Using set_sem_layout() for a Model With Observed Exogenous Variables

Shu Fai Cheung & Mark Hok Chio Lai

Goal

This article illustrates how to use set_sem_layout() from the package semptools (CRAN page) for a model with latent variables and one or more observed exogenous variables (a.k.a., predictors or independent variables in some disciplines), and the observed exogenous variables to be placed like other latent variables in a model diagram.

This article assumes basic knowledge in using semptools and set_sem_layout() (see vignette("semptools") and vignette("quick_start_sem") for illustrations).

Model and Data

The following model is to be fitted to the dataset sem_example, provided in the package semptools. It is fitted by lavaan::sem():

library(semptools)
library(lavaan)
#> This is lavaan 0.6-19
#> lavaan is FREE software! Please report any bugs.
mod <-
  'f1 =~ x01 + x02 + x03
   f3 =~ x08 + x09 + x10
   f4 =~ x11 + x12 + x13 + x14
   f3 ~ f1 + x04
   f4 ~ f3 + x05'
fit_sem <- lavaan::sem(mod, sem_example)

In this model, x04 and x05 are exogenous observed variables. They affect f3 and f4 but they themselves are not indicators of latent factors.

Setting indicator_order and indicator_factor

For a model in which all observed variables are indicators of latent factors, they are placed in the vector for indicator_order.

If an observed variable is not an indicator, then this is how to include it in the call to set_sem_layout():

• It should be placed in indicator_order and indicator_factor as if it were a latent factor and it were its own indicator.

• In the matrix for factor_layout, set its position as if it were a latent factor.

• No need to specify the position of its indicators in the matrix for factor_point_to. Just leave the cell NA.

We generate the basic diagram by semPlot::semPaths() first:

library(semPlot)
library(semptools)
p <- semPaths(fit_sem,
              whatLabels = "est",
              sizeMan = 5,
              nCharNodes = 0,
              nCharEdges = 0,
              edge.width = 0.8,
              node.width = 0.7,
              edge.label.cex = 0.6,
              style = "ram",
              mar = c(10, 10, 10, 10),
              DoNotPlot = TRUE)

These are the vectors for indicator_order and indicator_factor. Note that x04 and x05 appear on both vectors.

indicator_order  <- c("x04", "x05", "x01", "x02", "x03",
                      "x11", "x12", "x13", "x14", "x08", "x09", "x10")
indicator_factor <- c("x04", "x05", "f1",  "f1",  "f1",
                      "f4",  "f4",  "f4",  "f4",  "f3",  "f3",  "f3")

This is the matrix for factor_layout, created by layout_matrix():

factor_layout <- layout_matrix(f1 = c(1, 1),
                               f3 = c(1, 2),
                               f4 = c(1, 3),
                               x04 = c(2, 1),
                               x05 = c(2, 2))
factor_layout
#>      [,1]  [,2]  [,3]
#> [1,] "f1"  "f3"  "f4"
#> [2,] "x04" "x05" NA

This is the matrix for factor_point_to, created by auto_factor_point_to() (added in semptools 0.2.9.15) [^If not available, the matrix can be created manually by matrix().]

factor_point_to <- auto_factor_point_to(factor_layout,
                                        f1 = "up",
                                        f3 = "up",
                                        f4 = "up")
factor_point_to
#>      [,1] [,2] [,3]
#> [1,] "up" "up" "up"
#> [2,] NA   NA   NA

Last, we created more vectors to further modify the diagram:

indicator_spread <- c(f4 = 1.5)

p2 <- set_sem_layout(p,
                     indicator_order = indicator_order,
                     indicator_factor = indicator_factor,
                     factor_layout = factor_layout,
                     factor_point_to = factor_point_to,
                     indicator_spread = indicator_spread)
plot(p2)

Final Remarks

For further information on using set_sem_layout(), please refer to vignette("quick_start_sem"). For illustrations on how to modify a path diagram from semPlot::semPaths() using functions in semptools, please refer to vignette("semptools").