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Economics
Econometrics
Multivariate Cards Set Two
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Terms in this set (54)
Models are ALSO under-identified (unable to be estimated) if certain paths are not fixed.
WEIRD!
Why do you fix a path using path analysis?
This is because models are unidentified if you do not fix paths.
Every path from the error term to its endogenous variable should be set to _______.
1
In latent factor analysis, a path from a latent factor to one of its measured variables should be set to _________.
1
What are the 5 steps of SEM?
1) Hypothesize and collect data (based on theory/hypothesis, graphical depiction of data, and collection of participant data)
2) Model identification (use Bentler-Weeks equations to determine if model is over, under, or just-identified)
3) Estimate model (use software to specify dataset)
4) Evaluate fit indices (macro test) and paths (micro test)
5) Perform post-hoc modifications (add or delete paths and respecify model)
What are different SEM software types?
1) Mplus (most advanced and most innovative features, but least intuitive syntax)
2) EQS (Use Bentler-Weeks Equations and has most intuitive syntax; has point and click feature but it's clunky)
3) Amos (Bentler-Weeks Equations used to point and click, easiest to learn, least expensive)
4) R, SAS, LISREL, Stata (use syntax, less common)
What are the measurement scales that can be used for path analysis using SEM?
Exogenous variables: nominal (if dummy coded), ordinal, interval, or ratio scale
Endogenous variables: ordinal, interval, or ratio scale
What does the model x2 test assess? What is the caveat to the model x2 test?
It assesses the overall discrepancy/correspondence between the hypothesized model and the underlying data.
A significant chi-square test suggest that the model should be rejected because it is significantly different from the data. This is undesired.
The model should be retained if a nonsignificant model x2 test.
The caveat is that the model x2 test is a p-value based test and therefore is very sensitive to sample size. The smaller the N, the more likely the test is to be nonsignificant. The larger the N, the more likely the test is to be significant.
For the model x2 test, the smaller the N, the more likely the test is to be (significant/nonsignificant). The larger the N, the more likely the test is to be (significant/nonsignificant).
Nonsignificant
Significant
Explain the model x2 to df ratio.
It is a test of the correspondance or discrepancies between the hypothesized model and the underlying data. Unlike a model x2, the ratio is not as sensitive to increases and decreases in N. The lower the ratio, the better the model fit. The range is from 0 to infinity, with ratios of less than 2.00, 3.00, or 5.00 the desired (depending on what article you follow).
For the model x2 to df ratio, the (lower/higher) the ratio, the better the model fit.
lower
What do goodness-of-fit indices test? What are types of these indices?
How good does the model fit? These compare the hypothesized model to the worst fitting model (independence model). The range is .00 to 1.00, and desired values are high. >.90 is acceptable, and >.95.
Indices include CFI (Comparative Fit Index) and TLI (Tucker-Lewis Index).
What is an independence model?
This is the worst-fitting model in which none of the paths are estimated. It is the what if scenario in which none of the paths were estimated in the model. It produces the largest possible model x2 value.
What is a saturated model?
This is the best-fitting model in which all possible paths are estimated. It is the what if scenario in which the df is 0, and it produces the smallest possible model x2 value.
What paths do you always fix to 1 in multivariate techniques?
For all SEM types: Every path from the error term to its endogenous variables
For latent variables: A path from a latent factor to one of its measured variables
What is a badness-of-fit index? What are badness-of-fit indices?
How bad does the model fit? This compares the hypothesized model to the best fitting or saturated model possible. The scores range from .00 to 1.00.
.00 to .05: close fit
.05 to .08: fair fit
.08-.10 mediocre fit
>.10 poor fit
Root Mean Square Error of Approximation (RMSEA): only test to provide confidence intervals
Standardized Root Mean-Square Residual (SRMR)
What are the desired scores of badness-of-fit indices?
.00 to .05: close fit
.05 to .08: fair fit
.08-.10 mediocre fit
>.10 poor fit
Which fit index provides confidence intervals?
RMSEA
The (independence model/saturated model) produces the largest possible model x2 value, and the (independence model/saturated model) produces the smallest possible model x2 value.
Independence Model
Saturated Model
What is the equation for the CFI?
CFI = 1-((x2hyp-dfhyp)/(x2ind-dfind))
What are the 3 advantages of using SEM over multiple regression?
Remember: TOM likes SEM
1) It allows for a multivariate examination of complex relations, and you can test for more than 1 DV and use a mediational model
2) It decreases the risk of Type 1 error because you perform a single model
3) It offers additional information such as model fit indices, modification indices, and testing of competing models.
Two models are nested if _________________________________________________________.
1) Both models use the same sample
2) Both models contain the same measured variables
3) It is possible to go from one model to another by adding paths OR deleting paths (not both)
If two models are nested, what do you do?
You perform a model x2 difference test to assess if the models are significantly different in fit. They are significantly different if the x2diff is larger than the critical value in the x2 table.
If two models are not nested, what do you do?
You compare AIC values for each model. A smaller AIC is a relatively better model, but keep in mind that this is not a p-value test.
If you are adding paths in a nested model, aim for a (significant/nonsignificant) x2diff test.
If you are deleting paths in a nested model, aim for a (significant/nonsignificant) x2diff test.
Significant "Adding paths significantly improved the overall fit of the revised model compared to the hypothesized model"
Nonsignificant "Deleting paths did not significantly degrade the overall fit of the revised model compared to the hypothesized model"
What is a hanging variable?
It is a variable that is not significantly associated with variables in the model.
What should you do with a hanging variable?
One perspective is to delete it, as it is not necessary to explain relations and it compromises fit indices. However, once the variable is deleted, the models are no longer nested.
One perspective is to retain the variable if it is relevant to the framework being uses. This approach ensures that the original and revised models are nested.
It is (possible/impossible) for exogenous variables to be directly correlated with one another.
It is (possible/impossible) for endogenous variables to be directly correlated with one another).
Possible
Impossible
What can you do since endogenous variables cannot be directly correlated with one another?
You can correlate their predictive error terms as a proxy.
What is the difference between free, fixed, and constrained paths?
Free is when statistics are to be estimated in a proposed model.
Fixed is when you force a certain value (0 or 1, usually) so that these fixed paths are not estimated. Unestimated paths are implicitly fixed to 0. Paths from error term to variables are fixed to 1. You fix paths to other values in the cases of advanced SEM techniques, like latent growth curve modeling.
Constrained is when you force 2 paths to be equal to one another, which is what you do in the cases of advanced SEM techniques.
In the literature, fixed and constrained are used to refer to paths and are sometimes used interchangeably.
True.
(Predictive Error/Measurement Error) is unexplained variance after the predictor has had an effect on the outcome, and is assessed in path analyses).
(Predictive Error/Measurement Error) is error due to the unreliability of items in measuring the same latent factor, and is assessed in PAF, CFA, and SEM.
Predictive Error
Measurement Error
When is CFA ideally used (in contrast to PCA or PAF)?
It is used when you have specific hypotheses about what factors should load onto which items.
Explain the difference between a single-item measure, multiple-item composite, and latent factor.
A single-item measure does not triangulate on a construct, and is therefore highly susceptible to measurement error.
A multiple-item composite (non-latent factor) does not statistically remove measurement error, but better triangulates on a construct. Cronbach's alpha is used to indicate the degree of nonmeasurement error. In this way, you can report or measurement error, but you can't remove it.
Latent factors are created out of multiple items and can remove measurement error from each factor, such that you are essentially getting at what it would be like of Cronbach's alphas was 1.00
What are 3 advantages of CFA over PCA and PAF?
Remember: Fickle, Hilarious Moose
1) Fit indices are produced to measure how well the factor structure fits, like CFI, TLI, and RMSEA.
2) CFA is hypothesis-driven such that items are specified to load only on their hypothesized factors.
3) Measurement error is statistically removed (in both CFA and PAF) so that latent factors are uncontaminated by unreliability.
For each latent factor in CFA and SEM, you must fix one unstandardized item loading to 1. Why?
This gives a latent factor a starting numeric scale or metric.
What is the ideal number of items per latent factor in CFA and SEM?
3-5 items is the ideal aim. If you have >5 items, that's okay, but there is a greater likelihood of poor fit indices, so create parcels to manage this.
Why would you create parcels?
This is a way to decrease the likelihood of cross-loadings which cause poor fit indices in latent model. Parcels are when you divide the many items into 3 to 5 parcels to decrease the chance of poor fit indices.
CFA modells can be 1-factor structures, 2-factor structures, 3-factor structures, etc., which can all be nested.
...
When are two models nested in CFA if:
1) Both models use the same sample.
2) Both models contain the same measured variables.
3) It is possible to go from one model to another by adding paths or deleting paths.
What is a fully latent SEM?
It is a model in which only latent factors are used in predicting relations. It contains a measurement part (like CFA) and a structural part (like path analysis)
What three parts do you always specify for Bentler-Weeks equations?
1) Equations: list regression equations for each endogenous variable
2) Variances: list variances for each exogenous variable
3) Covariances: list correlations between exogenous variables
What is a hybrid SEM?
It is a model using a combination of latent factors and measured variables in predictive relations.
_____________________ and __________________ are considered unmeasured variables in SEM.
Latent factors and disturbances
What is the downside to imputation in SEM?
Imputation results in AMOS no longer generating modification indices.
What are alternative estimation or extraction methods in SEM?
1) Maximum likelihood (ML); this is the default, or most common in SEM); this assumes that variables are relatively normally distributed
2) Asymtotically distribution-free (ADF or WLS); this is used for nonnormal varibles and large N of 500 or 1000, N must be more than 10 times the estimated # of unknowns.
3) Bootsrapping is used for nonnormal variables, but a large N is not a prerequisite.
4) Generalized least squares (GLS), unweighted least squares (ULS), and scale-free least squares (SFLS) are available but not used in the literature. Avoid using these.
What does bootstrapping do?
Bootstrapping creates critical values of the null sampling distribution based on your data to determine all p-values. So, the degree of nonnormality is no longer a statistical assumption.
Mediational models must contain 1 or more of each: _____________________________________________________________________________.
Predictor (initial variable), mediator (intervening variable), outcome (final variable)
Mediational tests are also known as _______________________________________.
Tests of indirect effects.
How are mediation models tested?
Regression-based analyses, such as multiple regression, path model, hybrid SEM, and fully latent SEM.
What are the 2 approaches to mediation testing?
Baron and Kelly's 4 steps
Tests of indirect effects
What are the 4 steps of Baron and Kenny?
1) predictor is significantly related to the outcome (not controlling for the mediator; path c)
2) predictor is significantly related to the mediator (path a)
3) mediator is significantly related to the outcome (path b) while controlling for the predictor (path c')
4) If the first three steps are satisfied, compare c to c'.
In a partial mediation, path c' is reduced but still significant.
In a full mediation, path c' is reduced to near 0 and no longer significant.
What are the steps to the test of indirect effects?
1) test the direct effects relations to determine if the direct effects are significant
2) test the indirect effect relations from starting predictor through 2 or more single-headed arrow paths to the final outcome. The mediational effect is significant if the test of indirect effect is significant.
What are the 3 advantages of testing mediation in SEM over Multiple Regression?
Remember: LAS
1) Predictors, mediators, and outcomes may be represented with measured variables and/or latent factors, which statistically removes measurement errors.
2) Provides additional information, such as fit indices and modification indices.
3) It permits the testing of complex mediational relations in a single model.
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