Course introduction (lecture and audio posted on main page)

Background readings

1. Correlation and Causation: A Comment, Stephen Stigler

2. Secret to Winning a Nobel Prize? Eat More Chocolate (Time) Publication: Chocolate Consumption, Cognitive Function, and Nobel Laureates Franz H. Messerli, M.D. N Engl J Med 2012; 367:1562-1564 October 18, 2012

3.

From Association to Causation: Some Remarks on the History of Statistics;

Statistical Models for Causation: A critical review

Statistical Models and Shoe Leather,

Illustration using encouragement design representation in Holland (1988). copies of selected overheads.

Encouragement Designs. Potential outcomes formulation and IV parameter estimation in Holland (1988). Estimation handout

Do regression methods (path analysis) identify causal effects? Demonstrations of failure for Holland's encouragement design. class handout Encouragement design slides

Paul Holland, Causal Effects and Encouragement Designs. Causal Inference, Path Analysis, and Recursive Structural Equations Models

Paul W. Holland Sociological Methodology, Vol. 18. (1988), pp. 449-484. (Encouragement design results; sections 3-5)

Holland Appendix (esp pp. 475-480) presents the potential outcomes formulation.

Gelman-Hill text sec 10.5; Data Analysis Using Regression and Multilevel/Hierarchical Models

Publication: Feasibility and efficacy of sodium reduction in the Trials of Hypertension Prevention, phase I Trials of Hypertension Prevention Collaborative Research Group. S K Kumanyika, P R Hebert, J A Cutler, V I Lasser, C P Sugars, L Steffen-Batey, A A Brewer, MI. Hypertension doi: 10.1161/01.HYP.22.4.5021993;22:502-512

Barron-Kenny method via Sobel function in the multilevel package.

More extensive implementation (incl BCa bootstrapping) function

power and sample size calculations in package

data analysis example data file

Vignette for

Mediation Analysis David P. MacKinnon, Amanda J. Fairchild, and Matthew S. Fritz Department of Psychology, Arizona State University, Tempe, Arizona 85287-1104; Annu. Rev. Psychol. 2007. 58:593-614

Brader T, Valentino NA, Suhat E (2008). What Triggers Public Opposition to Immigration? Anxiety, Group Cues, and Immigration." American Journal of Political Science, 52(4), 959-978. jstor link

Data in

NYTimes:How Exercise May Help Keep Our Memory Sharp .

Publication: Exercise-linked FNDC5/irisin rescues synaptic plasticity and memory defects in Alzheimer's models

Stanford Medicine Common opioids less effective for patients on SSRI antidepressants Publication: Predicting inadequate postoperative pain management in depressed patients: A machine learning approach Arjun Parthipan,Imon Banerjee,Keith Humphreys,Steven M. Asch,Catherine Curtin,Ian Carroll ,Tina Hernandez-Boussard Published: February 6, 2019https://doi.org/10.1371/journal.pone.0210575

New Yorker. December 23, 2013. The Power of the Hoodie-Wearing C.E.O. Publication: The Red Sneakers Effect: Inferring Status and Competence from Signals of Nonconformity Author(s): Silvia Bellezza, Francesca Gino, and Anat Keinan Source:

Mediators and Moderators of Treatment Effects in Randomized Clinical Trials Helena Chmura Kraemer; G. Terence Wilson; Christopher G. Fairburn; W. Stewart Agras Arch Gen Psychiatry. 2002;59:877-883

additional technical papers. Causal Mediation Analysis Using R K. Imai, L. Keele, D. Tingley, and T. Yamamoto American Political Science Review Vol. 105, No. 4 November 2011 Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M.,West, S. G., Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83-104.

Chapter 14: Mediation and Moderation Alyssa Blair

Mediation and Moderation Analyses with R - OSF presentation slides

Question 1. Mediating Variable Computations: Class example continued

The data set shown in class example ss423 is linked above and in the legacy directory http://web.stanford.edu/~rag/stat209/ss423

for predictor (IV) 'belong' outcome 'depress' and (potential) mediating variable 'master' The class example showed you the Baron-Kenny analysis using functions from the multilevel and MBESS packages.

Here just use 'lm' basic regression and the recipees from the class handout to recreate point estimates and asymptotic standard errors, significance tests for the mediating variable effect.

Compare your result with the class example posting.

Extra: also try out the more 'sophisticated' functions in the mediation package.

Question 2. Potential Outcomes, Encouragement Design Estimation and (Causal) Mediation

Task 1. Create a potential Outcomes dataset following the first ALICE specification in the posted slides (week 3) ## ALICE example beta = 3 rho = 3 tau = 1, delta = 3 (I did n=400; larger would be better so I redid with n = 6400)

Task 2. Use the artificial data to show the results for the mediation (indirect) effect by hand doing the 3 regressions using multilevel package (sobel) using MBESS package using the causal mediation estimation ACME from the mediation package and compare with rho*beta

Task 3 estimate beta by the Wald estimator (assuming tau = 0) and estimate mediation effect

Question 3. Sesame Street: Encouragement Design research example

Sesame Street research setting and data description given pdf p.30 of Lecture 1 (also Gelman text).

For this exercise use

Use the encouragement design formulation to estimate the effect on child cognitive development (postnumb here) of watching more Sesame Street.

What assumption is necessary for the IV estimation in this design?

Obtain a point and interval estimate for the effect of viewing (use

From simple descriptives reproduce this instrumental variables estimate (Wald estimator).

The second approach (path analysis) analyzed by Holland requires what assumption?

Obtain the path analyses (regression) estimate for the effect on child cognitive development (postnumb here) of watching more Sesame Street.

Compare with the IV estimate (which employs different assumptions).

Moderating Variables in experimental studies (heterogeneous treatment effects)

0. Moderation, mediation recap slide

1. Review: formulation and purposes of analysis of covariance

basic (old) ancova exposition slides ancova and extensions, math notes

High School and Beyond (observational study) school means data example HSB ancova handout (ascii version) data for HSB ancova HSB ancova, scanned pdf

2. Moderating variables, Heterogeneous Treatment Effects (CATE).

Analyzing treatment effects as a function of covariate(s)

CNRL, including Johnson-Neyman technique cnrl data cnrl analysis (extended)

Rogosa, D. R. (1980). Comparing nonparallel regression lines.

R resources (below).

Aspirin may be less effective heart treatment for women than men

Publication: Aspirin Resistance in Patients with Stable Coronary Artery Disease, in the

Wash Post: Why smart people are better off with fewer friends .

Publication: Country roads, take me home... to my friends: How intelligence, population density, and friendship affect modern happiness.

Snow R.E. (1978) Aptitude-Treatment Interactions in Educational Research. In: Pervin L.A., Lewis M. (eds) Perspectives in Interactional Psychology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3997-7_10

package

package

Improving Present Practices in the Visual Display of Interactions Advances in Methods and Practices in Psychological Science

Covariance Adjustment in Randomized Experiments and Observational Studies Paul R. Rosenbaum

Some Aspects of Analysis of Covariance, A Biometrics Invited Paper with Discussion. D. R. Cox; P. McCullagh

Analysis of Covariance: Its Nature and Uses William G. Cochran

The Use of Covariance in Observational Studies W. G. Cochran

Estimation of the Slope and Analysis of Covariance when the Concomitant Variable is Measured with Error James S. Degracie; Wayne A. Fuller

Cronbach, L. J., & Snow, R. E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. Irvington

Regions of Significant Criterion Differences in Aptitude-Treatment-Interaction Research Leonard S. Cahen; Robert L. Linn

Identifying Regions of Significance in Aptitude-by-Treatment-Interaction Research Ronald C. Serlin; Joel R. Levin

Defining Johnson-Neyman Regions of Significance in the Three-Covariate ANCOVA Using Mathematica Steve Hunka; Jacqueline Leighton

discussion of substantive issues: Trait-Treatment Interaction and Learning David C. Berliner; Leonard S. Cahen

Question 1. Background: standard analysis of covariance.(no moderating variable)

A researcher is studying the effect of an incentive on the retention of subject matter and is also interested in the role of time devoted to study.

Subjects are randomly assigned to two groups, one receiving (C3 = 1) and the other not receiving (C3 = 0) an incentive. Within these groups, subjects are randomly assigned to 5, 10, 15, or 20 minutes of study (C2) of a passage specifically prepared for the experiment. At the end of the study period, a test of retention is administered.

Treat the study time as a covariate for investigating the differential effects of the incentive. Does using the covariate improve precision in estimating the effect of incentive?

Does the ancova assumption of a constant treatment effect at levels of StudyMin appear reasonable? full data are in file retention.dat http://statweb.stanford.edu/~rag/stat209/retention.dat

Question 2. Revisit High School and Beyond ancova from Week 2 lecture

In the class example we used school level (mean, gradient) outcomes and used school mean ses as a covariate. Investigate the usefulness of that covariate by comparing the ancova in class example with just a simple t-test (sector) on these school level outcomes. What is the difference in precision between using the covariate or not? As this is not an RCT (revisit in Unit 2), also look at differences in the estimate of the sector effect (bias?).

Question 3. Comparing Regressions (demonstration data, not an RCT)

Let's give recognition to the guys who made S (and R) and take some data from Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS. Third Edition. Springer (now up to 4th edition). Chap 6 section 1 considers analysis of the data set whiteside (available as part of MASS subset of VR package) to access

> library(MASS) # do need to load library, MASS is part of base R > data(whiteside) > ?whiteside

Description

Mr Derek Whiteside of the UK Building Research Station recorded the weekly gas consumption and average external temperature at his own house in south-east England for two heating seasons, one of 26 weeks before, and one of 30 weeks after cavity-wall insulation was installed. The object of the exercise was to assess the effect of the insulation on gas consumption.

Format The whiteside data frame has 56 rows and 3 columns.:

Insul A factor, before or after insulation.

Temp Purportedly the average outside temperature in degrees Celsius. (These values is far too low for any 56-week period in the 1960s in South-East England. It might be the weekly average of daily minima.)

Gas The weekly gas consumption in 1000s of cubic feet.

Source. A data set collected in the 1960s by Mr Derek Whiteside of the UK Building Research Station. Reported by Hand, D. J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets. Chapman & Hall, p. 69.

carry out a comparing regressions analysis with Insul as the group variable, Gas as outcome, and Temp as within-group predictor.

construct a 95% confidence interval for the effect of insul on on gas with temp = 4 (pick-a-point procedure)

for what values of temp does there appear to be an effect of Insul on Gas (simultaneous region of significance)

Question 4.