On line resources Should be able to use for homework

Transcription

1 On line resources Should be able to use for homework wer_applet.html ml (confidence intervals) wer_applet.html sas and mplus macros andcode.html Tasks Two lab reports (new one for today) Three homeworks Be prepared to discuss Remind them that they did first hwk 3 problem in class New homework for power and significance tests Shared file of possible questions Three annotated bibliographies Interviews with stakeholders Music/Neuroscience forum today 1

2 Homework Extra credit correlation problem, regression problem SPSS new Queensland study Test one mediation hypothesis Test one moderation hypothesis Find appropriate syntax 3 Assumptions: Multiple Regression Linear relationships Normal Distribution of Errors At least interval level of measurement of M and Y Equal Error Variance Independent observations No clustering X and M Do Not Interact to Cause Y 2

3 No XM Interaction: Linear Mediation Called Moderation in Baron & Kenny Add XM (and possibly other interaction terms, e.g., X 2 M) when explaining Y. Many contemporary analysts now see XM interaction as part of mediation. 5 Causal Assumptions 1. Perfect Reliability for M and X 2. No Omitted Variables all common causes of M and Y, X and M, and X and Y measured and controlled 3. No Reverse Causal Effects M and Y not cause X Y may not cause M (Guaranteed if X is manipulated.) 3

4 1. Unreliability Usually safe to assume that X is perfectly reliable. Measurement error in Y does not bias unstandardized regression coefficients. Measurement error in M is problematic. Effect of Unreliability in M b is attenuated (closer to zero) c is inflated (given consistent mediation) more as a increases more as b increases Note that the bigger the indirect, the greater the bias in c. 8 4

5 What to Do about Unreliability in M? Improve the reliability Adjust estimates using Structural Equation Modeling Conduct Sensitivity Analyses assuming different values of reliability Unreliability in M deflates ab and inflates c 2. Omitted Variables "Standard" Analysis Compliance should totally mediate this effect. Why is c' negative? 5

6 Results with an Omitted Variable Path c' fixed to zero. Omitted variables that causes M and Y. 11 Other Terms for an Omitted Variable Third variable. Confounder Term used in epidemiology Becoming increasingly popular An omitted variable usually deflates ab and inflates c. 6

7 What to Do about Omitted Variables? Do not omit them: Include them in the analysis as covariates. If there is good reason to believe that c = 0, they can be allowed for. Sometimes the omitted variable is shared method effects. If an issue, measure M and Y by different methods. Conduct sensitivity analyses Reverse Causation U1 1 M a b g 1 U2 X c' Y 14 7

8 What to Do about Reverse Causation? Longitudinal designs If c = 0, then the model can be estimated. Timing of mediator Mediator should be measured after X but before Y. X might be measured at the same time as Y (e.g., number of treatment sessions), but it must be assumed that X has not changed since when it affected Y. 15 Moderation Another tri variate unidirectional (thus causal) hypothesis: Under what conditions/for whom/when is a pre established statistical relationship evident? Completely different from mediation The presence of a third moderator variable (Mo) is also termed: a causal interaction effect (Wu & Zumbo, 2007) an effect modifier (Hinshaw, 2002) 16 8

9 Media on Modera on Mediation: Answers hypotheses of, How and, Why * Moderation: Answers hypotheses of, When and, For whom * X Y X Y Me Mo Me = Mediator Mo = Moderator Direct effects Moderated effect 17 Why the confusion? The simple similarity of the two words Their changing definitions over time The similar purposes for which both are used in research. Moderation and Mediation are both: 1. theories for refining and understanding a causal relationship (Wu & Zumbo, 2007) 2....tri variate hypotheses 3....unidirectional (thus causal) hypotheses They may even be combined to provide a powerful intellectual framework for specifying and testing multi variate hypotheses E.g. How does X manage to impact Y is it via intermediate effects on Z [mediation]? Further, under what conditions of W does Z express this role [moderation]? 18 9