Add a section on simulating data

Author: coatless

02-simcdm.Rmd

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+#  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
+```
+
+### 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
+```
+
+### $\eta$ Matrix Simulation
+
+Create the ideal response matrix for each trait ($J$ items by $2^K$ latent classes).
+
+```{r sim-eta-matrix}
+# Set a seed for reproducibility
+set.seed(4421)
+# Simulate an eta matrix
+eta = sim_eta_matrix(K, J, Q)
+eta
+```
+
+### 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),]
+```
+
+### 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
+```
+