02-simcdm.Rmd

#  simcdm: Simulate Cognitive Diagnostic Model Data {#simcdm}

```{r load-r-pkg, include = FALSE}
library(simcdm)
```

## Matrix Simulation

Simulations within this section are done underneath the following settings.

```{r setup-matrix-sims}
# Set a seed for reproducibility
set.seed(888)
# Setup Parameters
N = 15   # Number of Examinees / Subjects
J = 10   # Number of Items
K = 2    # Number of Skills / Attributes
```

### Attribute profile simulation

Generate latent attribute profile classes ($2^K$ latent classes by $K$ skills).

```{r attribute-classes-gen}
# Create a listing of all attribute classes 
class_alphas = attribute_classes(K)
class_alphas
```

Generate latent attribute profile class for each subject ($N$ subjects by $K$ skills).

```{r sim-subject-attributes}
# Set a seed for reproducibility
set.seed(5126)
# Create attributes for a subject 
subject_alphas = sim_subject_attributes(N, K)
subject_alphas
# Equivalent to:
# subject_alphas = class_alphas[sample(2 ^ K, N, replace = TRUE),]
```


### Identifiable Q Matrix Simulation

Simulate an identifiable $Q$ matrix  ($J$ items by $K$ skills).

```{r sim-q-matrix}
# Set a seed for reproducibility
set.seed(1512)
# Simulate an identifiable Q matrix
Q = sim_q_matrix(J, K)
Q
```

## DINA Simulation

Simulations within this section are done underneath the following settings.

```{r setup-sim-dina}
# Set a seed for reproducibility
set.seed(888)
# Setup Parameters
N = 15   # Number of Examinees / Subjects
J = 10   # Number of Items
K = 2    # Number of Skills / Attributes
# Assign slipping and guessing values for each item
ss = gs = rep(.2, J)
# Simulate identifiable Q matrix
Q = sim_q_matrix(J, K)
# Simulate subject attributes
subject_alphas = sim_subject_attributes(N, K)
```

### DINA Item Simulation

Simulate item data, $Y$, under DINA model ($N$ by $J$)

```{r sim-dina-items}
# Set a seed for reproducibility
set.seed(2019)
# Simulate items under the DINA model
items_dina = sim_dina_items(subject_alphas, Q, ss, gs)
items_dina
```

### DINA Attribute Simulation

Simulate attribute data under DINA model ($N$ by $J$)

```{r sim-dina-attributes}
# Set a seed for reproducibility
set.seed(51823)
# Simulate attributes under the DINA model
attributes = sim_dina_attributes(subject_alphas, Q)
attributes
```

## rRUM Simulation

The rRUM simulations are done using the following settings.

```{r rrum-sim-setup}
# Set a seed for reproducibility
set.seed(888)
# Setup Parameters
N = 15   # Number of Examinees / Subjects
J = 10   # Number of Items
K = 2    # Number of Skills / Attributes
# The probabilities of answering each item correctly for individuals 
# who do not lack any required attribute
pistar = rep(.9, J)
# Simulate an identifiable Q matrix
Q = sim_q_matrix(J, K)
# Penalties for failing to have each of the required attributes
rstar  = .5 * Q
# Latent Class Probabilities
pis = c(.1, .2, .3, .4)
# Generate latent attribute profile with custom probability (N subjects by K skills)
subject_alphas = sim_subject_attributes(N, K, prob = pis)
# Equivalent to:
# class_alphas = attribute_classes(K)
# subject_alphas = class_alphas[sample(2 ^ K, N, replace = TRUE, prob = pis),]
```

### Simulate rRUM items

Simulate rRUM item data $Y$ ($N$ by $J$)

```{r sim-rrum}
# Set a seed for reproducibility
set.seed(912)
# Generate rRUM items
rrum_items = sim_rrum_items(Q, rstar, pistar, subject_alphas)
rrum_items
```