Dear all,
According to the tutorial, inspect "returns a list of the model matrices that are used internally to represent
the model". But what exactly are those matrices?
For CFA, with these code:
model <- 'O =~ o1 + o2 + o3 + o4 + o5
T =~ t1 + t2 + t3 + t4
G =~ g1 + g2 + g3'
fit <- cfa(model, data=data) #data is just a table of data
inspect(fit, "standardized")
Output:
$lambda
O T G
o1 0.870 0.000 0.000
o2 0.909 0.000 0.000
o3 0.834 0.000 0.000
o4 0.830 0.000 0.000
o5 0.881 0.000 0.000
t1 0.000 0.834 0.000
t2 0.000 0.861 0.000
t3 0.000 0.804 0.000
t4 0.000 0.799 0.000
g1 0.000 0.000 0.811
g2 0.000 0.000 0.876
g3 0.000 0.000 0.893
$theta
o1 o2 o3 o4 o5 t1 t2 t3 t4 g1 g2 g3
o1 0.243
o2 0.000 0.173
o3 0.000 0.000 0.304
o4 0.000 0.000 0.000 0.311
o5 0.000 0.000 0.000 0.000 0.223
t1 0.000 0.000 0.000 0.000 0.000 0.305
t2 0.000 0.000 0.000 0.000 0.000 0.000 0.259
t3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.353
t4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.362
g1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.343
g2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.233
g3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.202
$psi
OC TC TGC
OC 1.000
TC 0.148 1.000
TGC 0.346 0.447 1.000
I believe lambda is factor loading; psi is the correlation between constructs. But what is theta?
For SEM, with these code:
model1 <- 'O =~ o1 + o2 + o3 + o4 + o5
T =~ t1 + t2 + t3 + t4
G =~ g1 + g2 + g3
P =~ p1 + p2 + p3
P ~ OC + TC + TGC'
fit1 <- sem(model1, data=data)
inspect(fit1)
Output:
$lambda
O T G P
o1 0 0 0 0
o2 1 0 0 0
o3 2 0 0 0
o4 3 0 0 0
o5 4 0 0 0
t1 0 0 0 0
t2 0 5 0 0
t3 0 6 0 0
t4 0 7 0 0
g1 0 0 0 0
g2 0 0 8 0
g3 0 0 9 0
p1 0 0 0 0
p2 0 0 0 10
p3 0 0 0 11
$theta
o1 o2 o3 o4 o5 t1 t2 t3 t4 g1 g2 g3 p1 p2 p3
o1 15
o2 0 16
o3 0 0 17
o4 0 0 0 18
o5 0 0 0 0 19
t1 0 0 0 0 0 20
t2 0 0 0 0 0 0 21
t3 0 0 0 0 0 0 0 22
t4 0 0 0 0 0 0 0 0 23
g1 0 0 0 0 0 0 0 0 0 24
g2 0 0 0 0 0 0 0 0 0 0 25
g3 0 0 0 0 0 0 0 0 0 0 0 26
p1 0 0 0 0 0 0 0 0 0 0 0 0 27
p2 0 0 0 0 0 0 0 0 0 0 0 0 0 28
p3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29
$psi
OC TC TGC P
OC 30
TC 34 31
TGC 35 36 32
P 0 0 0 33
$beta
OC TC TGC P
OC 0 0 0 0
TC 0 0 0 0
TGC 0 0 0 0
P 12 13 14 0
What do lambda, theta, psi and beta respectively represent?
Thank you in advance for your help!