Lecture 13_Path Analysis using MLR Flashcards Preview

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Flashcards in Lecture 13_Path Analysis using MLR Deck (16)
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1
Q

What is Path Analysis (PA)?

A

a method for decomposing the correlation coefficients
into component parts (direct and indirect effects) within a system of causally related variables (another way of applying MLR).
– requires the investigator to theorize about the causal relations among a set of variables and apply this framework to decompose the correlations among the variables.

2
Q

What are Path coefficients?

A

standardized regression coefficients (β) obtained from a set of inter-related regression models.

3
Q

What are three explanations for why X and Y appear correlated?

A

X causes Y
Y causes X
X and Y have a common cause Z

4
Q

What are the component parts of a correlation?

A

– Direct Effects (DE)
– Indirect Effects (IE)
– Spurious Effects (S) - due to common causes
– Unanalyzed Effects (U) - due to correlated causes

5
Q

How could a path model provide support for the proposed theory?

A

If the estimates from the path model are consistent with the observed data

6
Q

What are the 5 assumptions of Path Analysis?

A
  1. The relations among the variables are linear, additive, and causal.
  2. The residuals are uncorrelated (each residual is not correlated with the variables that precede it in the model).
  3. There is a one-way causal flow in the system. Reciprocal causation between variables is ruled out.
  4. The variables are measured on an interval level scale (categorical variables don’t work because no dummy coding).
  5. The variables are measured without error (use variables with high reliability).
7
Q

What is an exogenous variable?

A

a variable whose variability is assumed to be determined by causes outside the model.
– No attempt is made to explain its variability or its relations to other exogenous variables.
– Treated as “givens” and remain unanalyzed.

8
Q

What is an endogenous variable?

A

a variable that is predicted by other variables [variation is explained by exogenous (or other endogenous) variables in the system under study].
– can also be predictors too

9
Q

Describe the notation for a path coefficient (p₃₁ or p₃₂)

A

– the first number indicates the variable that the arrow points to
– the second number indicates where the arrow originates

10
Q

What is a just-identified path model?

A

number of path coefficients = the number of correlation coefficients
– has as many parameters as data points.
– always reproduce correlations perfectly

11
Q

What is a over-identified path model?

A

has fewer path coefficients than correlations (more knowns than unknowns)
– may reproduce the correlations adequately

12
Q

What is Theory Trimming in Path Analysis?

A

Deleting trivial paths to build a simpler model
– If does not significantly degrade the fit of the model, parsimony dictates that the simpler (over-identified) theory is to be preferred

13
Q

How can we assess the fit of an over-identified path model against a just-identified model?

A

in terms of variance explained.
• The proportion of variance explained by the just-identified model is defined as:
R²(sub-m) = 1 - [(1 - R²₁)(1 - R²₂) … (1 - R²ᵢ)]
• The proportion of variance explained by the over-identified model is defined as:
M = 1 - [(1 - R²₁)(1 - R²₂) … (1 - R²ᵢ)]
** The smaller M is, when compared to R²(sub-m), the poorer the fit of the over-identified model to the data.
(M &laquo_space;R²(sub-m) = over-identified model not good)

14
Q

What is a measure of relative goodness-of-fit?

A

Q = [1 - R²(sub-m)] / [1 - M]
• When Q is close to 1.0, the over-identified model fits the data well relative to the just-identified model
• Q is distributed as χ² and can be tested for significance (desired result is a nonsignificant test).
χ² = - (N - d) ln(Q)
[N = sample size and d = # of paths dropped (fixed to 0) in the over-identified model]

15
Q

Why do we want a nonsignificant Chi square test when measuring the fit of an over-identified path model?

A

a nonsignificant test indicates that the simpler (parsimonious) model is not significantly worse than the just-identified model

16
Q

What is the total effect of one variable on another?

A

the sum of the direct effect (DE) and indirect effects (IE)