Lecture 5 Flashcards
Why is SEM good?
- allows for complicated analysis that would usually take many steps
- allow for analysis of more than one relationship at one time
What shapes represent what things in SEM?
- rectangle: observed/manifest
- oval/ellipse: latent factor
- circle: error/residual (also unobserved)
- curved, double-arrow: correlation
- straight, single-arrow: regression
Why is CFA superior to EFA?
- can restrict factor loadings to take certain values (commonly 0)
- not all items have to load on all factors (lots of 0s implied)
- CFA has a test of fit; test if data fits the model to see if you have support for your hypothesis
- CFA: you assign the items to the factor, (in EFA, computer does it) test a theory
in EFA, can only restrict no. of factors and loadings to be uncorrelated (w orthogonal)
What’s the deal with sample size and CFA? What situations do you need a larger sample size?
- 200+
- large scale technique
- many fit indices are ASYMPTOTIC (become more like distro. as sample size increases)
- larger is better (400+)
- > 10 (20:1 is good) subjects for parameters
- no hard, fast rules
- more parameters = need larger sample
- missing data = need larger sample
What are the distributional assumptions of CFA? How can you get around this?
- assume multivariate normality (can check this in AMOS)
- ML is robust to mod. violations
- there are some other fully robust methods that you can use
What is the assumption of levels of measurement? Why?
- assumes continuous observed variables
- bc. working with variances and covariances, NOT raw data
- some programs do allow for ordered categorical data
- latent variables always assumed to be continuous
Explain identification
- CFA seeks parameter estimates that can best reproduce the variance-covariance matrix (MODELs this)
- underdetermined: not enough to estimate, need a new model
- just determined: exact no. of equations, no df/freedom, fits exactly
- overdetermined: what you want, more than enough equations > want more unique variance-covariance terms than parameters to estimate
How do you get identified CFA models? Why does this work?
- at least 3 observed variables loading on each factor
- fix one loading on each factor to a non-zero value (usually 1)
- this sets the scale of the factor to the scale of the variable > this establishes that the factor is measured on the same scale as the variable
- also set error covariance to 1 > determines scale for these
How do you assess model fit in CFA?
- chi-square (but sensitive)
- absolute: SRMR
- comparative: CFI
- parsimony: RMSEA
^^^ cite all!
What do you need to interpret in the CFA AMOS output?
- unstandardised and standardised parameter estimates
- modification indices
- assumptions of normality (don’t want c.r. above 2)
- model fit
What are observed variables sometimes called?
manifest variables
Why are error terms in circles?
because they are not directly observed
What is the measurement vs. structural model in CFA?
- measurement: the factor analysis, shows how the latent variables are created
- structural: the prediction of the constructs, regression
What type of model is CFA?
measurement
What is an identified model? What do you need for this?
- a model that be estimated unambigiously
- need to place constraints on the model (NOT data) for this to occur
What does it mean by CFA seeks parameters that best reproduce the variance-covariance matrix?
- parameters: factor loadings, factor correlations, unique variances (residuals)
- creates it’s own variance-covariance matrix based on these and you can then test fit
How do you know how many variances and covariances there are?
n(n+1)/2
- can draw up a table of the variables vs. the variables
- eg. 2 x 2 = 2 unique variances (one for each); 1 covariance repeated twice in table
Why is chi-square bad as a model fit measure?
- large sample: say it doesn’t fit
- small sample: say it does fit (insufficient power to reject)
^^ strange
How do you interpret CFA parameter estimates?
- a one unit increase in the latent variable results in a one unit increase/decrease in the item, holding constant scores on the other latent factor(s)
- standardised: standard deviation units
What are distinct sample moments?
- sample means, variances and covariances
- BUT amos ignores variances and covariances, therefore it’s only the variances and covarirances
What are the 2 types of SEM we learnt about?
- CFA
- path analysis
When do you not have an error/residual term?
- when there is no arrow pointing TO that variable in the model (i.e. nothing it predicting it)
What is the key difference between EFA and CFA in terms of factor loadings?
- EFA assumes all load on all latent variables (lots more lines in model!). Can suppress them, but they are still there
- CFA restricts many to be zero, not all load on all
What do absolute, comparative and parsimony measures of fit do?
- absolute: proportions of covariances in sample data matrix explained by model
- comparative: relative improvement in fit compared to baseline (baseline = no common factors, all variables are independent)
- parsimony: model-sample discrepancy adjusted for sample size and number of parameters; correction to “punish” more complex models
What does AMOS stand for?
Analysis of Moment Structures
How do you tell if a model is identified by looking at the AMOS output?
- df positive
- number of parameters to estiamte to be less than distinct sample moments
What does the MI value actually mean?
- conservative estimate of the decrease in X2
> the improvement in fit
If there are at least 2 factors, what is required for an identified model with only 2 variables loading per factor?
- factor correlated with another factor
- 1 variable loading is fixed to non-zero value
^^ for more complex models, these 2 rules may not apply
