test_that("implicit transformations", {


  set.seed(123)
  dataset <- simulate_moderated_nonlinear_factor_analysis(N = 2000)

  model <- "
  xi =~ x1 + x2 + x3
  eta =~ y1 + y2 + y3
  eta ~ a*xi

  !a0
  !a1
  a := a0 + data.k*a1
  "

  mod <- mxsem(model = model,
               data = dataset) |>
    mxTryHard()

  omxGetParameters(mod)

  testthat::expect_true(abs(omxGetParameters(mod)["a0"] - .7) < .1)
  testthat::expect_true(abs(omxGetParameters(mod)["a1"] - -.2) < .1)



  set.seed(123)
  dataset <- simulate_moderated_nonlinear_factor_analysis(N = 2000)

  model_implicit <- "
  xi =~ x1 + x2 + x3
  eta =~ y1 + y2 + y3
  eta ~ {a0 + data.k*a1}*xi
  "

  mod_implicit <- mxsem(model = model_implicit,
               data = dataset) |>
    mxTryHard()

  omxGetParameters(mod_implicit)

  testthat::expect_true(abs(omxGetParameters(mod_implicit)["a0"] - .7) < .1)
  testthat::expect_true(abs(omxGetParameters(mod_implicit)["a1"] - -.2) < .1)

  testthat::expect_true(abs(logLik(mod_implicit) - logLik(mod)) < 1e-4)

  model <- '
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a1*y2 + b1*y3 + c*y4
     dem65 =~ y5 + a2*y6 + b2*y7 + c*y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # residual correlations
    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8

'

  fit_base <- mxsem(model, data = OpenMx::Bollen) |>
    mxTryHard()

  model_transform <- '
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a1*y2 + b1*y3 + c*y4
     dem65 =~ y5 + {a1 + delta_a}*y6 + b2*y7 + c*y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # residual correlations
    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8

    !delta_b
    b2 := b1 + delta_b
'

  fit_transform <- mxsem(model_transform, data = OpenMx::Bollen) |>
    mxTryHard()

  testthat::expect_true(abs(logLik(fit_base) - logLik(fit_transform)) < 1e-4)
  testthat::expect_true(abs(omxGetParameters(fit_base)["a2"] -
                              sum(omxGetParameters(fit_transform)[c("a1", "delta_a")])) < 1e-4)

  model_transform <- '
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a1*y2 + b1*y3 + c*y4
     dem65 =~ y5 + {a1 +
     b2 +
          delta_a}*y6 + b2*y7 + c*y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # residual correlations
    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8

    !delta_b
    b2 := b1 + delta_b
'

  fit_transform <- mxsem(model_transform, data = OpenMx::Bollen) |>
    mxTryHard()

  testthat::expect_true(abs(logLik(fit_base) - logLik(fit_transform)) < 1e-4)
  testthat::expect_true(abs(omxGetParameters(fit_base)["a2"] -
                              sum(omxGetParameters(fit_transform)[c("a1", "delta_a", "b1", "delta_b")])) < 1e-4)

  model_transform <- '
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a1*y2 + b1*y3 + c*y4
     dem65 =~ y5 + {a2:=a1 +
     b2 +
          delta_a}*y6 + b2*y7 + c*y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # residual correlations
    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8

    !delta_b
    b2 := b1 + delta_b
'

  fit_transform <- mxsem(model_transform, data = OpenMx::Bollen) |>
    mxTryHard()

  testthat::expect_true(abs(logLik(fit_base) - logLik(fit_transform)) < 1e-4)
  testthat::expect_true(abs(omxGetParameters(fit_base)["a2"] -
                              sum(omxGetParameters(fit_transform)[c("a1", "delta_a", "b1", "delta_b")])) < 1e-4)

})