Build by parts
You can always build a model by parts - that is, you construct the observed, imply, loss and optimizer part seperately.
As an example on how this works, we will build A first model in parts.
First, we specify the model just as usual:
using StructuralEquationModels
data = example_data("political_democracy")
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
partable = ParameterTable(
latent_vars = latent_vars,
observed_vars = observed_vars,
graph = graph) -------- ---------------- -------- ------- ------------- --------- ------------
from parameter_type to free value_fixed start estimate ⋯
Symbol Symbol Symbol Bool Float64 Float64 Float64 ⋯
-------- ---------------- -------- ------- ------------- --------- ------------
ind60 → x1 false 1.0 0.0 0.0 ⋯
ind60 → x2 true 0.0 0.0 0.0 ⋯
ind60 → x3 true 0.0 0.0 0.0 ⋯
dem60 → y1 false 1.0 0.0 0.0 ⋯
dem60 → y2 true 0.0 0.0 0.0 ⋯
dem60 → y3 true 0.0 0.0 0.0 ⋯
dem60 → y4 true 0.0 0.0 0.0 ⋯
dem65 → y5 false 1.0 0.0 0.0 ⋯
dem65 → y6 true 0.0 0.0 0.0 ⋯
dem65 → y7 true 0.0 0.0 0.0 ⋯
dem65 → y8 true 0.0 0.0 0.0 ⋯
ind60 → dem60 true 0.0 0.0 0.0 ⋯
dem60 → dem65 true 0.0 0.0 0.0 ⋯
ind60 → dem65 true 0.0 0.0 0.0 ⋯
x1 ↔ x1 true 0.0 0.0 0.0 ⋯
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱
-------- ---------------- -------- ------- ------------- --------- ------------
1 column and 19 rows omitted
Latent Variables: [:ind60, :dem60, :dem65]
Observed Variables: [:x1, :x2, :x3, :y1, :y2, :y3, :y4, :y5, :y6, :y7, :y8]
Now, we construct the different parts:
# observed ---------------------------------------------------------------------------------
observed = SemObservedData(specification = partable, data = data)
# imply ------------------------------------------------------------------------------------
imply_ram = RAM(specification = partable)
# loss -------------------------------------------------------------------------------------
ml = SemML(observed = observed)
loss_ml = SemLoss(ml)
# optimizer -------------------------------------------------------------------------------------
optimizer = SemOptimizerOptim()
# model ------------------------------------------------------------------------------------
model_ml = Sem(observed, imply_ram, loss_ml, optimizer)Structural Equation Model
- Loss Functions
SemML
- Fields
observed: SemObservedData
imply: RAM
optimizer: SemOptimizerOptim