added dina independent

Author: sylee30

.DS_Store

@@ -1,3 +1,41 @@
+@article{Junker2001,
+  year={2001},
+  journal={Applied Psychological Measurement},
+  title={Cognitive assessment models with few assumptions, and connections with nonparametric item response theory},  
+  author={Junker, Brian, and  Sijtsma, Klaas },
+  pages={258-272},
+  volume = {25}
+}
+@book{tatsuoka1984,
+  title={Analysis of errors in fraction addition and subtraction problems},
+  author={Tatsuoka, Kikumi K},
+  year={1984},
+  publisher={Computer-based Education Research Laboratory, University of Illinois}
+}
+@article{de2009dina,
+  title={DINA model and parameter estimation: A didactic},
+  author={{de la Torre}, Jimmy},
+  journal={Journal of Educational and Behavioral Statistics},
+  volume={34},
+  number={1},
+  pages={115--130},
+  year={2009}
+}
+@book{rupp:2010,
+	Address = {New York},
+	Author = {Rupp, A. A. and Templin, J. L. and Henson, R. A.},
+	Publisher = {Guilford},
+	Title = {Diagnostic assessment: Theory, methods, and applications},
+	Year = 2010
+}
+@article{delatorre2004,
+  year={2004},
+  journal={Psychometrika},
+  title={Higher-order latent trait models for cognitive diagnosis},
+  author={Jimmy {de la torre} and Jeffrey A. Douglas  },
+  pages={333-353},
+  volume = {69}
+}
 @article{gelman2008weakly,
   title={A weakly informative default prior distribution for logistic and other regression models},
   author={Gelman, Andrew and Jakulin, Aleks and Pittau, Maria Grazia and Su, Yu-Sung},

education/.DS_Store

@@ -0,0 +1,76 @@
+data{
+	int<lower=1> I;			// # of items
+	int<lower=1> J;			// # of respondents		
+	int<lower=1> K;			// # of attributes
+	int<lower=1> C;			// # of attribute profiles (latent classes)	
+	matrix[J,I] y;			// response matrix
+	matrix[C,K] alpha;		// attribute profile matrix
+	matrix[I,C] xi;			// the global attribute mastery indicator (product of alpha^q-element)
+}
+
+parameters{
+	row_vector<lower=0,upper=1>[K] eta;	// probabilities of each attribute mastery
+	real<lower=0,upper=1> slip[I];		// slip parameter	
+	real<lower=0,upper=1> guess[I];		// guess parameter
+}
+
+transformed parameters{
+	simplex[C] nu; 					// probabilities of latent class membership
+	vector[C] log_nu;
+	for (c in 1:C){
+		nu[c] = 1;
+		for (k in 1:K){
+			nu[c] = nu[c] * eta[k]^alpha[c,k] 
+					* (1 - eta[k])^(1 - alpha[c,k]);		
+		}	
+	}
+	log_nu = log(nu);
+}
+
+model{
+	real ps[C];				// temp for log component densities
+	real pi;
+	real log_items[I];
+	slip ~ beta(5,25);
+	guess ~ beta(5,25);
+	for (j in 1:J){
+		for (c in 1:C){
+			for (i in 1:I){
+				pi = (1 - slip[i])^xi[i,c] * guess[i]^(1 - xi[i,c]);
+				log_items[i] = y[j,i] * log(pi)
+						+ (1 - y[j,i]) * log(1 - pi);		
+			}
+			ps[c] = log_nu[c] + sum(log_items);	
+		}
+		target += log_sum_exp(ps);
+	}
+
+}
+
+generated quantities {
+	matrix[J,C] prob_resp_class;	// posterior probabilities of respondent j being in latent class c 
+	matrix[J,K] prob_resp_attr;		// posterior probabilities of respondent j being a master of attribute k 
+	real pi;
+	real log_items[I];
+	row_vector[C] prob_joint;
+	real prob_attr_class[C];
+ 	for (j in 1:J){
+		for (c in 1:C){
+			for (i in 1:I){
+				pi = (1 - slip[i])^xi[i,c] * guess[i]^(1 - xi[i,c]);
+				log_items[i] = y[j,i] * log(pi)
+						+ (1 - y[j,i]) * log(1 - pi);
+			}
+			prob_joint[c] = nu[c] * exp(sum(log_items));
+		}
+		prob_resp_class[j] = prob_joint/sum(prob_joint);
+	}
+ 	for (j in 1:J){
+		for (k in 1:K){
+			for (c in 1:C){
+				prob_attr_class[c] = prob_resp_class[j,c] * alpha[c,k];
+			}		
+			prob_resp_attr[j,k] = sum(prob_attr_class);
+		}
+	}	
+}

education/bibliography.bib

@@ -0,0 +1,67 @@
+data{
+	int<lower=1> I;			// # of items
+	int<lower=1> J; 		// # of respondents	
+	int<lower=1> K;			// # of attributes
+	int<lower=1> C;			// # of attribute profiles (latent classes)	
+	matrix[J,I] y;			// response matrix
+	matrix[C,K] alpha;		// attribute profile matrix
+	matrix[I,C] xi;			// the global attribute mastery indicator (product of alpha^q-element)
+}
+
+parameters{
+	simplex[C] nu; 					    // probabilities of latent class membership
+	real<lower=0,upper=1> slip[I];		// slip parameter	
+	real<lower=0,upper=1> guess[I];		// guess parameter
+}
+
+transformed parameters{
+	vector[C] log_nu;
+	log_nu = log(nu);
+}
+
+model{
+	real ps[C];				// temp for log component densities
+	real pi;
+	real log_items[I];
+	slip ~ beta(5,25);
+	guess ~ beta(5,25);
+	for (j in 1:J){
+		for (c in 1:C){
+			for (i in 1:I){
+				pi = (1 - slip[i])^xi[i,c] * guess[i]^(1 - xi[i,c]);
+				log_items[i] = y[j,i] * log(pi)
+						+ (1 - y[j,i]) * log(1 - pi);
+			}
+			ps[c] = log_nu[c] + sum(log_items);	
+		}
+		target += log_sum_exp(ps);
+	}
+}
+
+generated quantities {
+	matrix[J,C] prob_resp_class;	// posterior probabilities of respondent j being in latent class c 
+	matrix[J,K] prob_resp_attr;		// posterior probabilities of respondent j being a master of attribute k 
+	real pi;
+	real log_items[I];
+	row_vector[C] prob_joint;
+	real prob_attr_class[C];
+ 	for (j in 1:J){
+		for (c in 1:C){
+			for (i in 1:I){
+				pi = (1 - slip[i])^xi[i,c] * guess[i]^(1 - xi[i,c]);
+				log_items[i] = y[j,i] * log(pi)
+						+ (1 - y[j,i]) * log(1 - pi);
+			}
+			prob_joint[c] = nu[c] * exp(sum(log_items));
+		}
+		prob_resp_class[j] = prob_joint/sum(prob_joint);
+	}
+ 	for (j in 1:J){
+		for (k in 1:K){
+			for (c in 1:C){
+				prob_attr_class[c] = prob_resp_class[j,c] * alpha[c,k];
+			}		
+			prob_resp_attr[j,k] = sum(prob_attr_class);
+		}
+	}	
+}