first_model.md

A first model

In this tutorial, we will fit an example SEM with our package. The example we are using is from the lavaan tutorial, so it may be familiar. It looks like this:

We assume the StructuralEquationModels package is already installed. To use it in the current session, we run

using StructuralEquationModels

We then first define the graph of our model in a syntax which is similar to the R-package lavaan:

observed_vars = [:x1, :x2, :x3, :y1, :y2, :y3, :y4, :y5, :y6, :y7, :y8]
latent_vars = [:ind60, :dem60, :dem65]

graph = @StenoGraph begin

    # loadings
    ind60 → fixed(1)*x1 + x2 + x3
    dem60 → fixed(1)*y1 + y2 + y3 + y4
    dem65 → fixed(1)*y5 + y6 + y7 + y8

    # latent regressions
    ind60 → dem60
    dem60 → dem65
    ind60 → dem65

    # variances
    _(observed_vars) ↔ _(observed_vars)
    _(latent_vars) ↔ _(latent_vars)

    # covariances
    y1 ↔ y5
    y2 ↔ y4 + y6
    y3 ↔ y7
    y8 ↔ y4 + y6

end

observed_vars = [:x1, :x2, :x3, :y1, :y2, :y3, :y4, :y5, :y6, :y7, :y8]
latent_vars = [:ind60, :dem60, :dem65]

graph = @StenoGraph begin

    # loadings
    ind60 → fixed(1)*x1 + x2 + x3
    dem60 → fixed(1)*y1 + y2 + y3 + y4
    dem65 → fixed(1)*y5 + y6 + y7 + y8

    # latent regressions
    ind60 → dem60
    dem60 → dem65
    ind60 → dem65

    # variances
    _(observed_vars) ↔ _(observed_vars)
    _(latent_vars) ↔ _(latent_vars)

    # covariances
    y1 ↔ y5
    y2 ↔ y4 + y6
    y3 ↔ y7
    y8 ↔ y4 + y6

end

!!! note "Time to first model" When executing the code from this tutorial the first time in a fresh julia session, you may wonder that it takes quite some time. This is not because the implementation is slow, but because the functions are compiled the first time you use them. Try rerunning the example a second time - you will see that all function executions after the first one are quite fast.

We then use this graph to define a ParameterTable object

partable = ParameterTable(
    latent_vars = latent_vars, 
    observed_vars = observed_vars, 
    graph = graph)

load the example data

data = example_data("political_democracy")

data = example_data("political_democracy")

and specify our model as

model = Sem(
    specification = partable,
    data = data
)

We can now fit the model via

model_fit = sem_fit(model)

and compute fit measures as

fit_measures(model_fit)

We can also get a bit more information about the fitted model via the sem_summary() function:

sem_summary(model_fit)

To investigate the parameter estimates, we can update our partable object to contain the new estimates:

update_estimate!(partable, model_fit)

and investigate the solution with

sem_summary(partable)

Congratulations, you fitted and inspected your very first model! We recommend continuing with Our Concept of a Structural Equation Model.