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1 Writing about SEM/Best Practices Presenting results Best Practices» specification» data» analysis» interpretation 1

2 Writing about SEM Summary of recommendation from Hoyle & Panter, McDonald & Ho, Kline» the model» the data» estimation and fit» parameter estimates» alternative models 2

3 Presenting the Model H&P suggest presenting a more abstract version of the model first ("conceptual model") followed by a concrete model specified in enough detail to allow the reader to reconstruct the analysis ("statistical model")» reader should be able to compute observations and degrees of freedom from statistical model» indicate clearly any parameters that were fixed M&H want to see more discussion of identifiability Both want readers to do more theoretical justification for presence and absence of paths 3

4 Data Check for violations of assumptions and present diagnostic information» esp., provide information about kurtosis» Mardia's coefficient gives information on multivariate normality Give information on missing data (how much?), and how this was handled (e.g., listwise deletion) Provide data» covariance matrix that includes all observed variables OR» correlation matrix and standard deviations» M&H: if > 30 variables, put on web or state that the data are available from the author 4

5 Estimation and Fit State what method of estimation you used» Maximum Likelihood best in most cases Present strategy for testing fit (H&P)» state which indices will be presented and give justifications for choosing them» give conceptual definition of each index used» state the cutoff values you will be using Give χ2, df, sample size and p value» can do this succinctly: χ2(48, N = 500) = , p <.001, TLI =.86, CFI =.90 5

6 H&P recommend Global Fit Indices» GFI because it's in the same metric as R» NNFI or IFI» CFI M&H recommend» RMSEA, RMR, CFI, GFI Kline recommends» RMSEA, CFI 6

7 More on Fit M&H and Kline suggest that discrepancy information should be presented» M&H say to present it in the other half of the variance/ covariance matrix of the observed variables M&H and Kline also both recommend a two-step testing strategy to insure that structural part of model fits well» See M&H Table 2 (p. 74) for examples in which structural portion did not fit well but this was masked by the overall good fit of the model 7

8 Parameter Estimates Report all parameter estimates» including variances» report standard errors as well» clearly indicate any paths that were fixed (e.g., to 1.0 to set the scale for a latent variable) M&H suggest presenting measurement model parameters in tabular form and leaving the observed variables out of the diagram, for clarity 8

9 Alternative Models Present and test alternative models If respecification is done, present this information clearly» H&P recommend that results for the hypothesized model be presented first» In a separate section, present the modified model Test equivalent models, if possible 9

10 Cross-Validation If you have a holdout sample, test your final model on them and present the results If you can't do this, provide estimates of the likelihood that your model will replicate» Browne & Cudeck cross-validation statistic 10

11 Keeping Up Recommendations are changing, so look for people to continue writing on this topic in:» Psychological Methods» Specialty journals Structural Equation Models Multivariate Behavioral Research Applied Psychological Measurement Psychometrika 11

12 Best Practices: Specification Lay out your model before you collect data» if it is not identified, you can add more measured variables Try to include all important causes that are already known When modeling latent variables, have enough indicators» Kenny (1979): "Two might be fine, three is better, four is best and anything more is gravy."» Number of indicators necessary for identification depends on the model 12

13 Best Practices: Specification Think hard about directionality» does the logic of the study design and protocol rule out some causal orders?» have some causal orders been confirmed or disconfirmed in other studies (especially longitudinal or experimental)?» if not, you may want to consider (and test) other causal orders Don't use feedback loops (causal arrows going both ways) as a way to get around thinking hard about directionality 13

14 Best Practices: Specification Add correlations between error or disturbance terms only when conceptually justified» try to work out ahead of time which error terms may need to be correlated» avoid correlating error terms solely to improve fit Try for indicators that load on one factor (latent variable) only» allow cross-loadings only if clearly justified theoretically 14

15 Best Practices: Data Implement quality control practices for examining data Minimize missing data» If much data is missing, imputation may be the best method, if data are not missing at random» watch for new developments Check for violations of assumptions» normal distributions for endogenous variables» linearity» independence Screen for outliers» As in regression and ANOVA, SEM is sensitive to outliers 15

16 Best Practices: Analysis Use theory and previous findings to guide respecification» modification indices (e.g., Lagrange) can be useful, but do not rely on them blindly (unless you like making Type I errors) Double check your syntax» make sure you are running the model you think you are Look carefully at your output for signs of problems» error messages (or not "all is ok" message)» negative variances (and other impossible things)» huge standard errors (and other unlikely things) 16

17 Best Practices: Analysis Report unstandardized as well as standardized estimates Check for multicollinearity» Kline says correlations >.85 may be problematic Check your sample size» At least 100 cases AND» 10:1 ratio for cases to parameters estimated (or, at an absolute minimum, 5:1) 17

18 Best Practices: Analysis Provide SEM program with start values, if it is having trouble» If program doesn't converge or there are other signs of problems, but estimates are printed, use those as start values» Kline has several appendices that give advice about providing start values Be aware of the possibility of empirical underidentification Evaluate the measurement and structural portions of the model separately 18

19 Best Practices: Interpretation Look at all of your output» fit indices are important but they are only part of the picture» be sure to look at matrix of residuals -- this lets you know if all of the model is fitting well or if there are some areas of misfit Do not assume, believe, or state that your model must be correct, because fit is good» we can disprove models (state that they must be incorrect) but we can't prove that a model is correct 19

20 Best Practices: Interpretation Remember that good fit does not imply anything about how much variance in the endogenous variables is explained» good fit means the variance in the variance-covariance matrix is well represented by the model» if you care about being able to predict large amounts in the variance in some or all endogenous variables, you have to look at that separately Consider and test alternative models If possible, consider mathematically equivalent models» nice if you can rule some out using theory or logic 20

21 Best Practices: Interpretation Remember that SEM is not a cure for poor theory or design Don't reify your factors» you tried to choose indicators so as to create a latent factor that represents the construct of interest» but you may not have succeeded» when reading other people's work, don't rely just on their name for the latent variable -- look critically at the indicators Report enough information so that readers can reproduce your analysis and try alternative models 21

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