The colon operator in specifying a lavaan model

[Shu Fai Cheung]

I've just learned from another post that we can use ":" to ask lavaan to create a product term (interaction term) when fitting a model. This is a very useful feature because, just like lm, we do not need to create the product terms in the data frame.

Is this a new feature? I checked the help page of lavaan syntax (version 0.6-9) and could not find the documentation on this operator. Is this an experimental feature?

I would be happy to introduce this to my students if it is not experimental.

-- Shu Fai

[Shu Fai Cheung]

Does the colon operator currently support only two-way interaction? I tried something like x1:x2:x3 and it does not work:

```

sigma <- matrix(.4, 4, 4)
diag(sigma) <- 1
set.seed(84324)
dat <- MASS::mvrnorm(100, rep(0, 4), sigma)
colnames(dat) <- paste0("x", 1:4)
mod <-
"
x4 ~ x1 + x2 + x3 + x1:x2 + x1:x3 + x2:x3 + x1:x2:x3
"
fit <- sem(mod, dat)
parameterEstimates(fit, remove.nonfree = TRUE)
```

The output:

```

> parameterEstimates(fit, remove.nonfree = TRUE)
  lhs op   rhs    est    se      z pvalue ci.lower ci.upper
1  x4  ~    x1  0.041 0.095  0.436  0.663   -0.144    0.227
2  x4  ~    x2  0.232 0.115  2.014  0.044    0.006    0.458
3  x4  ~    x3  0.266 0.105  2.526  0.012    0.060    0.473
4  x4  ~ x1:x2 -0.054 0.084 -0.640  0.522   -0.219    0.111
5  x4  ~ x1:x3 -0.034 0.106 -0.326  0.745   -0.242    0.173
6  x4  ~ x2:x3 -0.005 0.111 -0.046  0.963   -0.222    0.212
7  x4 ~~    x4  0.737 0.104  7.071  0.000    0.533    0.941

```

-- Shu Fai

[Terrence Jorgensen]

Is this a new feature? 

It has been around for about 5 years (0.5-21):   https://lavaan.ugent.be/history/dot5.html

But it is one of the details that has not made it into the ?model.syntax documentation.

Indeed, I don't think a three-way interaction was foreseen.  I posted your example on GitHub

https://github.com/yrosseel/lavaan/issues/220

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Shu Fai Cheung]

Thanks! My fault! Really need to read carefully the release history.

This is a good feature. It makes writing the model syntax more intuitive and also reduces the chance of human error in computing the product terms before calling lavaan. I will promote it to my students. :)

-- Shu Fai