# Models with Second-Order Factors" In semptools: Customizing Structural Equation Modelling Plots

```knitr::opts_chunk\$set(
collapse = TRUE,
comment = "#>",
fig.width  =  8,
fig.height =  6,
fig.align = "center"
)
```

# Introduction

This article illustrates how to use `set_sem_layout()` from the package semptools (CRAN page) for a model with second-order factors. Readers are assumed to have learned how to use `set_sem_layout()` (see `vignette("quick_start_sem")`).

# The Initial `semPaths` Plot

We will use `sem_2nd_order_example`, a sample SEM dataset from semptools with 21 variables for illustration.

```library(semptools)
```

This is the SEM model to be fitted:

```mod <-
'f1 =~ x01 + x02 + x03
f2 =~ x04 + x05 + x06 + x07
f3 =~ x08 + x09 + x10
f4 =~ x11 + x12 + x13 + x14
f5 =~ x15 + x16 + x17 + x18
f6 =~ x19 + x20 + x21
f21 =~ 1*f1 + f3 + f4
f22 =~ 1*f2 + f5 + f6
f22 ~ f21
'
```

Fitting the model using `lavaan::sem()`:

```library(lavaan)
fit <- lavaan::sem(mod, sem_2nd_order_example)
```

This is the plot from `semPaths`:

```library(semPlot)
p <- semPaths(fit, 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(5, 5, 5, 5))
```

# Modify the Plot

As described in `vignette("set_sem_layout")`, the plot can be modified by `set_sem_layout()`, with these special treatment:

## Special Treatment

To modify a plot with second order factors:

• The "indicators" of a second-order factor need to be included in the vector for the `indicator_order` argument.

• In the matrix for `factor_layout`, all factors, first or second order, should be included.

• Although a second-order factor has latent factors as their indicators, the direction of a second-order factor in the `factor_point_to` matrix is ignored. The position of the indicators of a second-order factor are determined by the `factor_layout` matrix.

In the example below, `f1` to `f6`, though latent factors themselves, are included in the vector for `indicator_order`.

## Example

```indicator_order  <- c("x01", "x03", "x02",
"x05", "x06", "x04", "x07",
"x08", "x09", "x10",
"x12", "x11", "x13", "x14",
"x16", "x15", "x18", "x17",
"x20", "x19", "x21",
"f1", "f3", "f4",
"f5", "f6", "f2")
indicator_factor <- c("f1", "f1", "f1",
"f2", "f2", "f2", "f2",
"f3", "f3", "f3",
"f4", "f4", "f4", "f4",
"f5", "f5", "f5", "f5",
"f6", "f6", "f6",
"f21", "f21", "f21",
"f22", "f22", "f22")
factor_layout <- matrix(c(  NA, "f21",   NA, NA,  NA, "f22",   NA,
"f1",  "f4", "f3", NA, "f2",  "f6", "f5"),
byrow = TRUE, 2, 7)
factor_layout <- matrix(c("f1",    NA,    NA, "f2",
"f4", "f21", "f22", "f6",
"f3",    NA,    NA, "f5"),
byrow = TRUE, 3, 4)
factor_point_to <- matrix(c("left",     NA,      NA, "right",
"left", "left", "right", "right",
"left",     NA,      NA, "right"),
byrow = TRUE, 3, 4)
f2 = 1.25,
f5 = 1.25)
p2 <- set_sem_layout(p,
indicator_order = indicator_order,
indicator_factor = indicator_factor,
factor_layout = factor_layout,
factor_point_to = factor_point_to,
```

This is the result:

```plot(p2)
```

The layout is acceptable. It can be further modified by other functions described in `vignette("semptools")`. For example, the residuals can be rotated:

```my_rotate_resid_list <- c(f4  =  45,
f21 =   0,
f22 =   0,
f6  = -45)
p3 <- rotate_resid(p2, my_rotate_resid_list)
plot(p3)
```

# Further information

Please refer to `vignette("quick_start_sem")` on other options of `set_sem_layout()` and how to use it with other functions in the package.

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semptools documentation built on Oct. 15, 2023, 5:07 p.m.