SEM
Terms
- beta
-
The direct effect of an eta on another eta
effects of dependent variable on another dependent variable
- beta matrix
- effects of eta's on each other
-
calculating df's
-
# of variances=p
# of covariances= 1/2 [(p)*(p-1)]
total elements (#of variances plus # of covariances) 1/2[p*(p+1)]
degrees of freedom= number of total elements-#freed parameters
-
delta vector
- q x 1 vector of measurement errors of x
- determinant
- the product of a diagonal. indicates shared variance. large is bad. if the determinant is zero or less, there is no solution (singular). if larger than zero, matrix is "positive definite"
- disturbances
-
amount of variance unexplained
-
epsilon vector
-
a p x 1 vector of the measurement errors of y
-
eta vector
-
m x 1 vector of latent endogenous variables
-
free v fixed in a matrix
-
1= free to be estimated
0=fixed
- Gamma
-
Effect of ksi's on etas
effects of indep variables on dep variables
- gamma matrix
- effects of ksi's on etas
- identification
-
whether or not you can estimate all freed parameters given the known parameters
-
identity matrix
-
matrix with 1s on diagonals and zeros off diagonal
1 0 0
0 1 0
0 0 1
-
implied correlations
- direct path between variables plus the sum of products of indirect paths plus non-causal
-
just identified model
-
(saturated model) has no df's
fit is perfect--cant be falsified
- ksi
-
an exogenous (indep) latent variable
-
ksi vector
-
an n x 1 vector of latent exogenous variables
- lambda-x
-
effects of ksi's on x's
- lambda-x matrix
- effects of etas on x's
- lambda-y
-
effects of eta's on y's
- lambda-y matrix
- effects of etas on y's
-
matrix inverse
-
what you multiply a matrix by to get the identity matrix. to see if your sigma matrix is close to the observed matrix, you multiply by the inverse and hope to get the identity matrix
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Model Equations : Structural
- eta= beta (eta) + gamma (ksi)+ zeta
- Model Equations: Measurement (Y)
-
Y= lambda (eta)+ epsilon
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Model Equations: Measurement (X)
-
X= lambda (ksi) +delta
-
overidentified model
-
has enough degrees of freedom to estimate multiple solutions (df=positive)
- Phi
-
covariance matrix of the ksi's
covariance between independent variables
along the diagonal
- phi matrix
- covariance of ksi's
- Psi
-
covariance matrix of zetas
covariance of structural error with Psi's on diagonal
- psi matrix
- covariance of zeta
- R^2
- variance explained by whole model
- theta-delta
-
covariance matrix of the disturbances (deltas) the measurement error of the X's
- theta-epsilon
-
covariance matrix of epsilon's (measurement error of y's)
includes variances on diagonal (correlation with self) and any correlations between errors
- theta-epsilon matrix
- covariance of errors (epsilons) or deltas
-
underidentified model
- not enough df's to generate a unique solution
-
x vector
-
a q x1 vector of observed exogenous variables
-
y vector
- a p x 1 vector of observed endogenous variables
-
zeta matrix
-
m x 1 vector of residuals representing errors in the equation that relates eta and ksi
part of structural equation
a vector