EFA/ CFA (Measurement Models)

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EFA/ CFA (Measurement Models)

• Ulf H. Olsson
• Professor of Statistics

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Factor Analysis

• Exploratory Factor Analysis (EFA)
• One wants to explore the empirical data to
  discover and detect characteristic features and
  interesting relationships without imposing any
  definite model on the data
• Confirmatory Factor Analysis (CFA)
• One builds a model assumed to describe, explain,
  or account for the empirical data in terms of
  relatively few parameters. The model is based on
  a priori information about the data structure in
  form of a specified theory or hypothesis

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The EFA model
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EFA

• Eigenvalue of factor j
• The total contribution of factor j to the total
  variance of the entire set of variables
• Comunality of variable i
• The common variance of a variable. The portion of
  a variables total variance that is accounted for
  by the common factors

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The CFA model

• In a confirmatory factor analysis, the
  investigator has such a knowledge about the
  factorial nature of the variables that he/she is
  able to specify that each xi depends only on a
  few of the factors. If xi does not depend on
  faktor j, the factor loading lambdaij is zero

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Nine Psychological Tests(EFA)
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Nine Psychological Tests(CFA)
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Measurement Models

• Consequences of Measurement Error
• Biased estimates
• Does the Model fit the Data
• The Chi-square test
• The RMSEA approach
• Detailed evaluation of the model
• Reliability
• Validity

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CFA and ML
k is the number of manifest
variables. If the observed variables
comes from a multivariate normal
distribution, and the model holds in the
population, then
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Testing Exact Fit
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Problems with the chi-square test

• The chi-square tends to be large in large samples
  if the model does not hold
• It is based on the assumption that the model
  holds in the population
• It is assumed that the observed variables comes
  from a multivariate normal distribution
• gt The chi-square test might be to strict, since
  it is based on unreasonable assumptions?!

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Alternative test- Testing Close fit
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How to Use RMSEA

• Use the 90 Confidence interval for EA
• Use The P-value for EA
• RMSEA as a descriptive Measure
• RMSEAlt 0.05 Good Fit
• 0.05 lt RMSEA lt 0.08 Acceptable Fit
• RMSEA gt 0.10 Not Acceptable Fit

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Other Fit Indices

• CN
• RMR
• GFI
• AGFI
• Evaluation of Reliability
• MI Modification Indices