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Jodie
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Path Analysis
Definition and advantages of a path analysis
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Primary goal of path analysis is to express relationships between variables in terms of direct or indirect effects based on a causal model assumed to be correct
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Used to decompose the correlations between variables
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Tests how well the model fits the actual data
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Calculates direct and indirect effects quickly
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Requires a path diagram which forces research to specify the model and consider casual correlations
Steps of a Path Analysis
1) Specify a model
Singleheaded arrows = indicate a hypothesised causal direction
Doubleheaded arrows = indicate correlation between exogenous variables, which might arise through a common cause or their reciprocal causation.
Squares = indicate the observed variables, something that is being directly measured
Circles = for latent variables
2) Identification
The rule is that the number of knowns must be equal or exceed the number of unknowns.
‘Knowns’ = how many correlations/paths there are = Variables x (Variables – 1) divided by 2
‘Unknowns’ = the number of paths between observed variables (total number of arrows) in the path diagram
Overidentified = more correlations than paths to estimate (good)
Justidentified = correlations equal to number of paths to estimate (good)
Underidentified = fewer correlations than there are paths to be estimated (bad)
3)
Estimate / running a model
Direct, Indirect and Total Effects
Direct Effect = the direct effect of the causal variable on the endogenous variable (DV) controlling for other variables going into the same endogenous variable (DV)
Indirect Effect = the effect of one variable on another via another mediating variable
Total Effect = the total causal effect of one variable on another Direct + Indirect = Total effect
0.10
Small effect
0.30
Medium effect
0.50
Large effect
Exogenous Variables and Endogenous Variables, Errors
Exo = Independent variables

No single headed arrows going in
Endo = Dependent variables

Have one or more arrows coming in
Errors/disturbances = Latent variables

Endogenous variable has an error term reflecting a unspecified causes, it is unmeasured (seen in the circles in the path diagram)
Recursive and NonRecursive Models
Recursive
Nonrecursive

Most common

One direction only (single headed arrows)

Always seen as identified

Bidirectional relationships

More complex to analyse

Arrows going both ways
Causation
Correlation = Causation
How to put together a causal model?
Time
If one variable occurs before another in time, easy to specify a causal direction
Theory
Causal direction of paths can be based on an informed theory
Previous research
Understanding of previous literature can influence the causal direction of paths
Logic
The flow of the paths should be logical and make sense
Model Fit
Chi
square
Need a nonsig result for good fit – tells you the model is nonsignificantly different from the perfect model despite fewer paths
Chisquare compares reduced paths model vs. the perfect (all paths) model
Saturated models are a good reference point because it offers prediction of all correlations
SRMR
SRMR of 0.10 (above) is a poor fit
Popular fit measure Asses the approx. fit of a model rewarding parsimony
A model with fewer paths will be favoured
CFI
CFI >0.95 (above) is a good fit
Different approach to model fit
Compares researchers’ model with baseline model
Samples and Implied Correlations

Sample correlations = actual correlations from the data

Implied correlations = predicted by the model, adding up the direct and indirect paths

Saturated model = when you include every path in your path diagram, such models are not recommended

Reduced model = only some paths are used based on theory estimation.
Covariance – used to see where there is misspecification
Covariance residuals:
The difference between the observed covariance based on the sample and the covariances that are implied
Standardised covariance residuals: more useful for identifying areas of potential misspecification. Look for values that exceed 1.96
Modification Indices / Model Refinement
Modification Indices (MI): Value indicates the degree of the chisquare goodness of fit value is expected to decrease because of adding a suggested path.

A value (more than)>3.84, giving p<.05 in MI column suggests that including an extra path will make the model more significantly a better model fit.

The larger the MI the greater the improvement in model fit

Used to add individual paths
EPC = estimates the path weight if the path was added
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Model Building: When a set of paths are added to the model, used for simpler models, adding extra paths significantly improves model fit
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Model Trimming: When a set of paths are removed from the model, usually used for complex models.
Theoretical approach vs Empirical approach
Theoretical
Empirical
Theory based considerations Previous research
prior
Based on statistical
Paths are examined to see which ones significantly improve the model Capitalise on chance Need to be replicated
Study