R08

		Confirmatory Factor Analysis

# Psychological Test Results Data (from book)

data(Harman74.cor)		
test.cor <- Harman74.cor$cov[c(6, 7, 9, 10, 12),c(6, 7, 9, 10, 12)]
colnames(test.cor) <- c("PARA","SENT","WORD","ADD","COUNT")
rownames(test.cor) <- colnames(test.cor)

test.cor


library(sem)		# CFA - A subset of Structural Equation Models
			# Requires installation of sem package
			

model2.test <- specify.model()		# Set up your model
F1 -> PARA,		lam11, NA	# Common Factor loadings
F1 -> SENT,		lam21, NA
F1 -> WORD,		lam31, NA
F2 -> ADD,		lam42, NA
F2 -> COUNT,		lam52, NA
PARA <-> PARA,		th1, NA		# Specific Factor Variances
SENT <-> SENT,		th2, NA
WORD <-> WORD,		th3, NA
ADD  <-> ADD,		th4, NA
COUNT <-> COUNT,	th5, NA
F1 <-> F2,		ph12, NA	# Common Factor Covariance(s)
F1 <-> F1,		NA, 1		# Common Factor Variances (fixed to 1)
F2 <-> F2,		NA, 1
					# Blank line to end input

model2.test

cfa2.test <- sem(model2.test, test.cor, 145)

cfa2.test
summary(cfa2.test)


model1.test <- specify.model()		# Change to 1-factor model
F1 -> PARA,		lam11, NA	
F1 -> SENT,		lam21, NA
F1 -> WORD,		lam31, NA
F2 -> ADD,		lam42, NA
F2 -> COUNT,		lam52, NA
PARA <-> PARA,		th1, NA		
SENT <-> SENT,		th2, NA
WORD <-> WORD,		th3, NA
ADD  <-> ADD,		th4, NA
COUNT <-> COUNT,	th5, NA
F1 <-> F2,		NA, 1		# Fix correlation as 1
F1 <-> F1,		NA, 1		# (forces factors to be the same)
F2 <-> F2,		NA, 1

cfa1.test <- sem(model1.test, test.cor, 145)

summary(cfa1.test)	# Note changes to chi-square, GFI, AGFI

# Likelihood ratio test comparing the two

pchisq(59.473 - 2.9306, 5 - 4, lower.tail=F)




# Expert Ratings of Wine-Growing Area's statuses

wine <- read.table("H:/S5600/Data sets/ASCII/Ch06/WINE_STATUS.txt")

wine

wine.cor <- cor(wine)

wine.cor

model1.wine <- specify.model()		# Single factor model
STATUS -> V1,		lam1, NA
STATUS -> V2,		lam2, NA
STATUS -> V3,		lam3, NA
STATUS -> V4,		lam4, NA
STATUS -> V5,		lam5, NA
V1 <-> V1,		th1, NA
V2 <-> V2,		th2, NA
V3 <-> V3,		th3, NA
V4 <-> V4,		th4, NA
V5 <-> V5,		th5, NA
STATUS <-> STATUS,	NA, 1

cfa1.wine <- sem(model1.wine, wine.cor, 59)

summary(cfa1.wine)

# Restrict to a common loading, and
# specific factor variance on the experts

model1r.wine <- specify.model()		
STATUS -> V1,		lam1, NA	# Note all loadings have the
STATUS -> V2,		lam1, NA	# same name now
STATUS -> V3,		lam1, NA
STATUS -> V4,		lam1, NA
STATUS -> V5,		lam1, NA
V1 <-> V1,		th1, NA		# As do all the variances
V2 <-> V2,		th1, NA
V3 <-> V3,		th1, NA
V4 <-> V4,		th1, NA
V5 <-> V5,		th1, NA
STATUS <-> STATUS,	NA, 1

cfa1r.wine <- sem(model1r.wine, wine.cor, 59)

summary(cfa1r.wine)

# Likelihood ratio test comparing the two

pchisq(15.618 - 6.755, 13 - 5, lower.tail=F)