Generating syntax for structural equation models

tidySEM offers a user-friendly, tidy workflow for generating syntax for SEM models. The workflow is top-down, meaning that syntax is generated based on conceptual model elements. In many cases, the generated syntax will suffice - but it is always customizable. The workflow also tries to intelligently guess which variables go together, but these defaults can be overridden.

The tidySEM workflow

The workflow underlying syntax generation in tidySEM is as follows:

Give the variables in your data object short, informative names, that are easily machine readable
Convert the data to a tidy_sem object by running model <- tidy_sem(data)
Add elements of syntax
- E.g., measurement(model)
Optionally, access the dictionary, data, and syntax elements in the tidy_sem object by calling dictionary(model), get_data(model), or syntax(model)
Optionally, modify the dictionary, data, and syntax elements in the tidy_sem object dictionary(model) <- ..., get_data(model) <- ..., and syntax(model) <- ...
Run the analysis, either by:
- Converting the tidy_sem object to lavaan syntax using as_lavaan(model) and using that as input for the lavaan functions sem, lavaan, or cfa
- Converting the tidy_sem object to OpenMx using as_ram(model), and using that as input for mxRun or `run_mx``
- Converting the tidy_sem object to Mplus using as_mplus(model), and using that as input for MplusAutomation::mplusObject()
- Using the functions estimate_lavaan(model), estimate_mx(model), or estimate_mplus(model)

All elements of the tidy_sem object are “tidy” data, i.e., tabular data.frames, and can be modified using the familiar suite of functions in the ‘tidyverse’. Thus, the data, dictionary, and syntax are all represented as data.frames.

Example: Running a CFA

Step 1: Check the variable names

As an example, let’s make a graph for a classic lavaan tutorial example for CFA. First, we check the data names:

df <- HolzingerSwineford1939
names(df)
#>  [1] "id"     "sex"    "ageyr"  "agemo"  "school" "grade"  "x1"     "x2"    
#>  [9] "x3"     "x4"     "x5"     "x6"     "x7"     "x8"     "x9"

These names are not informative, as the items named x.. are indicators of three different latent variables. We will rename them accordingly:

names(df)[grepl("^x", names(df))] <- c("vis_1", "vis_2", "vis_3", "tex_1", "tex_2", "tex_3", "spe_1", "spe_2", "spe_3")

Guidelines for naming variables

In general, it is good practice to name variables using the following information:

Scale name (or if the variable is not part of a scale, observed variable name)
Measurement occasion (if longitudinal)
Respondent id (if multiple respondents completed the same scales)
Scale item number, which tidySEM expects to be separated from the remainder of the variable name by a splitting character (e.g., scale_item)

Roughly speaking, elements of the variable name should be ordered from “slow-changing” to “fast-changing”; i.e.; there are only a few scales, with possibly several measurement occasions or respondents, and many items.

Step 2: Generate a dictionary

A dictionary indicates which variables in the data belong to, for example, the same scale. When the data have informative names, it is possible to construct a data dictionary automatically:

model <- tidy_sem(df)
model
#> A tidy_sem object
#> [0;30m[0;32mv  [0m  $dictionary[0m
#> [0;30m[0;32mv  [0m  $data[0m
#> [0;30m[0;37mo  [0m  $syntax[0m

Step 3: Generate syntax

We can automatically add basic syntax to the sem_syntax object, by passing it to a syntax-generating function like measurement(), which adds a measurement model for any scales in the object:

model |>
  measurement() -> model
model

#> A tidy_sem object
#> [0;30m[0;32mv  [0m  $dictionary[0m
#> [0;30m[0;32mv  [0m  $data[0m
#> [0;30m[0;32mv  [0m  $syntax[0m

Step 4: Run the model

The resulting model can be evaluated as ‘lavaan’ syntax, ‘OpenMx’ syntax, or ‘Mplus’ syntax, using the as_lavaan, as_ram, and as_mplus functions. For example, using lavaan:

model |>
  estimate_lavaan()

#> lavaan 0.6-19 ended normally after 35 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        30
#> 
#>   Number of observations                           301
#> 
#> Model Test User Model:
#>                                                       
#>   Test statistic                                85.306
#>   Degrees of freedom                                24
#>   P-value (Chi-square)                           0.000

The same model can be estimated with ‘OpenMx’ through the R-package OpenMx.

model |>
  estimate_mx()

The same model can be estimated in ‘Mplus’ through the R-package MplusAutomation. This requires ‘Mplus’ to be installed.

library(MplusAutomation)
model |>
  estimate_mplus()

Optional step 5: Access the dictionary, data, and syntax

The dictionary and syntax can be examined using dictionary(model) and syntax(model):

dictionary(model)
#>      name scale      type  label
#> 1      id  <NA>  observed     id
#> 2     sex  <NA>  observed    sex
#> 3   ageyr  <NA>  observed  ageyr
#> 4   agemo  <NA>  observed  agemo
#> 5  school  <NA>  observed school
#> 6   grade  <NA>  observed  grade
#> 7   vis_1   vis indicator  vis_1
#> 8   vis_2   vis indicator  vis_2
#> 9   vis_3   vis indicator  vis_3
#> 10  tex_1   tex indicator  tex_1
#> 11  tex_2   tex indicator  tex_2
#> 12  tex_3   tex indicator  tex_3
#> 13  spe_1   spe indicator  spe_1
#> 14  spe_2   spe indicator  spe_2
#> 15  spe_3   spe indicator  spe_3
#> 16    vis  <NA>    latent    vis
#> 17    tex  <NA>    latent    tex
#> 18    spe  <NA>    latent    spe

syntax(model)
#>      lhs op   rhs block group free label ustart plabel
#> 1    vis =~ vis_1     1     1    0            1   .p1.
#> 2    vis =~ vis_2     1     1    1           NA   .p2.
#> 3    vis =~ vis_3     1     1    1           NA   .p3.
#> 4    tex =~ tex_1     1     1    0            1   .p4.
#> 5    tex =~ tex_2     1     1    1           NA   .p5.
#> 6    tex =~ tex_3     1     1    1           NA   .p6.
#> 7    spe =~ spe_1     1     1    0            1   .p7.
#> 8    spe =~ spe_2     1     1    1           NA   .p8.
#> 9    spe =~ spe_3     1     1    1           NA   .p9.
#> 10 vis_1 ~~ vis_1     1     1    1           NA  .p10.
#> 11 vis_2 ~~ vis_2     1     1    1           NA  .p11.
#> 12 vis_3 ~~ vis_3     1     1    1           NA  .p12.
#> 13 tex_1 ~~ tex_1     1     1    1           NA  .p13.
#> 14 tex_2 ~~ tex_2     1     1    1           NA  .p14.
#> 15 tex_3 ~~ tex_3     1     1    1           NA  .p15.
#> 16 spe_1 ~~ spe_1     1     1    1           NA  .p16.
#> 17 spe_2 ~~ spe_2     1     1    1           NA  .p17.
#> 18 spe_3 ~~ spe_3     1     1    1           NA  .p18.
#> 19   vis ~~   vis     1     1    1           NA  .p19.
#> 20   tex ~~   tex     1     1    1           NA  .p20.
#> 21   spe ~~   spe     1     1    1           NA  .p21.
#> 22   vis ~~   tex     1     1    1           NA  .p22.
#> 23   vis ~~   spe     1     1    1           NA  .p23.
#> 24   tex ~~   spe     1     1    1           NA  .p24.
#> 25 vis_1 ~1           1     1    1           NA  .p25.
#> 26 vis_2 ~1           1     1    1           NA  .p26.
#> 27 vis_3 ~1           1     1    1           NA  .p27.
#> 28 tex_1 ~1           1     1    1           NA  .p28.
#> 29 tex_2 ~1           1     1    1           NA  .p29.
#> 30 tex_3 ~1           1     1    1           NA  .p30.
#> 31 spe_1 ~1           1     1    1           NA  .p31.
#> 32 spe_2 ~1           1     1    1           NA  .p32.
#> 33 spe_3 ~1           1     1    1           NA  .p33.
#> 34   vis ~1           1     1    0            0  .p34.
#> 35   tex ~1           1     1    0            0  .p35.
#> 36   spe ~1           1     1    0            0  .p36.

Optional step 6: Modify the dictionary and syntax

At this stage, we may want to modify the basic syntax slightly. The functions dictionary(model) <- ... and syntax(model) <- ... can be used to modify the dictionary and syntax:

dictionary(model) |>
  mutate(label = ifelse(label == "vis", "Visual", label))

#>      name scale      type  label
#> 1      id  <NA>  observed     id
#> 2     sex  <NA>  observed    sex
#> 3   ageyr  <NA>  observed  ageyr
#> 4   agemo  <NA>  observed  agemo
#> 5  school  <NA>  observed school
#> 6   grade  <NA>  observed  grade
#> 7   vis_1   vis indicator  vis_1
#> 8   vis_2   vis indicator  vis_2
#> 9   vis_3   vis indicator  vis_3
#> 10  tex_1   tex indicator  tex_1
#> 11  tex_2   tex indicator  tex_2
#> 12  tex_3   tex indicator  tex_3
#> 13  spe_1   spe indicator  spe_1
#> 14  spe_2   spe indicator  spe_2
#> 15  spe_3   spe indicator  spe_3
#> 16    vis  <NA>    latent Visual
#> 17    tex  <NA>    latent    tex
#> 18    spe  <NA>    latent    spe

For example, imagine we want to change the model, so that all items of the “spe” subscale load on the “tex” latent variable. We would first replace the latent variable “spe” with “tex”, and secondly remove all mention of the “spe” latent variable:

syntax(model) |>
  mutate(lhs = ifelse(lhs == "spe" & op == "=~", "tex", lhs)) |>
  filter(!(lhs == "spe" | rhs == "spe")) -> syntax(model)

Remember that both of the original latent variables were identified by fixing one indicator to be equal to 1, so we have to free up one of them:

syntax(model) |>
  mutate(free = ifelse(rhs == "spe_1", 1, free),
  ustart = ifelse(rhs == "spe_1", NA, ustart)) -> syntax(model)

The modified model could then be run:

estimate_lavaan(model)
#> lavaan 0.6-19 ended normally after 28 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        28
#> 
#>   Number of observations                           301
#> 
#> Model Test User Model:
#>                                                       
#>   Test statistic                               236.091
#>   Degrees of freedom                                26
#>   P-value (Chi-square)                           0.000

Optional step 7: Adding paths

In addition to the way of editing the data.frame with model syntax described in Step 6, it is also possible to add (or modify) paths by adding lavaan syntax. For example, imagine that - instead of having “vis” and “tex” correlate, we want to add a regression path between them:

model |>
  add_paths("vis ~ tex") |>
  estimate_lavaan() |>
  summary(estimates = TRUE)

#> lavaan 0.6-19 ended normally after 25 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        28
#> 
#>   Number of observations                           301
#> 
#> Model Test User Model:
#>                                                       
#>   Test statistic                               236.091
#>   Degrees of freedom                                26
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Expected
#>   Information saturated (h1) model          Structured
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   vis =~                                              
#>     vis_1             1.000                           
#>     vis_2             0.551    0.103    5.335    0.000
#>     vis_3             0.700    0.115    6.110    0.000
#>   tex =~                                              
#>     tex_1             1.000                           
#>     tex_2             1.109    0.066   16.892    0.000
#>     tex_3             0.927    0.056   16.636    0.000
#>     spe_1             0.198    0.067    2.969    0.003
#>     spe_2             0.198    0.062    3.192    0.001
#>     spe_3             0.299    0.061    4.907    0.000
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   vis ~                                               
#>     tex               0.447    0.068    6.569    0.000
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .vis_1             4.936    0.067   73.473    0.000
#>    .vis_2             6.088    0.068   89.855    0.000
#>    .vis_3             2.250    0.065   34.579    0.000
#>    .tex_1             3.061    0.067   45.694    0.000
#>    .tex_2             4.341    0.074   58.452    0.000
#>    .tex_3             2.186    0.063   34.667    0.000
#>    .spe_1             4.186    0.063   66.766    0.000
#>    .spe_2             5.527    0.058   94.854    0.000
#>    .spe_3             5.374    0.058   92.546    0.000
#>    .vis               0.000                           
#>     tex               0.000                           
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .vis_1             0.526    0.127    4.136    0.000
#>    .vis_2             1.129    0.102   11.030    0.000
#>    .vis_3             0.867    0.094    9.237    0.000
#>    .tex_1             0.376    0.048    7.885    0.000
#>    .tex_2             0.461    0.059    7.871    0.000
#>    .tex_3             0.358    0.043    8.334    0.000
#>    .spe_1             1.145    0.094   12.216    0.000
#>    .spe_2             0.984    0.081   12.207    0.000
#>    .spe_3             0.928    0.077   12.121    0.000
#>    .vis               0.638    0.136    4.692    0.000
#>     tex               0.975    0.112    8.714    0.000

This function accepts both quoted (character) and unquoted arguments. So, for example, if we want to add a cross-loading from “spe_1” on “vis”, in addition to the regression path before, we could use the following code:

model |>
  add_paths("vis ~ tex", vis =~ spe_1) |>
  estimate_lavaan()

#> lavaan 0.6-19 ended normally after 31 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        28
#> 
#>   Number of observations                           301
#> 
#> Model Test User Model:
#>                                                       
#>   Test statistic                               288.451
#>   Degrees of freedom                                26
#>   P-value (Chi-square)                           0.000

- The tidySEM workflow
- Example: Running a CFA