---
title: "DINA_FOHM"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{DINA_FOHM}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
library(hmcdm)
```

### Load the spatial rotation data

```{r}
N = length(Test_versions)
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = nrow(Test_order)
Jt = J/L
```


## (1) Simulate responses and response times based on the DINA_FOHM model

```{r}
TP <- TPmat(K)
Omega_true <- rOmega(TP)
class_0 <- sample(1:2^K, N, replace = L)
Alphas_0 <- matrix(0,N,K)
for(i in 1:N){
 Alphas_0[i,] <- inv_bijectionvector(K,(class_0[i]-1))
}
Alphas <- sim_alphas(model="FOHM", Omega = Omega_true, N=N, L=L)
itempars_true <- matrix(runif(J*2,.1,.2), ncol=2)

Y_sim <- sim_hmcdm(model="DINA",Alphas,Q_matrix,Design_array,
                   itempars=itempars_true)
```


## (2) Run the MCMC to sample parameters from the posterior distribution

```{r}
output_FOHM = hmcdm(Y_sim,Q_matrix,"DINA_FOHM",Design_array,100,30)
output_FOHM
summary(output_FOHM)
a <- summary(output_FOHM)
head(a$ss_EAP)
```

## (3) Check for parameter estimation accuracy

```{r}
AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec

PAR_vec <- numeric(L)
for(t in 1:L){
  PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
```


## (4) Evaluate the fit of the model to the observed response

```{r}
a$DIC
head(a$PPP_total_scores)
head(a$PPP_item_means)
head(a$PPP_item_ORs)

```