Path Analysis

Question 1

Exogenous variable

Answer 1

not caused by any other variable in the model

Question 2

Endogenous variable

Answer 2

at least partially by other variables in the model

Question 3

Direct effect

Answer 3

a direct effect on a variable is not mediated by any other variables (e.g. ability has an indirect effect on achievement via motivation)

Question 4

Indirect effect

Answer 4

an indirect effect on a variable is mediated by one or more variables (e.g. ability has an indirect effect on achievement via motivation).

Question 5

Spurious

Answer 5

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.

Question 6

Total Effect

Answer 6

Direct Effects + Indirect Effects.

Question 7

Correlation

Answer 7

Total effects (direct effects + indirect effects) + Spurious

Question 8

Disturbances

Answer 8

are any influences on the outcome not explained by the model (errors or residuals) - Sqrt (1-Rsquared).

Question 9

Observed variables are which shape and unobserved are:

Answer 9

Observed variables are rectangles.

Unobserved variables are circles

Question 10

Paths or causes

Answer 10

single headed arrow.

Question 11

Covariance

Answer 11

double headed arrow, non-causal

Question 12

Recursive Model

Answer 12

a variable cannot affect itself through another variable (i.e. you cannot loop back from that variable to itself)

Question 13

Non-Recursive Model

Answer 13

A variable affects itself through another variable (i.e. you can loop from that variable back to itself).

Question 14

Constraints on a path

Answer 14

prevent that path from being estimated or hold it constant

Question 15

Information

Answer 15

number of observed variables (k)

Question 16

Parameters or distinct sample moments (variances + covariances)

Answer 16

k(k+1)/2

degrees of freedom

Question 17

Identified model

Answer 17

has enough information to arrive at a unique solution for parameters

Question 18

Saturated or Just identified model

Answer 18

No missing paths (zero degrees of freedom).

Question 19

Under Identified model

Answer 19

Not enough information to solve for estimates (we have ‘extra’ paths such as two single arrow paths between two observed variables).

Question 20

Over Identified Model

Answer 20

Contains more than enough information to solve for the estimates (we are missing –> less paths than correlations –> multiple solutions for paths).

Question 21

Assumptions of Path Modelling

Answer 21

1. Errors normally distributed, independence amongst observations.
2. Exogenous variables perfectly measured.
3. State of equilibrium reached (the estimates are stable over time and therefore it’s reasonable to make those estimates).
4. Model includes common causes.
5. Paths in right direction

Question 22

Goodness of Fit

Answer 22

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.

Question 23

Degrees of Freedom: Parameters or distinct sample moments

Answer 23

This consists of variances + covariances

kx(k+1/2)

where k is the number of exogenous or endogenous variables

Question 24

Degrees of Freedom: Covariances

Answer 24

k (k-1/2)

Question 25

Number of parameters to be estimated

Answer 25

Number of Exogenous variables + Number of Disturbances/Errors + Paths (number of single headed arrows) + Covariances (number of double headed arrows)

Question 26

Baron and Kenny’s 4 steps for establishing mediation

Answer 26

1. Make sure the IV is correlated with the DV and it’s significant (do not model the MV).
2. Make sure the IV is correlated with the MV and it’s significant (do not model the DV).
3. Make sure the MV is correlated with the DV and it’s significant (make sure you include the IV in your model).
4. 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.