Structural equations modelling
Covariance matrix
actual relationships between variables
Variables
Exogenous
independent
explain others but cannot be explained by variables
Endogenous
dependent
mediators
explained by other variables in model
correlation between them
confounding
Spss
Coefficients
standardized coefficients
Beta
Unstandardized coefficients
scale dependent
difficult to compare
0.1 small
0.3 medium
0.5 large
Models
saturated
always perfectly repoduced
not very informative
recursive
all paths go in one direction
Can also be tested in spss
least squares estimates
Lisrel uses Maximum likelyhood
Correlation matrix
amount of elements (variances and covariances)
k=amout of observed variables
k(k+10/2
k variances
matrices
Gamma matrix
regression of endogenous on exogenous
Beta matrix
regression endogenous on endogenous
phi matrix
(co)variance of exogenous variables
psi
error (co)variance of endogenous
Improving model
Modelling
freeing
Relaxes model
improves fit
Fixing
restricts model
improves parsimony
Identifiability
not identified cannot be estimated
nr of parameters you want to estimate shouldn't exceed the nr of independent elements in covariance matrix
nr of free parameters < k(k+1)/2
Fitted matrix trick
Fit
Local
significance of free parameters
modification indices of fixed parameters
Global
how wel it fits covariance matrix
how parsimoneous is the model
Output
T-value
should be >2
modification indices (MI)
for paths that are fixed to zero
Chi square
the lower the better
How much the chi square will decrease if path is freed
if >4 freeing will significantly improve fit
Should also make sense
2 values
minimum fit function
normal theory weigted
significant
bad fit
Dependent on N and DF
So not best measure of fit
Non normed fit index
best measure of fit
independence model
Assumes no relationships between variables
The closer to 1 the better
structural equations
direct effects
Reduced form equations
total effects
indirect and direct for exogenous
covariance matrix
phi matrix?
variances and covariances between exogenous
Also original covariance matrix
fitted covariance matrix
how they are reproduced
Residuals
Should be close to 0
Scale dependent
Fitted residuals
Standardized residuals
2 = not reproduced well
not scale dependent
Global fit measures
Goodness of fit
Assumptions
Normal distribution of variables
linear relations
Exceptions
exo var may be non normal/binary
Degrees of freedom
Formula
(co)variances - free parameters
(co)variances
(k(k+1))/2
Difference between nr of available (co)variances and nr of model parameters
If 0
Not parsimoneous
Free parameters
amount of relations that are specified