#First, I estimate the model without equality constraints:

library(sem)

library(matrixcalc)

txt <- "1

.661 1

.630 .643 1

.270 .300 .268 1

.297 .265 .225 .805 1

.290 .287 .248 .796 .779 1"

memory.matrix <- data.matrix( read.table(text=txt, fill=TRUE, col.names=paste("X", 1:6)))

memory.matrix[upper.tri(memory.matrix)] <- t(memory.matrix)[upper.tri(memory.matrix)]

memory.matrix

rownames(memory.matrix)<-c("X.1", "X.2", "X.3", "X.4", "X.5", "X.6")

#verify that matrix is symmetric

isSymmetric(memory.matrix)

#verify that matrix is positive definite

is.positive.definite(memory.matrix, tol=0)

sd<-c(2.61, 2.66, 2.59, 1.94, 2.03, 2.05)

mean<-c(0,0,0,0,0,0)

memory<-cov2raw(memory.matrix, mean, 200, sd)

memory.model<-cfa(reference.indicators=FALSE)

Auditory: X.1, X.2, X.3

Visual: X.4, X.5, X.6

memory.fit <- sem(memory.model, memory, 200)

summary(memory.fit, digits=5, conf.level=.95,

fit.indices=c("GFI", "AGFI", "RMSEA", "NFI", "NNFI", "CFI", "RNI",

"IFI", "SRMR", "AIC", "AICc", "BIC", "CAIC"))

modIndices(memory.fit)

standardizedCoefficients(memory.fit)

#This model produces output and works fine

#respecify the model to test tau equivalence of auditory memory indicators

#we do this by constraining their factor loadings to be equal

memory2.model<-cfa(reference.indicators=FALSE)

Auditory:X.1=X.2=X.3

Visual: X.4, X.5, X.6

memory2.fit <- sem(memory2.model, memory, 200)

summary(memory2.fit, digits=5, conf.level=.95,

fit.indices=c("GFI", "AGFI", "RMSEA", "NFI", "NNFI", "CFI", "RNI",

"IFI", "SRMR", "AIC", "AICc", "BIC", "CAIC"))

#This model does not run. It says I have -3 df with the following error message:

#Error in sem.default(ram, S = S, N = N, raw = raw, data = data, pattern.number = #pattern.number, :

# The model has negative degrees of freedom = -3

#In addition: Warning message:

#In sem.semmod(memory2.model, memory, 200) :

# The following observed variables are in the input covariance or raw-moment #matrix but do not appear in the model:

#Intercept, X.1, X.2, X.3

Any advice you have would be greatly appreciated