G Lecture 11 G Session 12 Analyses with missing data What should be reported?  Hoyle and Panter  McDonald and Moon-Ho (2002)

G Lecture 12 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

G Lecture 13 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(M|Y)=Prob(M)  The missing data pattern is ignorable. Analyzing available complete data is just fine.

G Lecture 14 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(M|Y)=Prob(M|Y observed )  E.g. Lower educated respondents might not answer a certain question.  Missingness can be treated as ignorable

G Lecture 15 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.

G Lecture 16 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

G Lecture 17 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

G Lecture 18 Example of CFA with Means Model

G Lecture 19 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:

G Lecture 110 Multiple Imputation Substitute expected values plus noise for missing values. Repeat >5 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:

G Lecture 111 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

G Lecture 112 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

G Lecture 113 Talking Points of Hoyle&Panter, McDonald&Ho Model specification  Theoretical justification  Identifiability Measurement Model Structural Model Model estimation  Characteristics of data Distribution form Sample size Missing data

G Lecture 114 Talking Points of Hoyle&Panter, McDonald&Ho 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?