M5 - CFA Flashcards
Part A - Question: Which of the following statements is correct?
- Whereas exploratory factor analysis uses dimensions/factors to explain shared variance among variables in the analysis, confirmatory factor analysis uses dimensions/factors to account for all variance (shared and unique) in the model.
- Confirmatory factor analysis allows us to test a proposed model about how variables relate to each other.
- Factor analysis suggests that two variables are related, but doesn’t propose a shared third-variable to explain this association.
- Factor analysis takes a small number of variables and combines into a large number of factors
- Confirmatory factor analysis allows us to test a proposed model about how variables relate to each other.
Part E - Question: Based on the information here, which model would you prefer?
Model 1: Chi square = 44.59, p = .002 CFI = .876 RMSEA = .12 SRMR = .08
Model 2: Chi square = 123.45, p < .001 CFI = .622 RMSEA = .37 SRMR = .12
- Model 1.
- Model 2.
- Neither.
- Both.
- Neither.
Although Model 1 has better fit, neither is a good fit to the data and hence we would not be satisfied with either.
What is confirmatory factor analysis?
What is CFA?
- a Data Reduction method
- useful to summarise large number of variables into a smaller number of factors (latent variables).
- tests plausibility of the model –> more control over result
- Occurs when 2 variables are related but it is due to an underlying cause. Factors explain variance in the variables and correlations amongst them (third variable scenario)
What does a Confirmatory factor analysis imply?
It implies:
- there is a latent variable
- correlations between measured variables are due to a shared underlying factor
- after controlling for the underlying factor, the variables should no longer correlate (no residual relationship between the variables remain)
- with two+ latent factors, associations between variables from different latent factors are entirely accounted for by factor correlation (oblique model)
Explain scaling.
Scaling helps to fix the scores so that we can ascertain the relationship between the variables and the factors
Two methods:
1 - Constrain factor variance to 1 (eg standardised variables into z scores - where SD is 1)
2 - Constrain one of the factor loadings to 1 (most common approach)
Need to do this with
- a path from each latent variable to a related measured variable
- for every error term
Otherwise AMOS won’t run
Having these both set to 1 allows us to have the sense of total variance being 100% (partly latent –> measured, partly measured to error)
What are five problems with chi square?
- Favours complexity
- harder to get p > .05 good fit no sig. diff with parsimonious model - Overly sensitive to non-normality
- inflates chi2
- more likely to reject the model - sensitive to sample size
- harder to achieve p> .05 with larger sample - sensitive to size of correlation
- model fit punished more by omission of big correlations than small - sensitive to measurement error
- measurement error reduces power by reducing possible size of correlation
- bias in favour of accepting your model (this is why its important to measure internal consistency)
What are the alternative fit indices beyond chi square.
Global Fit Statistics
Absolute fit –> comparing against perfectly fitting model
- SRMR is the Standardised Root Mean Residual. It is the average error of all things to be reproduced by our model
- RMSEA is the Root Mean Square Error of Approximation = average error accounting for model complexity and sample size. It punishes a model that is overly complex, compared to chi-2 which favours complexity
Incremental fit –> comparing against worst fitting model (null)
- CFI is Comparative Fit Index
expressed as:
x2 - df (null) - x2 - df (proposed) / x2 - df (null)
- TLI is Tucker Lewis Index
punishes for model complexity
expressed as:
x2 /df (null) - x2 / df (proposed) / [(x2/ (df (null) - 1)]
What are oblique and orthogonal factors?
In a confirmatory factor analysis where there are multiple factors, the researcher must specify whether they are oblique or orthogonal
Oblique - expected to correlate
orthogonal - expected not to correlate
Why use CFA?
- Useful for working out construct validity of research measures like self report scales
- Focus on separating unique from shared variance
When should you use CFA?
- Test in SPSS AMOS when we have an idea of the how the variables are related
- Test after researching the literature, designing the theoretical model and collecting the data.
How should the fit statistics for CFA be interpreted?
Global good fit Chi2 = CMIN closer to zero and non-significant Normative chi2 <3 RMSEA < .08 SRMR < .06 CFI >.95 TLI > .95
Local Fit
covariance = unstandardised correlation - are the variables related to the factor proposed?)
correlation - standardised
Use Cohen’s 0.1, 0.3, 0.5 guidelines for assessing strength of correlation
R2 communalities
If a communality is < .1 (< 10% of variance) then it might be an outlier and it should be considered to remove it. Then the remaining factor will likely increase in their relationship (but the scale can no longer be compared with other
- One way around this would be to split the sample it half and try to recreate the results research with other samples
Explain what the CFA Global Fit Output CMIN, NPAR and DF relate to
What is meant by Default, Saturated and Independence models?
CMIN is Chi-Sq minimum - is a representation of Chi Square
NPAR - the number of parameters that have the be estimated in the model
DF - degrees of freedom - # additional paths that we could draw in the model than we currently have drawn
Models
- Default - Proposed
- Saturated - Perfect fitting - all relationship between variables identified
- Independence - Worst fitting - no relationships between models identified
What is a good fit for global fit indices?
Good fit is:
X2 low and not significant normative chi2 < 3 RMSEA < .08 SRMR < .06 CLO and TFI > .95
Explain CFA local fit output
Covariance is unstandardised
Correlation is standardised
Use Cohen’s guidelines for weak, moderate strong correlation (.1 .3 .5)
C.R critical ratio - estimate / SE = T test
if there is an even more important predictor in the true model that hasnt been identified or drawn, the predictor may look better than they actually are, so should be taken with a grain of salt
Outline the Key Output for CFA
Global Fit Statistics Unstandardised Factor loadings Standardised Factor Loadings Covariances and Correlations R Squared Estimate (communalities)
