18-one-covariate-auto.Rmd

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, 
                      warning = FALSE,
                      message = FALSE) #Here, I have made it so that when you knit your .rmd, warnings and messages will not show up in the html markdown. 
library(extrafont)
loadfonts()
```

# Automatic 3-Step Covariate Only

------------------------------------------------------------------------

**Data source:**

This utilizes a dataset on undergraduate *Cheating* available from the `poLCA` package (Dayton, 1998): [See documentation here](https://cran.r-project.org/web/packages/poLCA/poLCA.pdf)

------------------------------------------------------------------------

## Load packages

```{r}
library(MplusAutomation)
library(tidyverse) #collection of R packages designed for data science
library(here) #helps with filepaths
library(janitor) #clean_names
library(gt) # create tables
library(cowplot) # a ggplot theme
library(DiagrammeR) # create path diagrams
library(glue) # allows us to paste expressions into R code
library(data.table) # used for `melt()` function  
library(poLCA)
library(reshape2)
```

------------------------------------------------------------------------

## Automated Three-Step

------------------------------------------------------------------------

*Application: Undergraduate Cheating behavior*


"Dichotomous self-report responses by 319 undergraduates to four questions about cheating behavior" (poLCA, 2016).

------------------------------------------------------------------------

Prepare data

```{r}

data(cheating)

cheating <- cheating %>% clean_names() 

df_cheat <-  cheating %>%                                  
  dplyr::select(1:4) %>%                                  
  mutate_all(funs(.-1)) %>%                                
  mutate(gpa = cheating$gpa)

# Detaching packages that mask the dpylr functions 
detach(package:poLCA, unload = TRUE)
detach(package:MASS, unload = TRUE)
```

------------------------------------------------------------------------

### R3STEP

**R3STEP** incorporates latent class predictors with mixture models. However, it is recommended to use the manual three-step.

------------------------------------------------------------------------

```{r, echo=FALSE, eval=TRUE, fig.align='center'}

grViz(" digraph cfa_model {

# The `graph` statement - No editing needed

    graph [layout = dot, overlap = true]
 
# Two `node` statements
 
# One for measured variables (box) 

    node [shape=box]
    GPA LieExam LiePaper Fraud CopyExam;
 
# One for latent variables (circle) 
 
    node [shape=circle]
    bully [label=<Cheating <br/>Behavior <br/>C<sub>k=2</sub>>];
    
# `edge` statements
 
    edge [minlen = 2]
    bully -> {LieExam LiePaper Fraud CopyExam}
    GPA -> bully [minlen = 4];
    
 {rank = same; bully; GPA}
 
 }") 
```

------------------------------------------------------------------------

#### Run the **R3STEP** model with `gpa` as the latent class predictor

```{r, cache = TRUE}

m_stepr  <- mplusObject(
  TITLE = "R3STEP - GPA as Predictor", 
  VARIABLE = 
   "categorical = lieexam-copyexam; 
    usevar = lieexam-copyexam;
    auxiliary = gpa (R3STEP);
    classes = c(2);",
  
  ANALYSIS = 
   "estimator = mlr; 
    type = mixture;
    starts = 500 100; 
    processors = 10;",
  
  OUTPUT = "sampstat patterns tech11 tech14;",
  
  PLOT = 
    "type = plot3; 
     series = lieexam-copyexam(*);",
  
  usevariables = colnames(df_cheat),
  rdata = df_cheat)

m_stepr_fit <- mplusModeler(m_stepr, 
                            dataout=here("three_step", "auto_3step", "r3step.dat"),
                            modelout=here("three_step", "auto_3step", "c2_r3step.inp") ,
                            check=TRUE, run = TRUE, hashfilename = FALSE)

```

------------------------------------------------------------------------

#### Regression slopes and odds ratios 


```
TESTS OF CATEGORICAL LATENT VARIABLE MULTINOMIAL LOGISTIC REGRESSIONS USING
THE 3-STEP PROCEDURE

   WARNING:  LISTWISE DELETION IS APPLIED TO THE AUXILIARY VARIABLES IN THE
   ANALYSIS.  TO AVOID LISTWISE DELETION, DATA IMPUTATION CAN BE USED
   FOR THE AUXILIARY VARIABLES FOLLOWED BY ANALYSIS WITH TYPE=IMPUTATION.
   NUMBER OF DELETED OBSERVATIONS:  4
   NUMBER OF OBSERVATIONS USED:  315

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

 C#1        ON
    GPA               -0.698      0.255     -2.739      0.006

 Intercepts
    C#1               -0.241      0.460     -0.523      0.601

Parameterization using Reference Class 1

 C#2        ON
    GPA                0.698      0.255      2.739      0.006

 Intercepts
    C#2                0.241      0.460      0.523      0.601


ODDS RATIOS FOR TESTS OF CATEGORICAL LATENT VARIABLE MULTINOMIAL LOGISTIC REGRESSIONS
USING THE 3-STEP PROCEDURE

                                                95% C.I.
                    Estimate       S.E. Lower 2.5% Upper 2.5%

 C#1        ON
    GPA                0.498      0.127      0.302      0.820


Parameterization using Reference Class 1

 C#2        ON
    GPA                2.009      0.512      1.220      3.310
```



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