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title: "Estimator-Settings"
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**lavaan** is an extremely versatile package for structural equation modeling.
It covers a wide range of different estimation procedures beyond the basic 
maximum likelihood estimation with listwise deletion of missings. **lessSEM**
tries to cover some of these procedures out of the box. That is, when 
provided with a **lavaan** model, **lessSEM** will check the estimator, missing
data procedure, etc. and try to match it.

> **lessSEM** may not yet provide all procedures implemented in **lavaan**. If
you run into cases where **lessSEM** does not match the **lavaan** model correctly, 
please let us know at [GitHub](https://github.com/jhorzek/lessSEM/issues).

## Maximum Likelihood Estimation

By default, **lavaan** will use maximum likelihood estimation with listwise deletion
of missing data. If you pass such a "default" model to **lessSEM**, the same
procedures will be used as well:




```r
library(lessSEM)

dataset <- simulateExampleData()

lavaanSyntax <- "
f =~ l1*y1 + l2*y2 + l3*y3 + l4*y4 + l5*y5 + 
     l6*y6 + l7*y7 + l8*y8 + l9*y9 + l10*y10 + 
     l11*y11 + l12*y12 + l13*y13 + l14*y14 + l15*y15
f ~~ 1*f
"

lavaanModel <- lavaan::sem(lavaanSyntax,
                           data = dataset,
                           std.lv = TRUE)

lsem <- lasso(
  lavaanModel = lavaanModel,
  regularized = paste0("l", 6:15),
  nLambdas = 50)
```

You can also use `meanstructure = TRUE` and **lessSEM** will automatically add a meanstructure
as well.

### Missing data

Missing data is a very common problem in real data analysis. Different procedures have
been developed to address with issue, with full-information-maximum-likelihood being
among the most famous ones. In lavaan, you can use this procedure by setting 
`missing = "ml"`:




```r
library(lessSEM)

dataset <- simulateExampleData(percentMissing = 20)

lavaanSyntax <- "
f =~ l1*y1 + l2*y2 + l3*y3 + l4*y4 + l5*y5 + 
     l6*y6 + l7*y7 + l8*y8 + l9*y9 + l10*y10 + 
     l11*y11 + l12*y12 + l13*y13 + l14*y14 + l15*y15
f ~~ 1*f
"

lavaanModel <- lavaan::sem(lavaanSyntax,
                           data = dataset,
                           std.lv = TRUE, 
                           # note: we change the missing procedure
                           missing = "ml")

lsem <- lasso(
  lavaanModel = lavaanModel,
  regularized = paste0("l", 6:15),
  nLambdas = 50)
```

## Weighted Least Squares

> **Warning** WLS is under development and not fully supported at the moment.

Weighted least squares estimation is an alternative to maximum likelihood
estimation that is prominent in case of non-normal data. Again, **lavaan**
covers a wide range of different weighted least squares estimators that 
can be selected with the `estimator = x` option. These estimators differ in
their weight matrix. **lessSEM** extracts the weights automatically from 
**lavaan**. The following weighted least squares variants are supported: 
`estimator = "wls"`, `estimator = "dwls"`, `estimator = "gls"`, and 
`estimator = "uls"`. 

Again, **lessSEM** will try to copy the procedure used in **lavaan** automatically:




```r
library(lessSEM)

# Note: WLS needs much larger sample sizes
dataset <- simulateExampleData(N = 1000)

lavaanSyntax <- "
f =~ l1*y1 + l2*y2 + l3*y3 + l4*y4 + l5*y5 + 
     l6*y6 + l7*y7 + l8*y8 + l9*y9 + l10*y10 + 
     l11*y11 + l12*y12 + l13*y13 + l14*y14 + l15*y15
f ~~ 1*f
"

lavaanModel <- lavaan::sem(lavaanSyntax,
                           data = dataset,
                           std.lv = TRUE,
                           estimator = "wls")

lsem <- lasso(
  lavaanModel = lavaanModel,
  regularized = paste0("l", 6:15),
  nLambdas = 50)
```

Changing the estimator just requires replacing `estimator = "wls"` with any
of the other weighted least squares variants mentioned above:



```r
library(lessSEM)

# Note: WLS needs much larger sample sizes
dataset <- simulateExampleData(N = 1000)

lavaanSyntax <- "
f =~ l1*y1 + l2*y2 + l3*y3 + l4*y4 + l5*y5 + 
     l6*y6 + l7*y7 + l8*y8 + l9*y9 + l10*y10 + 
     l11*y11 + l12*y12 + l13*y13 + l14*y14 + l15*y15
f ~~ 1*f
"

lavaanModel <- lavaan::sem(lavaanSyntax,
                           data = dataset,
                           std.lv = TRUE,
                           estimator = "uls")

lsem <- lasso(
  lavaanModel = lavaanModel,
  regularized = paste0("l", 6:15),
  nLambdas = 50)
```

Currently, the only procedure to select final parameters that is supported
by **lessSEM** out of the box is cross-validation. AIC or BIC are not supported.

### Ordered data

**lavaan** supports ordered data. This is not yet implemented in **lessSEM**.
Check **lslx** for an implementation of regularized SEM with categorical data
(Huang, 2020).


# Bibliography

- Huang, P.-H. (2020). Penalized Least Squares for Structural Equation Modeling with Ordinal Responses. Multivariate Behavioral Research, 1–19. https://doi.org/10.1080/00273171.2020.1820309
- Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02