Ch. 11 CFA

Question 1

what’s involved with a CFA hypothesis

Answer 1

decide factors; distance between items implies how closely correlated they are to each other; factor analysis can help us determine which items hand together (share more variance) and seem to represent similar underlying constructs

Question 2

Exploratory factor analysis: purpose

Answer 2

generally used to discover the factor structure of a measure and to examine its internal reliability; often used when researchers have no hypothesis; three basis decision points

Question 3

EFA steps

Answer 3

1. Decide number of factors 2. Choosing an extraction method 3. Choosing a rotation method

Question 4

CFA

Answer 4

statistical procedure for evaluating dimensionality, when there are clear hypotheses

Question 5

CFA and Internal Structure: Preliminary Steps

Answer 5

Steps 1. Initial development of measure 2. collect responses to measure (large N needed)

Question 6

CFA and Internal Structure: Core Steps

Answer 6

1. Specify measurement model 2. Submit data to analysis 3. Interpret output 4. Modify model and re-run analysis (if necessary)

Question 7

CFA and Internal Structure: specify measurement model (key points/issues)

Answer 7

Key issues include 1. Number of factors 2. Which item load on which factors 3. Whether factors are orthogonal or potentially correlated (if >1 factor in model)

Question 8

General guidelines for CFA

Answer 8

1. Every item related to some factor 2. Each item is generally only linked to one factor 3. Next, look at the connection between the variables 4. Is there some kind of hierarchical structure that may be causing these factors and responses on these items?

Question 9

CFA and Internal Structure: Submit Data to Analysis

Answer 9

Key steps 1. Actual data is used to estimate parameters of the measurement model, as specified by researcher 2. Evaluates how well the actual data “fit” with the measurement model in general

Question 10

CFA and Internal Structure: Interpret Results. What types of results?

Answer 10

Key results 1. Fit indices: how well does the actual data “fit” the measurement model; Chi squared, RMSEA, SRMR, GFI, (names not important) and so on; if good, then examine parameter estimates; if poor, then (often) examine modification indices 2. Parameter estimates: include aspects of the measurement model; factor loadings, inter-factor correlations, and so on 3. Modification indices: if fit poor (i.e., data are inconsistent with model); clues about how to change model to bring it more in line with actual data

Question 11

CFA and Internal Structure: Modify Model and Re-analyze

Answer 11

if indices were poor and if modification indices supplied reasonable clues; change measure model, re-run analysis, examine new fit indices, and so on; blurs distinction between confirmatory and exploratory analysis; may never identify a good model that fits data well

Question 12

FA in Validity

Answer 12

a test’s internal structure is important because the appropriate interpretation of a test’s scores depends on the match between actual internal structure and internal structure of the indented constructs

Question 13

FA in Reliability

Answer 13

: a test’s dimensionality or internal structure reflects the test’s internal consistency

Question 14

EFA v CFA

Answer 14

• 1. EFA has been used more frequently than CFA 2. EFA is more appropriate for the early phases of the test and CFA is more appropriate for later phases
• -CFA allows test developers and evaluators to understand the degree to which their hypothesized measurement models are consistent with actual data produced by respondents

Question 15

Preliminary steps (book)

Answer 15

1. Clarification of the psychological construct
   and initial item development
   
   2. collection of large number of responses to the test
   3. Reverse score negatively keyed items

Question 16

Step 1: Specification of the Measurement Model (book)

Answer 16

• Translate the hypothesized measurement model into a statistical package
• Specify the links between items and factors (which items load on which factors)
• Facets of measurement model
  1. Number of factors
  2. Associations between factors and items
  3. The potential associations between factors (if multidimensional)
  4. (possible) exact values of one or more parameters
  5. (possible) equality of parameters
• Each item only linked to one latent variable

Question 17

Step 2: Computations (book)

Answer 17

1. Actual variances and covariances
2. Parameter estimates (and inferential tests)
   a. Variances and covariances used to estimate parameters that researcher indicates such as factor loadings for each item
   b. Also computes inferential statistics (i.e., significance test); null is that parameter’s estimated value is 0
3. Implied variances and covariances: uses estimated from phase 2 to compute implied
   a. Assess match or mismatch between actual
4. Indices of model fit—compares implied variances/covariances with the actual variances/covariances and it computes indices of “fit model” and modification

Question 18

Step 3: Interpreting and Reporting Output

Answer 18

1. Fit indices: a good fit indicates that the hypothesized measurement model is consistent with the actual response to the test and supports the validity of the test
   a. Chi-square statistic: indicates the poorness of fit; other tests
2. Parameter estimates and significance tests
   a. After deciding the model has adequate fit, we examine a variety of parameter estimates
   b. Obtain estimated value for parameters such as factor loadings and interfactor associations
   i. If an item is hypothesized to load on a fact, we expect to see large, positive, and statistically significant factor loadings

Question 19

Step 4: Model Modification and Reanalysis (if necessary) (book)

Answer 19

-the magnitude of a modification index reflects the potential impact of revising the relevant parameter
Two cautions in modification
1. Modification obscures differences between CFA and EFA
2. Test developers should be hesitant to perform many modifications with particular hesitancy about modifications that lack clear conceptual basis

Question 20

Jackson, Gillaspy, & Purc-Stephenson (2009) Article

Answer 20

• There are clear reporting guidelines for CFA that many researchers don’t follow
• Goal was to assess the current reporting practices for CFA and see how they can be improved
• 1. How well recommended guidelines were followed? 2. How well authors understood methodology (if they altered their criteria for fit indices with new research)? 3. Do authors pick fit measures that best support their preferred model?
• Most papers included more than one model a priori and reported chi-square, DF, and p values and they reported multiple fit measures
• Most studies did NOT indicate type of matrix used, factor loadings, and latent variable correlations.
• Also did not report data preparation or properly discuss missing data or fit indices cutoffs
• Suggest to report: 1. All models they propose to test and label poc hoc modifications as such 2. Alternate models that are theoretically plausible and identify plausible equivalent models 3. Description of data cleaning and assessment of normality 4. Identify missing data and how it was handled 5. Covariance matrix or equivalent information should be included 6. Software application name 7. Other approaches to assessing fit 8. Report all parameter estimates necessary