The following presents an example of how to use the functions in this package to fit the simple mediation model on generated data in the Data Generation article.
Maximum Likelihood
Missing Data
Parameters of the simple mediation model are estimated using full-information maximum likelihood to handle missing data.
fit_ml <- FitModelML(
data_missing,
mplus_bin = mplus_bin
)
fit_ml
#> $fit
#> free_parameters h0_loglikelihood h1_loglikelihood aic
#> 9.000000e+00 -1.225911e+03 -1.225911e+03 2.469821e+03
#> bic sabic chisq chisq_df
#> 2.504645e+03 2.476093e+03 8.237393e-06 0.000000e+00
#> chisq_p cfi tli rmsea
#> 0.000000e+00 9.999994e-01 1.000000e+00 0.000000e+00
#> rmsea_low rmsea_up rmsea_p srmr
#> 0.000000e+00 0.000000e+00 0.000000e+00 5.887405e-05
#> condition_number
#> 1.837067e-02
#>
#> $coef
#> m~1 y~1 x~1 m~x y~m y~x
#> 0.006934506 0.336487350 0.411909970 0.369397850 0.152114330 0.151127860
#> m~~m y~~y x~~x
#> 1.211989500 1.149110200 0.241468090
#>
#> $vcov
#> m~1 y~1 x~1 m~x y~m
#> m~1 6.200529e-03 4.010312e-05 -7.774377e-05 -6.518637e-03 6.355296e-05
#> y~1 4.010312e-05 6.012550e-03 -7.506271e-05 -7.453915e-05 1.085284e-04
#> x~1 -7.774377e-05 -7.506271e-05 7.515655e-04 1.438111e-04 -9.078051e-06
#> m~x -6.518637e-03 -7.453915e-05 1.438111e-04 1.649430e-02 3.655520e-05
#> y~m 6.355296e-05 1.085284e-04 -9.078051e-06 3.655520e-05 3.115320e-03
#> y~x -1.365620e-04 -6.342203e-03 1.720138e-04 8.861812e-05 -1.121932e-03
#> m~~m 1.191213e-04 1.111450e-05 -2.519574e-05 -2.088454e-04 -2.211516e-06
#> y~~y -9.056253e-06 4.214630e-05 -1.378773e-05 -3.796332e-05 -3.804997e-05
#> x~~x -5.274115e-06 -4.978534e-06 7.624901e-06 6.937207e-06 -1.102431e-06
#> y~x m~~m y~~y x~~x
#> m~1 -1.365620e-04 1.191213e-04 -9.056253e-06 -5.274115e-06
#> y~1 -6.342203e-03 1.111450e-05 4.214630e-05 -4.978534e-06
#> x~1 1.720138e-04 -2.519574e-05 -1.378773e-05 7.624901e-06
#> m~x 8.861812e-05 -2.088454e-04 -3.796332e-05 6.937207e-06
#> y~m -1.121932e-03 -2.211516e-06 -3.804997e-05 -1.102431e-06
#> y~x 1.622654e-02 -3.583622e-05 -7.859534e-05 1.124238e-05
#> m~~m -3.583622e-05 8.808493e-03 -4.183286e-06 -4.881001e-06
#> y~~y -7.859534e-05 -4.183286e-06 8.050239e-03 -1.407881e-06
#> x~~x 1.124238e-05 -4.881001e-06 -1.407881e-06 3.625790e-04
#>
#> $output
#> [1] "Mplus VERSION 8.8 DEMO (Linux)"
#> [2] "MUTHEN & MUTHEN"
#> [3] "09/18/2023 11:19 AM"
#> [4] ""
#> [5] "INPUT INSTRUCTIONS"
#> [6] ""
#> [7] " DATA:"
#> [8] " FILE = file8ff2d006c69;"
#> [9] " VARIABLE:"
#> [10] " NAMES = X M Y;"
#> [11] " USEVARIABLES = X M Y;"
#> [12] " MISSING = ALL (-999);"
#> [13] " ANALYSIS:"
#> [14] " TYPE = GENERAL;"
#> [15] " ESTIMATOR = ML;"
#> [16] " MODEL:"
#> [17] " Y ON X;"
#> [18] " Y ON M (B);"
#> [19] " M ON X (A);"
#> [20] " X WITH X;"
#> [21] " SAVEDATA:"
#> [22] " RESULTS ARE file8ff1a81ca4f;"
#> [23] " TECH3 IS file8ff6a233e79;"
#> [24] ""
#> [25] ""
#> [26] ""
#> [27] ""
#> [28] "INPUT READING TERMINATED NORMALLY"
#> [29] ""
#> [30] ""
#> [31] ""
#> [32] ""
#> [33] "SUMMARY OF ANALYSIS"
#> [34] ""
#> [35] "Number of groups 1"
#> [36] "Number of observations 354"
#> [37] ""
#> [38] "Number of dependent variables 2"
#> [39] "Number of independent variables 1"
#> [40] "Number of continuous latent variables 0"
#> [41] ""
#> [42] "Observed dependent variables"
#> [43] ""
#> [44] " Continuous"
#> [45] " M Y"
#> [46] ""
#> [47] "Observed independent variables"
#> [48] " X"
#> [49] ""
#> [50] ""
#> [51] "Estimator ML"
#> [52] "Information matrix OBSERVED"
#> [53] "Maximum number of iterations 1000"
#> [54] "Convergence criterion 0.500D-04"
#> [55] "Maximum number of steepest descent iterations 20"
#> [56] "Maximum number of iterations for H1 2000"
#> [57] "Convergence criterion for H1 0.100D-03"
#> [58] ""
#> [59] "Input data file(s)"
#> [60] " file8ff2d006c69"
#> [61] ""
#> [62] "Input data format FREE"
#> [63] ""
#> [64] ""
#> [65] "SUMMARY OF DATA"
#> [66] ""
#> [67] " Number of missing data patterns 7"
#> [68] ""
#> [69] ""
#> [70] "COVARIANCE COVERAGE OF DATA"
#> [71] ""
#> [72] "Minimum covariance coverage value 0.100"
#> [73] ""
#> [74] ""
#> [75] " PROPORTION OF DATA PRESENT"
#> [76] ""
#> [77] ""
#> [78] " Covariance Coverage"
#> [79] " M Y X"
#> [80] " ________ ________ ________"
#> [81] " M 0.946"
#> [82] " Y 0.890 0.929"
#> [83] " X 0.879 0.876 0.910"
#> [84] ""
#> [85] ""
#> [86] ""
#> [87] "UNIVARIATE SAMPLE STATISTICS"
#> [88] ""
#> [89] ""
#> [90] " UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS"
#> [91] ""
#> [92] " Variable/ Mean/ Skewness/ Minimum/ % with Percentiles"
#> [93] " Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median"
#> [94] ""
#> [95] " M 0.148 -0.290 -5.000 0.30% -0.667 0.000 0.000"
#> [96] " 335.000 1.244 2.398 4.000 0.30% 0.333 1.000"
#> [97] " Y 0.412 0.246 -3.000 0.30% -0.333 0.000 0.333"
#> [98] " 329.000 1.186 0.597 4.000 0.61% 0.667 1.333"
#> [99] " X 0.407 0.379 0.000 59.32% 0.000 0.000 0.000"
#> [100] " 322.000 0.241 -1.856 1.000 40.68% 1.000 1.000"
#> [101] ""
#> [102] ""
#> [103] "THE MODEL ESTIMATION TERMINATED NORMALLY"
#> [104] ""
#> [105] ""
#> [106] ""
#> [107] "MODEL FIT INFORMATION"
#> [108] ""
#> [109] "Number of Free Parameters 9"
#> [110] ""
#> [111] "Loglikelihood"
#> [112] ""
#> [113] " H0 Value -1225.911"
#> [114] " H1 Value -1225.911"
#> [115] ""
#> [116] "Information Criteria"
#> [117] ""
#> [118] " Akaike (AIC) 2469.821"
#> [119] " Bayesian (BIC) 2504.645"
#> [120] " Sample-Size Adjusted BIC 2476.093"
#> [121] " (n* = (n + 2) / 24)"
#> [122] ""
#> [123] "Chi-Square Test of Model Fit"
#> [124] ""
#> [125] " Value 0.000"
#> [126] " Degrees of Freedom 0"
#> [127] " P-Value 0.0000"
#> [128] ""
#> [129] "RMSEA (Root Mean Square Error Of Approximation)"
#> [130] ""
#> [131] " Estimate 0.000"
#> [132] " 90 Percent C.I. 0.000 0.000"
#> [133] " Probability RMSEA <= .05 0.000"
#> [134] ""
#> [135] "CFI/TLI"
#> [136] ""
#> [137] " CFI 1.000"
#> [138] " TLI 1.000"
#> [139] ""
#> [140] "Chi-Square Test of Model Fit for the Baseline Model"
#> [141] ""
#> [142] " Value 17.825"
#> [143] " Degrees of Freedom 3"
#> [144] " P-Value 0.0005"
#> [145] ""
#> [146] "SRMR (Standardized Root Mean Square Residual)"
#> [147] ""
#> [148] " Value 0.000"
#> [149] ""
#> [150] ""
#> [151] ""
#> [152] "MODEL RESULTS"
#> [153] ""
#> [154] " Two-Tailed"
#> [155] " Estimate S.E. Est./S.E. P-Value"
#> [156] ""
#> [157] " Y ON"
#> [158] " X 0.151 0.127 1.186 0.235"
#> [159] " M 0.152 0.056 2.725 0.006"
#> [160] ""
#> [161] " M ON"
#> [162] " X 0.369 0.128 2.876 0.004"
#> [163] ""
#> [164] " Means"
#> [165] " X 0.412 0.027 15.025 0.000"
#> [166] ""
#> [167] " Intercepts"
#> [168] " M 0.007 0.079 0.088 0.930"
#> [169] " Y 0.336 0.078 4.339 0.000"
#> [170] ""
#> [171] " Variances"
#> [172] " X 0.241 0.019 12.681 0.000"
#> [173] ""
#> [174] " Residual Variances"
#> [175] " M 1.212 0.094 12.914 0.000"
#> [176] " Y 1.149 0.090 12.807 0.000"
#> [177] ""
#> [178] ""
#> [179] "QUALITY OF NUMERICAL RESULTS"
#> [180] ""
#> [181] " Condition Number for the Information Matrix 0.184E-01"
#> [182] " (ratio of smallest to largest eigenvalue)"
#> [183] ""
#> [184] ""
#> [185] "RESULTS SAVING INFORMATION"
#> [186] ""
#> [187] " Order of data"
#> [188] ""
#> [189] " Parameter estimates"
#> [190] " (saved in order shown in Technical 1 output)"
#> [191] " Standard errors"
#> [192] " (saved in order shown in Technical 1 output)"
#> [193] " Number of Free Parameters"
#> [194] " H0 Loglikelihood"
#> [195] " H1 Loglikelihood"
#> [196] " Akaike (AIC)"
#> [197] " Bayesian (BIC)"
#> [198] " Sample-Size Adjusted BIC"
#> [199] " Chi-square : Value"
#> [200] " Chi-square : Degrees of Freedom"
#> [201] " Chi-square : P-Value"
#> [202] " CFI"
#> [203] " TLI"
#> [204] " RMSEA : Estimate"
#> [205] " RMSEA : Low CI"
#> [206] " RMSEA : High CI"
#> [207] " RMSEA : Probability"
#> [208] " SRMR"
#> [209] " Condition Number"
#> [210] ""
#> [211] " Save file"
#> [212] " file8ff1a81ca4f"
#> [213] ""
#> [214] " Save file format Free"
#> [215] ""
#> [216] ""
#> [217] "SAVEDATA INFORMATION"
#> [218] ""
#> [219] ""
#> [220] " Estimated Covariance Matrix for the Parameter Estimates"
#> [221] ""
#> [222] " Save file"
#> [223] " file8ff6a233e79"
#> [224] " Save format Free"
#> [225] ""
#> [226] " Beginning Time: 11:19:16"
#> [227] " Ending Time: 11:19:16"
#> [228] " Elapsed Time: 00:00:00"
#> [229] ""
#> [230] ""
#> [231] "Mplus VERSION 8.8 DEMO (Linux) has the following limitations:"
#> [232] " Maximum number of dependent variables: 6"
#> [233] " Maximum number of independent variables: 2"
#> [234] " Maximum number of between variables: 2"
#> [235] " Maximum number of continuous latent variables in time series analysis: 2"
#> [236] ""
#> [237] ""
#> [238] "MUTHEN & MUTHEN"
#> [239] "3463 Stoner Ave."
#> [240] "Los Angeles, CA 90066"
#> [241] ""
#> [242] "Tel: (310) 391-9971"
#> [243] "Fax: (310) 391-8971"
#> [244] "Web: www.StatModel.com"
#> [245] "Support: Support@StatModel.com"
#> [246] ""
#> [247] "Copyright (c) 1998-2022 Muthen & Muthen"Multiple Imputation
Parameters of the simple mediation model are estimated using normal theory maximum likelihood for each of the imputed data sets. The parameter estimates and their sampling covariance matrix are pooled.
fit_mi <- FitModelMI(
data_mi,
mplus_bin = mplus_bin
)
fit_mi
#> $coef
#> m~1 y~1 x~1 m~x y~m y~x
#> 0.005019703 0.332799419 0.412956299 0.377266653 0.150139986 0.153136568
#> m~~m y~~y x~~x
#> 1.211805873 1.146497984 0.242038727
#>
#> $vcov
#> m~1 y~1 x~1 m~x y~m
#> m~1 6.281569e-03 4.792023e-05 -9.324596e-05 -6.536580e-03 9.710301e-05
#> y~1 4.792023e-05 6.055600e-03 -6.372941e-05 -3.871823e-05 4.660348e-05
#> x~1 -9.324596e-05 -6.372941e-05 7.506654e-04 1.650903e-04 -8.964939e-06
#> m~x -6.536580e-03 -3.871823e-05 1.650903e-04 1.636016e-02 2.054703e-04
#> y~m 9.710301e-05 4.660348e-05 -8.964939e-06 2.054703e-04 3.194082e-03
#> y~x -6.691576e-05 -6.394353e-03 1.484601e-04 3.590605e-06 -1.068989e-03
#> m~~m 1.478045e-04 6.851728e-06 -3.582386e-05 -1.735251e-04 1.950598e-05
#> y~~y -3.229702e-05 5.311397e-05 -3.383887e-06 6.281239e-05 -1.973814e-05
#> x~~x 2.838276e-06 -1.069720e-05 1.271110e-05 5.582597e-06 2.221033e-05
#> y~x m~~m y~~y x~~x
#> m~1 -6.691576e-05 1.478045e-04 -3.229702e-05 2.838276e-06
#> y~1 -6.394353e-03 6.851728e-06 5.311397e-05 -1.069720e-05
#> x~1 1.484601e-04 -3.582386e-05 -3.383887e-06 1.271110e-05
#> m~x 3.590605e-06 -1.735251e-04 6.281239e-05 5.582597e-06
#> y~m -1.068989e-03 1.950598e-05 -1.973814e-05 2.221033e-05
#> y~x 1.623913e-02 9.434976e-05 -9.770793e-05 1.040343e-05
#> m~~m 9.434976e-05 8.866444e-03 2.301444e-05 -4.864670e-06
#> y~~y -9.770793e-05 2.301444e-05 7.891514e-03 -3.294018e-05
#> x~~x 1.040343e-05 -4.864670e-06 -3.294018e-05 3.692912e-04
#>
#> $vcov_tilde
#> m~1 y~1 x~1 m~x y~m
#> m~1 6.506328e-03 2.295136e-20 3.436532e-21 -6.513577e-03 -6.495798e-21
#> y~1 2.295136e-20 6.157602e-03 -3.839789e-21 -3.685758e-20 -1.408258e-05
#> x~1 3.436532e-21 -3.839789e-21 7.621849e-04 -1.200686e-20 -4.103301e-22
#> m~x -6.513577e-03 -3.685758e-20 -1.200686e-20 1.577610e-02 1.893660e-20
#> y~m -6.495798e-21 -1.408258e-05 -4.103301e-22 1.893660e-20 2.980379e-03
#> y~x -3.090516e-20 -6.160213e-03 6.016538e-21 6.635324e-20 -1.125836e-03
#> m~~m 1.131546e-06 -4.854797e-21 1.522422e-24 -2.193906e-06 2.148737e-20
#> y~~y -1.025535e-21 3.430788e-07 -3.969870e-25 2.327993e-21 4.900495e-08
#> x~~x 7.277823e-21 1.524870e-21 1.754247e-19 -1.740443e-20 6.227598e-22
#> y~x m~~m y~~y x~~x
#> m~1 -3.090516e-20 1.131546e-06 -1.025535e-21 7.277823e-21
#> y~1 -6.160213e-03 -4.854797e-21 3.430788e-07 1.524870e-21
#> x~1 6.016538e-21 1.522422e-24 -3.969870e-25 1.754247e-19
#> m~x 6.635324e-20 -2.193906e-06 2.327993e-21 -1.740443e-20
#> y~m -1.125836e-03 2.148737e-20 4.900495e-08 6.227598e-22
#> y~x 1.535902e-02 2.688057e-21 -6.866015e-07 -3.851020e-21
#> m~~m 2.688057e-21 9.252007e-03 -2.232232e-21 -1.277703e-22
#> y~~y -6.866015e-07 -2.232232e-21 8.281364e-03 1.063728e-23
#> x~~x -3.851020e-21 -1.277703e-22 1.063728e-23 3.691856e-04
#>
#> $vcov_between
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 4.405999e-04 4.744578e-05 -9.232273e-05 -6.866482e-04 9.614160e-05
#> [2,] 4.744578e-05 5.265992e-04 -6.309842e-05 -3.833489e-05 5.864989e-05
#> [3,] -9.232273e-05 -6.309842e-05 6.627736e-05 1.634557e-04 -8.876177e-06
#> [4,] -6.866482e-04 -3.833489e-05 1.634557e-04 2.186203e-03 2.034359e-04
#> [5,] 9.614160e-05 5.864989e-05 -8.876177e-06 2.034359e-04 5.153510e-04
#> [6,] -6.625323e-05 -8.596794e-04 1.469902e-04 3.555055e-06 -5.846278e-05
#> [7,] 1.453361e-04 6.783889e-06 -3.546917e-05 -1.698585e-04 1.931285e-05
#> [8,] -3.197724e-05 5.228337e-05 -3.350383e-06 6.219048e-05 -1.958624e-05
#> [9,] 2.810174e-06 -1.059128e-05 1.258525e-05 5.527323e-06 2.199042e-05
#> [,6] [,7] [,8] [,9]
#> [1,] -6.625323e-05 1.453361e-04 -3.197724e-05 2.810174e-06
#> [2,] -8.596794e-04 6.783889e-06 5.228337e-05 -1.059128e-05
#> [3,] 1.469902e-04 -3.546917e-05 -3.350383e-06 1.258525e-05
#> [4,] 3.555055e-06 -1.698585e-04 6.219048e-05 5.527323e-06
#> [5,] -5.846278e-05 1.931285e-05 -1.958624e-05 2.199042e-05
#> [6,] 2.436800e-03 9.341561e-05 -9.613070e-05 1.030043e-05
#> [7,] 9.341561e-05 5.612308e-04 2.278657e-05 -4.816505e-06
#> [8,] -9.613070e-05 2.278657e-05 4.580570e-04 -3.261404e-05
#> [9,] 1.030043e-05 -4.816505e-06 -3.261404e-05 3.773239e-05
#>
#> $vcov_within
#> m~1 y~1 x~1 m~x y~m
#> m~1 5.836563e-03 2.058873e-20 3.082773e-21 -5.843066e-03 -5.827117e-21
#> y~1 2.058873e-20 5.523735e-03 -3.444519e-21 -3.306344e-20 -1.263291e-05
#> x~1 3.082773e-21 -3.444519e-21 6.837252e-04 -1.077087e-20 -3.680905e-22
#> m~x -5.843066e-03 -3.306344e-20 -1.077087e-20 1.415210e-02 1.698725e-20
#> y~m -5.827117e-21 -1.263291e-05 -3.680905e-22 1.698725e-20 2.673577e-03
#> y~x -2.772376e-20 -5.526077e-03 5.397193e-21 5.952281e-20 -1.009942e-03
#> m~~m 1.015064e-06 -4.355042e-21 1.365703e-24 -1.968064e-06 1.927545e-20
#> y~~y -9.199656e-22 3.077621e-07 -3.561210e-25 2.088349e-21 4.396036e-08
#> x~~x 6.528640e-21 1.367899e-21 1.573664e-19 -1.561281e-20 5.586526e-22
#> y~x m~~m y~~y x~~x
#> m~1 -2.772376e-20 1.015064e-06 -9.199656e-22 6.528640e-21
#> y~1 -5.526077e-03 -4.355042e-21 3.077621e-07 1.367899e-21
#> x~1 5.397193e-21 1.365703e-24 -3.561210e-25 1.573664e-19
#> m~x 5.952281e-20 -1.968064e-06 2.088349e-21 -1.561281e-20
#> y~m -1.009942e-03 1.927545e-20 4.396036e-08 5.586526e-22
#> y~x 1.377796e-02 2.411347e-21 -6.159224e-07 -3.454594e-21
#> m~~m 2.411347e-21 8.299601e-03 -2.002445e-21 -1.146176e-22
#> y~~y -6.159224e-07 -2.002445e-21 7.428876e-03 9.542269e-24
#> x~~x -3.454594e-21 -1.146176e-22 9.542269e-24 3.311815e-04
#>
#> $ariv
#> [1] 0.1147533
#>
#> $m
#> [1] 100
#>
#> $k
#> [1] 9
#>
#> $nu1
#> [1] 9
#>
#> $nu2
#> [1] 83372.16
#>
#> $d1
#> [1] 86.11739