Tabulating results from structural equation models

library(tidySEM)
library(lavaan)
library(MplusAutomation)

tidySEM tabulates the results of different types of models in the same uniform way. This facilitates parsing the output into Tables and Figures for publication. The function to tabulate output is table_results(). The function to tabulate fit indices is table_fit().

Let’s use a classic lavaan tutorial example for a multiple group model, using the HolzingerSwineford1939 data. The tidySEM package has a function measurement() to generate measurement models automatically. It guesses which latent variable an observed variable belongs to by splitting the names (by default, at the last _ symbol), so it helps to rename the variables:

df <- HolzingerSwineford1939
names(df)[7:15] <- paste0(rep(c("vis", "tex", "spe"), each = 3), "_", rep(1:3, 3))
df |>
  subset(select = c("school", "vis_1", "vis_2", "vis_3", "tex_1", "tex_2", "tex_3", "spe_1", 
"spe_2", "spe_3")) -> df

Now, let’s construct the model.

df |>
  tidy_sem() |>
  measurement() -> model

Output from lavaan

Now, let’s run the model in lavaan. You can either use lavaan to run it,

model |>
  estimate_lavaan() -> fit_lav

The results can be tabulated using table_results():

table_results(fit_lav)
#>              label est_sig   se pval      confint
#> 1     vis.BY.vis_1    1.00 0.00 <NA> [1.00, 1.00]
#> 2     vis.BY.vis_2 0.55*** 0.10 0.00 [0.36, 0.75]
#> 3     vis.BY.vis_3 0.73*** 0.11 0.00 [0.52, 0.94]
#> 4     tex.BY.tex_1    1.00 0.00 <NA> [1.00, 1.00]
#> 5     tex.BY.tex_2 1.11*** 0.07 0.00 [0.98, 1.24]
#> 6     tex.BY.tex_3 0.93*** 0.06 0.00 [0.82, 1.03]
#> 7     spe.BY.spe_1    1.00 0.00 <NA> [1.00, 1.00]
#> 8     spe.BY.spe_2 1.18*** 0.16 0.00 [0.86, 1.50]
#> 9     spe.BY.spe_3 1.08*** 0.15 0.00 [0.79, 1.38]
#> 10 Variances.vis_1 0.55*** 0.11 0.00 [0.33, 0.77]
#> 11 Variances.vis_2 1.13*** 0.10 0.00 [0.93, 1.33]
#> 12 Variances.vis_3 0.84*** 0.09 0.00 [0.67, 1.02]
#> 13 Variances.tex_1 0.37*** 0.05 0.00 [0.28, 0.46]
#> 14 Variances.tex_2 0.45*** 0.06 0.00 [0.33, 0.56]
#> 15 Variances.tex_3 0.36*** 0.04 0.00 [0.27, 0.44]
#> 16 Variances.spe_1 0.80*** 0.08 0.00 [0.64, 0.96]
#> 17 Variances.spe_2 0.49*** 0.07 0.00 [0.34, 0.63]
#> 18 Variances.spe_3 0.57*** 0.07 0.00 [0.43, 0.70]
#> 19   Variances.vis 0.81*** 0.15 0.00 [0.52, 1.09]
#> 20   Variances.tex 0.98*** 0.11 0.00 [0.76, 1.20]
#> 21   Variances.spe 0.38*** 0.09 0.00 [0.21, 0.55]
#> 22    vis.WITH.tex 0.41*** 0.07 0.00 [0.26, 0.55]
#> 23    vis.WITH.spe 0.26*** 0.06 0.00 [0.15, 0.37]
#> 24    tex.WITH.spe 0.17*** 0.05 0.00 [0.08, 0.27]
#> 25     Means.vis_1 4.94*** 0.07 0.00 [4.80, 5.07]
#> 26     Means.vis_2 6.09*** 0.07 0.00 [5.96, 6.22]
#> 27     Means.vis_3 2.25*** 0.07 0.00 [2.12, 2.38]
#> 28     Means.tex_1 3.06*** 0.07 0.00 [2.93, 3.19]
#> 29     Means.tex_2 4.34*** 0.07 0.00 [4.19, 4.49]
#> 30     Means.tex_3 2.19*** 0.06 0.00 [2.06, 2.31]
#> 31     Means.spe_1 4.19*** 0.06 0.00 [4.06, 4.31]
#> 32     Means.spe_2 5.53*** 0.06 0.00 [5.41, 5.64]
#> 33     Means.spe_3 5.37*** 0.06 0.00 [5.26, 5.49]
#> 34       Means.vis    0.00 0.00 <NA> [0.00, 0.00]
#> 35       Means.tex    0.00 0.00 <NA> [0.00, 0.00]
#> 36       Means.spe    0.00 0.00 <NA> [0.00, 0.00]

table_fit(fit_lav)
#>      Name Parameters fmin chisq df  pvalue baseline.chisq baseline.df
#> 1 fit_lav         30 0.14    85 24 8.5e-09            919          36
#>   baseline.pvalue  cfi tli nnfi  rfi  nfi pnfi  ifi  rni    LL
#> 1               0 0.93 0.9  0.9 0.86 0.91  0.6 0.93 0.93 -3738
#>   unrestricted.logl  aic  bic   n bic2 rmsea rmsea.ci.lower rmsea.ci.upper
#> 1             -3695 7535 7647 301 7552 0.092          0.071           0.11
#>   rmsea.ci.level rmsea.pvalue rmsea.close.h0 rmsea.notclose.pvalue
#> 1            0.9      0.00066           0.05                  0.84
#>   rmsea.notclose.h0   rmr rmr_nomean srmr srmr_bentler srmr_bentler_nomean
#> 1              0.08 0.075      0.082 0.06         0.06               0.065
#>    crmr crmr_nomean srmr_mplus srmr_mplus_nomean cn_05 cn_01 gfi agfi pgfi mfi
#> 1 0.065       0.073       0.06             0.065   129   153   1 0.99 0.44 0.9
#>   ecvi
#> 1 0.48

Output from OpenMx

Now, we’ll reproduce the same analysis in ‘OpenMx’. First, we run the model:

model |>
  estimate_mx() -> fit_mx
table_results(fit_mx)
table_fit(fit_mx)

#> Running model with 30 parameters
#>                       label est_sig   se pval      confint
#> 1     Loadings.vis.BY.vis_1    1.00 <NA> <NA>         <NA>
#> 2     Loadings.vis.BY.vis_2 0.55*** 0.11 0.00 [0.34, 0.77]
#> 3     Loadings.vis.BY.vis_3 0.73*** 0.12 0.00 [0.50, 0.96]
#> 4     Loadings.tex.BY.tex_1    1.00 <NA> <NA>         <NA>
#> 5     Loadings.tex.BY.tex_2 1.11*** 0.06 0.00 [0.99, 1.24]
#> 6     Loadings.tex.BY.tex_3 0.93*** 0.06 0.00 [0.82, 1.04]
#> 7     Loadings.spe.BY.spe_1    1.00 <NA> <NA>         <NA>
#> 8     Loadings.spe.BY.spe_2 1.18*** 0.15 0.00 [0.89, 1.47]
#> 9     Loadings.spe.BY.spe_3 1.08*** 0.20 0.00 [0.70, 1.46]
#> 10              Means.vis_1 4.94*** 0.07 0.00 [4.80, 5.07]
#> 11              Means.vis_2 6.09*** 0.07 0.00 [5.96, 6.22]
#> 12              Means.vis_3 2.25*** 0.07 0.00 [2.12, 2.38]
#> 13              Means.tex_1 3.06*** 0.07 0.00 [2.93, 3.19]
#> 14              Means.tex_2 4.34*** 0.07 0.00 [4.19, 4.49]
#> 15              Means.tex_3 2.19*** 0.06 0.00 [2.06, 2.31]
#> 16              Means.spe_1 4.19*** 0.06 0.00 [4.06, 4.31]
#> 17              Means.spe_2 5.53*** 0.06 0.00 [5.41, 5.64]
#> 18              Means.spe_3 5.37*** 0.06 0.00 [5.26, 5.49]
#> 19          Variances.vis_1 0.55*** 0.12 0.00 [0.32, 0.78]
#> 20            Variances.vis 0.81*** 0.15 0.00 [0.52, 1.10]
#> 21 Covariances.vis.WITH.tex 0.41*** 0.08 0.00 [0.25, 0.56]
#> 22 Covariances.vis.WITH.spe 0.26*** 0.06 0.00 [0.15, 0.37]
#> 23            Variances.tex 0.98*** 0.11 0.00 [0.76, 1.20]
#> 24 Covariances.tex.WITH.spe 0.17*** 0.05 0.00 [0.08, 0.27]
#> 25            Variances.spe 0.38*** 0.09 0.00 [0.20, 0.56]
#> 26          Variances.vis_2 1.13*** 0.10 0.00 [0.93, 1.34]
#> 27          Variances.vis_3 0.84*** 0.10 0.00 [0.66, 1.03]
#> 28          Variances.tex_1 0.37*** 0.05 0.00 [0.28, 0.47]
#> 29          Variances.tex_2 0.45*** 0.06 0.00 [0.33, 0.56]
#> 30          Variances.tex_3 0.36*** 0.04 0.00 [0.27, 0.44]
#> 31          Variances.spe_1 0.80*** 0.09 0.00 [0.63, 0.97]
#> 32          Variances.spe_2 0.49*** 0.09 0.00 [0.31, 0.67]
#> 33          Variances.spe_3 0.57*** 0.09 0.00 [0.39, 0.74]
#>   Minus2LogLikelihood   n Parameters observedStatistics   df saturatedDoF
#> 1                7475 301         30               2709 2679         2655
#>   independenceDoF saturatedParameters independenceParameters ChiDoF satDoF
#> 1            2691                  54                     18     24   2655
#>   indDoF RMSEANull modelName  AIC  BIC saBIC    LL
#> 1   2691      0.05     model 7535 7647  7552 -3738

Output from Mplus

Now, we’ll reproduce the same analysis in ‘Mplus’. To illustrate the fact that tidySEM is compatible with existing solutions, we will specify the syntax for this example manually, using the package MplusAutomation. This code will only work on your machine if you have Mplus installed and R can find it. First, we run the model:

fit_mplus <- mplusModeler(mplusObject(VARIABLE = "grouping IS school (1 = GW 2 = Pas);",
                                MODEL = c("visual BY vis_1 vis_2 vis_3;",
                                          "textual BY tex_1 tex_2 tex_3;",
                                          "speed BY spe_1 spe_2 spe_3;"),
                                usevariables = names(df),
                                rdata = df),
                    modelout = "example.inp",
                    run = 1L)
table_results(fit_mplus)

table_results(fit_mplus)
#> Calculated confidence intervals from est and se.
#>                           label  est_sig   se pval        confint group
#> 1            VISUAL.BY.VIS_1.GW     1.00 <NA> <NA>           <NA>    GW
#> 2            VISUAL.BY.VIS_2.GW  0.58*** 0.11 0.00 [ 0.36,  0.79]    GW
#> 3            VISUAL.BY.VIS_3.GW  0.80*** 0.13 0.00 [ 0.54,  1.05]    GW
#> 4           TEXTUAL.BY.TEX_1.GW     1.00 <NA> <NA>           <NA>    GW
#> 5           TEXTUAL.BY.TEX_2.GW  1.12*** 0.07 0.00 [ 0.99,  1.25]    GW
#> 6           TEXTUAL.BY.TEX_3.GW  0.93*** 0.06 0.00 [ 0.82,  1.04]    GW
#> 7             SPEED.BY.SPE_1.GW     1.00 <NA> <NA>           <NA>    GW
#> 8             SPEED.BY.SPE_2.GW  1.13*** 0.14 0.00 [ 0.86,  1.40]    GW
#> 9             SPEED.BY.SPE_3.GW  1.01*** 0.16 0.00 [ 0.70,  1.32]    GW
#> 10       TEXTUAL.WITH.VISUAL.GW  0.43*** 0.10 0.00 [ 0.23,  0.62]    GW
#> 11         SPEED.WITH.VISUAL.GW  0.33*** 0.08 0.00 [ 0.16,  0.49]    GW
#> 12        SPEED.WITH.TEXTUAL.GW   0.24** 0.07 0.00 [ 0.09,  0.38]    GW
#> 13              Means.VISUAL.GW     0.00 <NA> <NA>           <NA>    GW
#> 14             Means.TEXTUAL.GW     0.00 <NA> <NA>           <NA>    GW
#> 15               Means.SPEED.GW     0.00 <NA> <NA>           <NA>    GW
#> 16          Intercepts.VIS_1.GW  4.85*** 0.09 0.00 [ 4.67,  5.04]    GW
#> 17          Intercepts.VIS_2.GW  6.07*** 0.08 0.00 [ 5.92,  6.22]    GW
#> 18          Intercepts.VIS_3.GW  2.15*** 0.08 0.00 [ 1.99,  2.32]    GW
#> 19          Intercepts.TEX_1.GW  3.35*** 0.09 0.00 [ 3.18,  3.53]    GW
#> 20          Intercepts.TEX_2.GW  4.68*** 0.10 0.00 [ 4.49,  4.87]    GW
#> 21          Intercepts.TEX_3.GW  2.46*** 0.08 0.00 [ 2.30,  2.63]    GW
#> 22          Intercepts.SPE_1.GW  4.07*** 0.08 0.00 [ 3.90,  4.23]    GW
#> 23          Intercepts.SPE_2.GW  5.43*** 0.08 0.00 [ 5.27,  5.59]    GW
#> 24          Intercepts.SPE_3.GW  5.29*** 0.08 0.00 [ 5.13,  5.44]    GW
#> 25          Variances.VISUAL.GW  0.71*** 0.16 0.00 [ 0.39,  1.03]    GW
#> 26         Variances.TEXTUAL.GW  0.87*** 0.13 0.00 [ 0.61,  1.13]    GW
#> 27           Variances.SPEED.GW  0.51*** 0.12 0.00 [ 0.27,  0.74]    GW
#> 28  Residual.Variances.VIS_1.GW  0.65*** 0.13 0.00 [ 0.40,  0.91]    GW
#> 29  Residual.Variances.VIS_2.GW  0.96*** 0.13 0.00 [ 0.72,  1.21]    GW
#> 30  Residual.Variances.VIS_3.GW  0.64*** 0.11 0.00 [ 0.42,  0.86]    GW
#> 31  Residual.Variances.TEX_1.GW  0.34*** 0.06 0.00 [ 0.22,  0.47]    GW
#> 32  Residual.Variances.TEX_2.GW  0.38*** 0.07 0.00 [ 0.23,  0.52]    GW
#> 33  Residual.Variances.TEX_3.GW  0.44*** 0.07 0.00 [ 0.30,  0.57]    GW
#> 34  Residual.Variances.SPE_1.GW  0.62*** 0.10 0.00 [ 0.42,  0.83]    GW
#> 35  Residual.Variances.SPE_2.GW  0.43*** 0.10 0.00 [ 0.24,  0.63]    GW
#> 36  Residual.Variances.SPE_3.GW  0.52*** 0.10 0.00 [ 0.32,  0.72]    GW
#> 37          VISUAL.BY.VIS_1.PAS     1.00 <NA> <NA>           <NA>   PAS
#> 38          VISUAL.BY.VIS_2.PAS  0.58*** 0.11 0.00 [ 0.36,  0.79]   PAS
#> 39          VISUAL.BY.VIS_3.PAS  0.80*** 0.13 0.00 [ 0.54,  1.05]   PAS
#> 40         TEXTUAL.BY.TEX_1.PAS     1.00 <NA> <NA>           <NA>   PAS
#> 41         TEXTUAL.BY.TEX_2.PAS  1.12*** 0.07 0.00 [ 0.99,  1.25]   PAS
#> 42         TEXTUAL.BY.TEX_3.PAS  0.93*** 0.06 0.00 [ 0.82,  1.04]   PAS
#> 43           SPEED.BY.SPE_1.PAS     1.00 <NA> <NA>           <NA>   PAS
#> 44           SPEED.BY.SPE_2.PAS  1.13*** 0.14 0.00 [ 0.86,  1.40]   PAS
#> 45           SPEED.BY.SPE_3.PAS  1.01*** 0.16 0.00 [ 0.70,  1.32]   PAS
#> 46      TEXTUAL.WITH.VISUAL.PAS  0.41*** 0.11 0.00 [ 0.20,  0.62]   PAS
#> 47        SPEED.WITH.VISUAL.PAS   0.18** 0.07 0.01 [ 0.05,  0.31]   PAS
#> 48       SPEED.WITH.TEXTUAL.PAS   0.18** 0.06 0.00 [ 0.06,  0.30]   PAS
#> 49             Means.VISUAL.PAS     0.15 0.13 0.24 [-0.10,  0.40]   PAS
#> 50            Means.TEXTUAL.PAS -0.58*** 0.12 0.00 [-0.81, -0.35]   PAS
#> 51              Means.SPEED.PAS     0.18 0.09 0.06 [-0.01,  0.36]   PAS
#> 52         Intercepts.VIS_1.PAS  4.85*** 0.09 0.00 [ 4.67,  5.04]   PAS
#> 53         Intercepts.VIS_2.PAS  6.07*** 0.08 0.00 [ 5.92,  6.22]   PAS
#> 54         Intercepts.VIS_3.PAS  2.15*** 0.08 0.00 [ 1.99,  2.32]   PAS
#> 55         Intercepts.TEX_1.PAS  3.35*** 0.09 0.00 [ 3.18,  3.53]   PAS
#> 56         Intercepts.TEX_2.PAS  4.68*** 0.10 0.00 [ 4.49,  4.87]   PAS
#> 57         Intercepts.TEX_3.PAS  2.46*** 0.08 0.00 [ 2.30,  2.63]   PAS
#> 58         Intercepts.SPE_1.PAS  4.07*** 0.08 0.00 [ 3.90,  4.23]   PAS
#> 59         Intercepts.SPE_2.PAS  5.43*** 0.08 0.00 [ 5.27,  5.59]   PAS
#> 60         Intercepts.SPE_3.PAS  5.29*** 0.08 0.00 [ 5.13,  5.44]   PAS
#> 61         Variances.VISUAL.PAS  0.80*** 0.19 0.00 [ 0.42,  1.17]   PAS
#> 62        Variances.TEXTUAL.PAS  0.88*** 0.13 0.00 [ 0.62,  1.14]   PAS
#> 63          Variances.SPEED.PAS  0.32*** 0.09 0.00 [ 0.16,  0.49]   PAS
#> 64 Residual.Variances.VIS_1.PAS  0.56*** 0.16 0.00 [ 0.25,  0.86]   PAS
#> 65 Residual.Variances.VIS_2.PAS  1.30*** 0.16 0.00 [ 0.98,  1.61]   PAS
#> 66 Residual.Variances.VIS_3.PAS  0.94*** 0.15 0.00 [ 0.65,  1.23]   PAS
#> 67 Residual.Variances.TEX_1.PAS  0.45*** 0.07 0.00 [ 0.30,  0.59]   PAS
#> 68 Residual.Variances.TEX_2.PAS  0.50*** 0.09 0.00 [ 0.33,  0.67]   PAS
#> 69 Residual.Variances.TEX_3.PAS  0.26*** 0.05 0.00 [ 0.16,  0.36]   PAS
#> 70 Residual.Variances.SPE_1.PAS  0.89*** 0.13 0.00 [ 0.64,  1.14]   PAS
#> 71 Residual.Variances.SPE_2.PAS  0.54*** 0.10 0.00 [ 0.35,  0.74]   PAS
#> 72 Residual.Variances.SPE_3.PAS  0.65*** 0.10 0.00 [ 0.46,  0.85]   PAS
table_fit(fit_mplus)
#>   Mplus.version Name AnalysisType   DataType Estimator   n NGroups
#> 1           8.6           GENERAL INDIVIDUAL        ML 301       2
#>   NDependentVars NIndependentVars NContinuousLatentVars Parameters ChiSqM_Value
#> 1              9                0                     3         48          164
#>   ChiSqM_DF ChiSqM_PValue ChiSqBaseline_Value ChiSqBaseline_DF
#> 1        60             0                 958               72
#>   ChiSqBaseline_PValue    LL UnrestrictedLL  CFI  TLI  AIC  BIC aBIC
#> 1                    0 -3706          -3624 0.88 0.86 7509 7687 7534
#>   RMSEA_Estimate RMSEA_90CI_LB RMSEA_90CI_UB RMSEA_pLT05  SRMR AICC    Filename
#> 1           0.11         0.088          0.13           0 0.087 7527 example.out