Path Analysis Flashcards
Exogenous variable
not caused by any other variable in the model
Endogenous variable
at least partially by other variables in the model
Direct effect
a direct effect on a variable is not mediated by any other variables (e.g. ability has an indirect effect on achievement via motivation)
Indirect effect
an indirect effect on a variable is mediated by one or more variables (e.g. ability has an indirect effect on achievement via motivation).
Spurious
is when the two variables are both being caused by a third variable (or more than one variable). For example, if we examine just motivation and achievement, ability is spurious.
Total Effect
Direct Effects + Indirect Effects.
Correlation
Total effects (direct effects + indirect effects) + Spurious
Disturbances
are any influences on the outcome not explained by the model (errors or residuals) - Sqrt (1-Rsquared).
Observed variables are which shape and unobserved are:
Observed variables are rectangles.
Unobserved variables are circles
Paths or causes
single headed arrow.
Covariance
double headed arrow, non-causal
Recursive Model
a variable cannot affect itself through another variable (i.e. you cannot loop back from that variable to itself)
Non-Recursive Model
A variable affects itself through another variable (i.e. you can loop from that variable back to itself).
Constraints on a path
prevent that path from being estimated or hold it constant
Information
number of observed variables (k)
Parameters or distinct sample moments (variances + covariances)
k(k+1)/2
degrees of freedom
Identified model
has enough information to arrive at a unique solution for parameters
Saturated or Just identified model
No missing paths (zero degrees of freedom).
Under Identified model
Not enough information to solve for estimates (we have ‘extra’ paths such as two single arrow paths between two observed variables).
Over Identified Model
Contains more than enough information to solve for the estimates (we are missing –> less paths than correlations –> multiple solutions for paths).
Assumptions of Path Modelling
- Errors normally distributed, independence amongst observations.
- Exogenous variables perfectly measured.
- State of equilibrium reached (the estimates are stable over time and therefore it’s reasonable to make those estimates).
- Model includes common causes.
- Paths in right direction
Goodness of Fit
This is a measure of how accurately the original variances can be reproduced from the estimated parameters of the model. This is reported as the magnitude of the discrepancies between the observed and reproduced variance-covariance matrices. It is not variance accounted for.
The default model is the one we wish to test. Our Chi Square statistic is given under CMin. It measures the difference between the reproduced covariance matrix and the entered matrix. We want a non-significant CMin because we don’t want a significant difference between our model and our data.
Degrees of Freedom: Parameters or distinct sample moments
This consists of variances + covariances
kx(k+1/2)
where k is the number of exogenous or endogenous variables
Degrees of Freedom: Covariances
k (k-1/2)
Number of parameters to be estimated
Number of Exogenous variables + Number of Disturbances/Errors + Paths (number of single headed arrows) + Covariances (number of double headed arrows)
Baron and Kenny’s 4 steps for establishing mediation
- Make sure the IV is correlated with the DV and it’s significant (do not model the MV).
- Make sure the IV is correlated with the MV and it’s significant (do not model the DV).
- Make sure the MV is correlated with the DV and it’s significant (make sure you include the IV in your model).
- Model the IV with the DV including the MV and ensure that the effect is reduced compared to modeling just the IV with the DV.
If the entire effect of the direct is due to the indirect effect, this is complete mediation. Otherwise it’s partial mediation.
