Statistical Methods for the Analysis of Change

1. G89.2247 Class 1 1 Statistical Methods for the Analysis of Change Administrative Issues Why study change? Overview of methodological issues Overview of statistical issues and methods

2. G89.2247 Class 1 2 Administrative Issues Review of syllabus Final Project Weekly assignments Weekly lab session Grades (40% homework, 20% presentation, 40% paper)

3. G89.2247 Class 1 3 Why study change? Description of phenomena in time Trajectories How do children learn words? Cycles Stress patterns over a week Historical record Numbers of shelter requests over days Forecasting and Prediction Social planning Interventions for college drinking Financial planning and investment Value of blue chips over holiday period

4. G89.2247 Class 1 4 Why study change?(Continued) Modeling social and behavioral processes Behavioral phenomena are located in time Relations among multiple variables are often dynamic Systems view of behavior Making inferences about causality Causal relations are temporal Baseline allows efficient inference in experiments Baseline measure as covariate Adjusting for selection in observational studies Holding constant initial value before causal factor

5. G89.2247 Class 1 5 Some examples of change studies Stress and coping example Other NYU Studies Adolph, Bates, Fuligni, Hughes, Ruble, Seidman, Shinn, Yoshikowa

6. G89.2247 Class 1 6 Overview of methodological issues History suggests that studying change is difficult Cronbach and Furby (1970) How should we measure change � or should we? Problems are often associated with panel designs Measurements taken 2 or 3 times Y1, Y2, and Y3 Spacing often set arbitrarily (month, year)

7. G89.2247 Class 1 7 Problems that have been noted Difference scores D=Y2 � Y1 Advantages Easy to compute Easy to interpret Problems Spacing of observations may not match effect Missing values: missing either time makes D missing D is usually correlated (negatively) with starting point D is doubly affected by unreliability

8. G89.2247 Class 1 8 Reliability of Difference Scores Suppose Y1 = T + e1, and Y2 = T + d + e2. T is the stable "true" score of the subject at time 1 d is the "true" change from time 1 to time 2 e1 and e2 are random error terms D = d + e2 - e1 While Var(Y2) = V(T) + V(d) + V(e2)Var(D) = V(d) + V(e2) + V(e1)

9. G89.2247 Class 1 9 Review of problems Regression methods Y2 = b0 + b1Y1 + b2X + e Issues Spacing of observations Missing values Regression artifacts (Reliability of Y1) Trajectory methods Issues Specification of trajectory form Missing values

10. G89.2247 Class 1 10 Overview of methodological issues Other issues Trade off within subject n and between subject n Effects of taking repeated measurements Thinking about variation Interindividual differences in level Interindividual differences in trajectory Intraindividual changes that are systematic Intraindividual changes that are error

11. G89.2247 Class 1 11 Overview of statistical issues Non-independence of observations over subjects Y1, Y2, Y3, Y4 for John are likely to be more similar than Y1, Y2, Y3, Y4 for Mary Non-independence of observations in the temporal sequence Y1& Y2 will be more similar to each other than either is to Y4 Traditional statistical methods assume independence

12. G89.2247 Class 1 12 Overview of statistical issues Categorical, ordinal, continuous vs normal response variables Many psychological variables are made up of individual counts Did I have a headache today? Did Jerry answer the first question correctly Statistical models for counts, and for dependence among variables are quite different than those for normally distributed process variables.

13. G89.2247 Class 1 13 Overview of statistical issues Missing data Can observations over time be imputed or modeled? Can patterns of dependence be used in imputation? How is varying amount of information taken into account in statistical tests?

14. G89.2247 Class 1 14 Overview of Methods to be discussed ANOVA, MANOVA and difference score analysis Regression based panel analyses Structural equation methods Random regression methods Latent growth curve models Generalized linear models Some special methods for binary outcomes Simple survival analysis

15. G89.2247 Class 1 15 Missing in our discussion Time series analyses (Box and Jenkins, ARIMA methods) Markov transition models