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)*(p1)]
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 noncausal

just identified model

(saturated model) has no df's
fit is perfectcant be falsified
 ksi

an exogenous (indep) latent variable

ksi vector

an n x 1 vector of latent exogenous variables
 lambdax

effects of ksi's on x's
 lambdax matrix
 effects of etas on x's
 lambday

effects of eta's on y's
 lambday 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

Model Equations : Structural
 eta= beta (eta) + gamma (ksi)+ zeta
 Model Equations: Measurement (Y)

Y= lambda (eta)+ epsilon

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
 thetadelta

covariance matrix of the disturbances (deltas) the measurement error of the X's
 thetaepsilon

covariance matrix of epsilon's (measurement error of y's)
includes variances on diagonal (correlation with self) and any correlations between errors
 thetaepsilon 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