.904.379.531
    LMEM, RI-only, MCMC.291.361.772.899.379.531
  • \(\alpha\)=.10
    Type IType IPowerPowerC.PowerC.Power
    122412241224
    min-\(F'\).061.068.463.643.327.512
    LMEM, Maximal, \(\chi^2_{LR}\).113.108.582.717.433.591
    LMEM, Max-NRC, \(\chi^2_{LR}\).113.107.582.717.432.593
    \(F_1{\times}F_2\).112.130.568.746.416.578
    LMEM, Max-NWI \(\chi^2_{LR}\).107.108.561.708.416.579
    LMEM, Maximal, \(t\).126.115.603.727.434.592
    LMEM, Max-NRC, \(t\).127.115.604.727.432.593
    LMEM, Max-NWI, \(t\).121.115.586.722.416.58
    \(F_1\).251.210.725.800.345.506
    LMEM, RI-only, \(\chi^2_{LR}\).514.567.883.949.379.531
    LMEM, RI-only, \(t\).515.568.883.949.379.531
    LMEM, RI-only, MCMC.491.554.876.947.379.531

2 Heatmaps for 12-item designs

2.1 Between items

  • Type I Error

    img/heatmap-h0-wsbi-12.png

  • Power

    img/heatmap-h1-wsbi-12.png

2.2 Within items

  • Type I Error

    img/heatmap-h0-wswi-12.png

  • Power

    img/heatmap-h1-wswi-12.png

3 Performance of model selection

3.1 Between-items design

img/wsbi-ms-main.png

Author: Dale J. Barr, Roger Levy, Christoph Scheepers, and Harry J. Tily (daleb@daleb-pc)

Date: March 27, 2012

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