---
title: "Unstandardized Estimates"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Unstandardized Estimates}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  message = FALSE,
  warning = FALSE
)

library(plssem)
```

In general, the PLS-SEM framework and the `pls()` function assume that
the model is fully standardized (i.e., all observed and latent variables
have zero mean and unit variance). However, it is possible to get
unstandardized estimates for your models using a post-estimation
procedure. This can be done either by using the `unstandardized_estimates()`
function or by passing `unstandardized = TRUE` to the `summary()` function.
Here is an example using `summary()`.

```{r}
m <- '
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  Y ~ X + Z + X:Z + X:X
'

fit <- pls(m, modsem::oneInt, bootstrap = TRUE, boot.R = 100)
summary(fit, unstandardized = TRUE)
```

To get more detailed results, including standard errors, we can use the
`unstandardized_estimates()` function directly.

```{r}
unstandardized_estimates(fit)
```

It is also possible to pass a vector of variable names, detailing which
variables should be unstandardized. The rules for different variables
are as follows:

  - **Observed Continuous Variables** are rescaled to their original standard deviations in the input data.
  - **Latent Variables** get rescaled by fixing their first factor loadings to 1.
  - **Composite Variables** are rescaled by fixing their first weight to 1.
  - **Observed Ordinal Variables** have their residual variance constrained to 1. If they do not have a residual
    variance (e.g., if they belong to a composite), they remain standardized.

Note that the observed and latent variables can be standardized separately. This
has implications for latent variables. Since we unstandardize latent/composite variables
by fixing the first loading/weight to 1, their scale is inherited from the first
indicator. That means that we will get a different result depending on whether the
first indicator gets unstandardized or not.

Here, for example, we can see that we get different results if we do not
unstandardize `x1` when unstandardizing `X`.

```{r}
# x1 is unstandardized
subset(
  unstandardized_estimates(fit, unstandardized = c("x1", "X")),
  lhs == "X" | rhs == "X"
)

# x1 is standardized
subset(
  unstandardized_estimates(fit, unstandardized = "X"),
  lhs == "X" | rhs == "X"
)
```