Steps to Fitting a Model in lavaan.Rmd

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```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE, warning = FALSE, message = FALSE)

library(tidySEM)
library(lavaan)
library(dplyr)
```
# Steps to Fitting a Model in `lavaan`

## 1. Draw your model on a piece of paper!

> Color any paths you may be interested in.

```{r, fig.height=2.5, out.width = '60%', fig.align='center'}
mod <- "
   Lat =~ 0.1*ind1 + 0.1*ind2 + 0.1*ind3
  ind1 ~~ 0.1*ind2
  ind1 ~~ 1*ind1
  ind2 ~~ 1*ind2
  ind3 ~~ 1*ind3
  Obs1 ~~ 0.1*Obs2
  Obs3 ~ 0.1*Obs1 + 0.1*Obs2
  Obs3 ~~ 1*Obs3
   Lat ~ 0.1*Obs1
   Lat ~~ 0*Lat
   Lat ~~ 0*Obs3
"

# lavaanify(mod, fixed.x=FALSE)

d <- simulateData(mod, sample.nobs = 100, fixed.x=FALSE, standardized = FALSE)

fit <- sem(mod, data = d)

lay <- get_layout(
  NA,     NA,    "Obs1", NA,     "Obs2",
  "ind1", NA,    NA,     NA,     NA,
  "ind2", "Lat", NA,     NA,     NA,
  "ind3", NA,    NA,     NA,     NA,
  NA,     NA,    NA,     "Obs3", NA,
  rows = 5
)

g <- prepare_graph(fit, layout = lay,
                   rect_height = 1.2,
                   ellipses_height = 1.2,
                   variance_diameter = 0.6)

edges(g) <- edges(g) %>% 
  filter(!(to == from & to %in% c("Lat", "Obs1", "Obs2")),
         !(from == "Lat" & to == "Obs3")) %>% 
  mutate(
    label = NA,
    linetype = "solid",
    color = "black",
    color = replace(color, from == "Obs1" & to == "Obs2", "orange"),
    color = replace(color, from == "Obs1" & to == "Obs3", "orange"),
    color = replace(color, from == "Obs2" & to == "Obs3", "blue"),
    arrow = replace(arrow, arrow=="none", "both"),
    connect_from = replace(connect_from, from==to & from == "ind1", "bottom"),
    connect_to = replace(connect_to, from==to & from == "ind1", "bottom"),
    connect_to = replace(connect_to, from=="Obs1" & to=="Lat", "right"),
    size = 0.5,
    size = replace(size, color != "black", 1)
  )

plot(g)
```

## 2. Write out your model speficication 

***Remember to use modifiers and to set fixed values where you need to!***

***Don't forget `lavaan`'s defaults:***

1. Loading to first indicator is fixed at 1.
2. All covariances between latent variables are estimated.
3. All error terms are estimated.

### 2.1. Identify each **latent variable** by its indicators (`=~`)

```
Lat =~ ind1 + ind2 + ind3
```

### 2.2. Predict each **endogenous variable** with a regression formula (`~`)

... according to its *incoming* arrows.

```
 Lat ~ Obs1
Obs3 ~ b * Obs1 + c * Obs2
```

### 2.3. Estimate co/variances (`~~`) for each **two headed arrow**

These include *auto-correlations*, and possibly any *error* / *disturbances* / *uniqueness variances*.

```
Obs1 ~~ a * Obs2
ind1 ~~ ind2

 Lat ~~ 0 * Lat
```

### 2.4. Define any computed parameters (`:=`)

(paths, differences, simple slopes, etc.)

```
indirect_path := a * b
  direct_path := c
        total := indirect_path + direct_path
```

### 2.5. Don't forget to add self-regressors

... if you have any covariances between **latent** and **observed** variables.

(You can also use single-indicator latent variables instead.)

## 3. Fit the model (`sem()` / `cfa()` / `growth()` / `lavaan()`)

## 4. Plot your model and look at the parameter table

Make sure there are no missing (or too many) arrows / parameters!

## 5. Carry on...

Asses fit, test hypotheses, compare models...