G89.2247 Session 12

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G89.2247Session 12

• Analyses with missing data
• What should be reported?
• Hoyle and Panter
• McDonald and Moon-Ho (2002)

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Missing Data in SEM

• Data can be missing for a variety of reasons
• Study Design (planned nesting)
• Longitudinal Studies
• Random events
• Accidents, fire alarms, blackouts
• Systematic nonresponse
• Refusals
• Dropouts

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Missing Data Mechanisms

• Terms suggested by Rubin
• Rubin (1976), Little Rubin (1987)
• MISSING COMPLETELY AT RANDOM (MCAR)
• Which data point is missing cannot be predicted
  by any variable, measured or unmeasured.
• Prob(MY)Prob(M)
• The missing data pattern is ignorable. Analyzing
  available complete data is just fine.

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Missing Data Mechanisms

• MISSING AT RANDOM (MAR)
• Which data point is missing is systematically
  related to subject characteristics, but these are
  all measured
• Conditional on observed variables, missingness is
  random
• Prob(MY)Prob(MYobserved)
• E.g. Lower educated respondents might not answer
  a certain question.
• Missingness can be treated as ignorable

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Missing Data Mechanisms

• NOT MISSING AT RANDOM (NMAR)
• Data are missing because of process related to
  value that is unavailable
• Someone was too depressed to come report about
  depression
• Abused woman is not allowed to meet interviewer
• Missing data pattern is not ignorable.
• Whether missing data are MAR or NMAR can not
  usually be established empirically.

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Approaches to Missing Data

• Listwise deletion
• If a person is missing on any analysis variable,
  he is dropped from the analysis.
• Pairwise deletion
• Correlations/Covariances are computed using all
  available pairs of data.
• Imputation of missing data values.
• Model-based use of complete data
• E-M (estimation-maximization approach)
• SEM-based FIML

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EM and FIML

• Use available data to infer sample moment matrix.
• Uses information from assumed multivariate
  distribution
• Patterns of associations can be structured or
  unstructured.
• Now implemented in AMOS, EQS, Mplus

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Example of CFA with Means Model
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Missing Pattern Group Approach

• Suppose that one group is missing a whole set of
  items related to a latent variable. This group
  can be defined as separate stratum
• The effects for the missing variables can be
  constrained to be equal to the effects estimated
  in the group with complete data.
• This can be tedious, but it gives FIML results.
• See Enders Bandalos (2001) The relative
  performance of FIML for missing data in SEM.
  Structural Equation Modeling, 8 430-457.

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Multiple Imputation

• Substitute expected values plus noise for missing
  values.
• Repeat gt5 times.
• Combine estimates and standard errors using
  formulas described by Rubin (1987). See also
  Schafer Grahm (2002) Missing data Our view of
  the state of the art. Psychological Methods, 7
  147-177.

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Inference from Multiple Imputation

• Rubin (1987) recommends computing for each
  regression weight
• An average across the K imputations
• An estimate of the standard error that takes into
  account the variation over imputations

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Communicating SEM Results

• Keeping up with the expert recommendations
• Psychological Methods
• Specialty journals
• Structural Equation Models
• Multivariate Behavioral Research
• Applied Psychological Measurement
• Psychometrika
• Two kinds of audiences
• Researchers interested in the substance of the
  empirical contribution
• Experts in SEM

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Talking Points of HoylePanter, McDonaldHo

• Model specification
• Theoretical justification
• Identifiability
• Measurement Model
• Structural Model
• Model estimation
• Characteristics of data
• Distribution form
• Sample size
• Missing data

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Talking Points of HoylePanter, McDonaldHo

• Model estimation
• Estimation method ML, GLS, ULS, ADF
• Goodness of estimates and standard errors
• Model Selection and Fit Statistics
• Alternative and Equivalent Models
• Reporting Results
• Path diagrams
• Tabular information
• Use software conventions?