Lecture 6 Flashcards
What does path analysis look at?
- regular regression model
- observed variables only (no latent/unobserved variables)
When is correlation consistent with prediction? (According to Wright, 1921)
- temporal ordering of variables (cause before effect)
- covariation/correlation among variables
- other causes controlled for
What is a recursive model?
- unidirectional paths
- independent error/residuals
- can be tested with standard multiple regression
What are non-recursive models?
- bidirectional paths
- correlated error terms
- feedback loops
- need SEM programs (AMOS)
Why might you get different numbers in AMOS compared to normal regression? What numbers will differ?
if you don’t correlate the IVs/predictors
- regression weights will be the same
- SEs, standardised weights and squared multiple correlation (R2) will differ
Why is path analysis better than regression?
- gives more information (tells you which correlations b/w variables are significant, can remove to make more parsimonious)
- much more accurate
- really advantageous when there are latent variables predicting a further latent variable
What is a multi-step path analysis?
A > M > B
- A = predictor
- M = both predictor and predicted (intervening variable)
- B = predicted
What 2 ways can you do a multi-step analysis?
- you can do 2 regressions
- you can use AMOS (remember to correlate predictors)
What do you need to do to get accurate measures if you choose to do 2 regressions?
- R2 = combine R2 values together
- direct effects are normal
- indirect effects: need to multiply the two beta values together
Why do you need additional fit indices to X2?
- it is sensitive
- large sample: trivial diffs may be sig.
- small sample: may not be exactly X2 distributed > inaccurate probability levels
What are the comparative fit indices?
- NFI
- CFI
- RMSEA
What are the proportion of variance explained fit measures?
- GFI
- AGFI
What are the degree of parsimony fit indices?
- PGFI
- AIC
- CAIC
What are the residual based fit indices?
- RMR
- SRMR
Which fit indices do you usually report?
- if they agree, it is usually up to personal choice. Often report multiple.
COMMONLY:
CFI, RMSEA
maybe SRMR
AIC and CAIC for comparing models
What do you look at in the modification indices?
the MI values (expected decrease in X2)
What does it mean if AMOS says that some variances are negative?
it is an error message
NOT a good model
What do multivariate normality values means?
- less than 1 = negligible
- 1-10 = moderate non-normality
- 10+ = severe non-normality
What is mahalanobis distance?
measure of how close specific cases are to the centroid (the multivariate version of the mean)
When do you use bootstrapping? Why?
- when assumptions are not met
- when distribution is not normal
- bc: model can be incorrectly rejected as not fitting
- SEs can be smaller than they really are (this can make parameters seem sig. when they are not)
What is bootstrapping? What is diff about Bollen Stine compared to Naive?
- repeated samples of the data
- allow each observation to be taken more than once in any sample
- sampling with replacement
- calculate statistic (eg. mean) for each bootstrapped sample and make sampling distro/bootstrap distro.
- calc. SD for sampling distribution - this is the SE!!
Bollen-Stine: calculate ML for each BS sample to make bootstrap/sampling distro. Find 5% mark on distro.
When do you use Bollen-Stine bootstrapping? When would you use Naive bootstrapping?
- BS so assess overall fit
- Naive to get standard error
How is Bollen-Stine different to regular bootstrapping
- it transforms the parent sample into a sample with perfect fit
- the variance-covaraince matrix fits prefectly with the model BUT still has same distributional aspects of original parent sample
- thus would expect the bootstrapped sample to fit very well
- want parent to have better fit than 5% of the bootstrapped ones > suggests good fit
How do you interpret bootstrap iterations?
- BOLLEN: method 1, see if the parent fit better >5% of times
NAIVE:
- first SE = bootstrapped SE
- SE - SE = diff b/w bootstrap and usual
- “mean” = regression weight
- bootstrap CI: not include 0 = sig. parameter!
What is the factor vs. the regression model? How can you combine the 2 models?
- factor: observed variable predicted by unobserved factors (coefficient is lambda, x is predictor)
- regression: dependent predicted by independent (coefficient is beta, x is predicted)
NOTE: x = observed variable, this makes sense!
COMBINE: sub X from factor model into regression model, run regression using latent variables as predictors
What is an advantage of latent variable modeling?
model characteristics rather than just scores
When can you get a reliability of 1? What does that mean?
- never
- observed score never fully captures info in latent variable
What type of model is path analysis?
Structural
What did Sewell say was the 4th criteria that is not right?
variables must be measures on at least and interval scale
In what specific way is path analysis more accurate than regression?
regression models correlations among IVs but does not show or tell you this
How do you combine the r2 values? What is this called?
1 - (1 - .R2) x (1 - .R2)
- generalised squared multiple correlation
What are Mahalanobis d2, p1 and p2 in Mahalanobis distance?
- M D2: distance being referred to in the following 2 columns
- p1: prob that any observation could be so far out (want small).
- assuming normality, the probability that ANY case will exceed the D2 value
- p2: prob that this particular case should be so far out (want large, small p2 indicates many outliers)
- assuming normality, the probability that the highest D2 value will exceed that value (second row = prob of 2nd highest D2 value)
What is the test theory and how does this relate to the latent and regression equations? How do you calculate reliability from this?
O = T + E (observed = true + error)
- O = x in both latent and regression models (observed variable)
- T = f in factor model (latent variable, acting as predictor)
reliability: var(true) / var(observed)
How are regression and correlation similar and different?
- they are the same thing, just scaled differently
- correlation is symmetric, but regression is kind of one way
What is the equation for bivariate regression?
y = (beta)x + e
When interpreting regression, what is the difference between writing out an equation for y(predicted) vs. y?
- predicted/yhat has no residual term
Why is it better to use observed to predict latent variables (using CFA) rather than use sums?
- usually get higher R2 values and higher coefficients
- in sums: assume that all variables have equal weighting
How do you word regressions?
- regress Y on X1, X2 and X3
What types of models can you compare with AIC and CAIC?
- NON-nested models
What are nested models? What can you compare when using nested models?
- nested = one is a subset of the other
- simpler nested inside more complex
- can compare the X2 value, and how much it has decreased
How could you calculate the p value for Bollen-Stine bootstrapping?
- no. of times THE BOOTSTRAP fit worse/no. of times it fit better (x100)
- i.e. no. of times parent fit better/parent fit worse
- want >.05 (more than 5%)
What are the key differences between the factor and regression equations?
- factor: xp = (lambda)p1f1 … until (lamb)pk(f)k + up
- regression: Yp = BpX1 …. + ep
- error: factor = u, regression = e
- coefficient: factor = lambda, regression = beta
- predicted: factor = X, regression = Y
- predictors: factor = f, regression = x
NOTE: X always = observed variable
What types of models are the regression (1) and factor (2) models? And what is the other name for the combination (1 + 2)?
- regression: structural model (path analysis)
- factor: measurement model
- both: SEM
How do you interpret the Multiple R2 in Path Analysis? and the GSMC?
- R2: proportion of variance in the endogenous variable that is explained by direct effects
- GSMC: overall contribution of direct and indirect effects
What is SEM also known as?
- causal modelling
- causal analysis
- simultaneous equation modelling
- analysis of covariance structures
