pcirm-examples

Note: the estimation process can be time consuming depending on the computing power. You can same some time by reducing the length of the chains.

Dichotomous Data with Local Dependence and Minor Trait:

1. Load the package, obtain the data, loading pattern (qlam), and no. of factors/traits.

library(LAWBL)
dat <- sim24ccfa21$dat
head(dat)
R>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
R> [1,]    2    1    2    2    2    2    1    2    1     1     1     1     1     1
R> [2,]    2    1    2    1    2    2    2    2    2     2     2     2     2     1
R> [3,]    1    1    1    1    1    1    1    1    2     2     1     1     2     2
R> [4,]    1    1    1    1    1    1    1    1    1     1     1     1     2     2
R> [5,]    1    1    1    2    1    1    1    1    2     1     1     2     1     1
R> [6,]    1    2    2    2    2    1    2    1    2     1     1     1     1     1
R>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
R> [1,]     1     1     2     2     1     1     1     1     1     1
R> [2,]     1     1     2     2     2     2     2     2     1     2
R> [3,]     2     1     1     1     1     2     1     1     2     1
R> [4,]     2     2     1     1     2     2     2     1     2     2
R> [5,]     1     1     1     1     1     1     1     1     1     1
R> [6,]     1     1     1     2     1     1     1     1     1     1
J <- ncol(dat) # no. of items
qlam <- sim24ccfa21$qlam
qlam
R>       [,1] [,2] [,3] [,4]
R>  [1,]  0.7  0.0  0.0 0.00
R>  [2,]  0.7  0.0  0.0 0.00
R>  [3,]  0.7  0.0  0.0 0.00
R>  [4,]  0.7  0.0  0.0 0.00
R>  [5,]  0.7  0.0  0.0 0.00
R>  [6,]  0.7  0.0  0.0 0.00
R>  [7,]  0.7  0.0  0.0 0.00
R>  [8,]  0.7  0.0  0.0 0.00
R>  [9,]  0.0  0.7  0.0 0.00
R> [10,]  0.0  0.7  0.0 0.00
R> [11,]  0.0  0.7  0.0 0.00
R> [12,]  0.0  0.7  0.0 0.00
R> [13,]  0.0  0.7  0.0 0.00
R> [14,]  0.0  0.7  0.0 0.00
R> [15,]  0.0  0.7  0.0 0.55
R> [16,]  0.0  0.7  0.0 0.55
R> [17,]  0.0  0.0  0.7 0.00
R> [18,]  0.0  0.0  0.7 0.00
R> [19,]  0.0  0.0  0.7 0.00
R> [20,]  0.0  0.0  0.7 0.00
R> [21,]  0.0  0.0  0.7 0.00
R> [22,]  0.0  0.0  0.7 0.00
R> [23,]  0.0  0.0  0.7 0.55
R> [24,]  0.0  0.0  0.7 0.55
K <- ncol(qlam) # no. of factors

2. PCIRM with primary loadings and three traits specified. Longer chain is suggested for stabler performance (burn=iter=5,000 by default).

ipf <- 8
Q<-matrix(-1,J,K-1); # -1 for unspecified items
Q[1:8,1]<-Q[9:16,2]<-Q[17:24,3]<-1
Q
m0<-pcirm(dat = dat,Q=  Q,LD = TRUE,cati = -1,burn = 2000,iter = 2000,verbose = TRUE)
summary(m0)
summary(m0, what = 'qlambda')
summary(m0, what = 'offpsx') #summarize significant LD terms
summary(m0,what='int')
summary(m0,what='eigen')

#plotting factorial eigenvalue
plot_eigen(m0) # trace
plot_eigen(m0, what='density') #density
plot_eigen(m0, what='APSR') #adj, PSRF

3. PCIRM-LI with four traits and two cross-loadings specified based on results from previous step. Longer chain is suggested for stabler performance.

Q<-cbind(Q,-1);
Q[c(15:16),K] <- 1

m1<-pcirm(dat = dat,Q=  Q,LD = FALSE, cati = -1,burn = 4000,iter = 4000,verbose = TRUE)
summary(m1)
summary(m1, what = 'qlambda') #close to qlam

4. PCIRM with four traits and four cross-loadings specified based on results from previous step. Longer chain is suggested for stabler performance.

tmp<-summary(m1, what="qlambda")
Q<-matrix(-1,J,K)
Q[tmp!=0]<-1
Q

m2<-pcirm(dat = dat,Q=  Q,LD = TRUE,cati = -1,burn = 4000,iter = 4000,verbose = TRUE)
summary(m2)
summary(m2, what = 'qlambda')
summary(m2, what = 'offpsx') #summarize significant LD terms
summary(m2,what='int')
summary(m2,what='eigen')

#plotting factorial eigenvalue
plot_eigen(m2) # trace
plot_eigen(m2, what='density') #density
plot_eigen(m2, what='APSR') #adj, PSRF