Time series analysis and the individual in psychological research

1. Time series analysisand the individual inpsychological research Ellen Hamaker Methods and Statistics Faculty of Social Sciences Utrecht University

2. Outline History Problem Time series analysis Examples: - academic performance - extraversion & neuroticism states - dyadic interaction Discussion

3. The subject of psychological research Psychological research is often nomothetic, i.e., based on studying characteristics of the population. We may distinguish between: general psychology and differential psychology

4. General and differential psychology General psychology concerns means t-test ANOVA MANOVA Differential psychology concerns covariance structure correlation regression analysis factor analysis path analysis Means and covariance structures combined in SEM

5. How did it all start? 1878 Charcot began to demonstrate the effects of hypnosis on hysterical patients. Subject: psychologically disturbed mind 1879 Wundt founded the first psychological laboratory in Leipzig. Subject: general mind 1884 Galton established his anthropometric laboratory and measured mental faculties and physical appearances of 9000 visitors. Subject: variation in the population

6. Variation in the population Galton believed most mental and physical features were inherited. He was worried that the protection of the weak (i.e., the poor) would interfere with the mechanisms of natural selection. Galton is the founder of eugenics.

7. Other important eugenicists Pearson follower of Galton, and inventor of the product-moment correlation coefficient Spearman student of Wundt, and inventor of factor analysis, and the concept of general intelligence Fisher mathematician, and inventor of: ANOVA, experimental designs, principle of maximum likelihood, inferential statistics, null-hypothesis testing, F-test, Fisher information, non-parameteric statistics, et cetera, et cetera…

8. Mathematical statistics The statistical techniques used in the social sciences were developed to study heredity. Hence, they have two important features: a. heredity operates at level of population: same holds for these techniques b. biometrics is concerned with studying trait-like variables, not processes

9. Outline History Problem Time series analysis Examples: - academic performance - extraversion & neuroticism states - dyadic interaction Discussion

10. Psychological processes Many psychological theories concern processes. Examples are: learning; habituation; conditioning adaptation; coping; affect regulation interacting; communication problem solving; information processing development; decline Process implies some form of change at the level of the individual.

11. What is the problem? Our standard techniques focus on characteristics of the population: means, correlations, and proportions. Results are not always generalizable to the individual. For instance: • if we find a beneficial effect of therapy at the group level, this does not guarantee that every individual improved • if we find a smooth change at the group level, it is possible that at the individual level there is a sudden change • if 20% of clients are cured after treatment, this does not imply that an individual has a 20% change of being cured

12. E.g., correlation interindividual intraindividual mistakes mistakes words per minute words per minute

13. Who makes this mistake? Personality processes, by definition, involve some change in thoughts, feelings and actions of an individual; all these intra-individual changes seem to be mirrored by interindividual differences in characteristic ways of thinking, feeling and acting. McCrae & John (1992) shy sociable

14. The same in formulas…

15. Questions about processes Is the relationship at the INTRAindividual level identical to the relationship at the INTERindividual level? If not, is there an universal relationship? If not, can the differences between individuals with respect to their dynamics be related to other individual differences?

16. Outline History Problem Time series analysis Examples: - academic performance - extraversion & neuroticism states - dyadic interaction Discussion

17. Dynamic system A DS is a set of equations that describe how the state of the system changes as a function of its previous state. Characteristics of a DS: • 1 or more variables • state = values of the variables • stochastic/deterministic • discrete or continuous time • linear or nonlinear Time series analysis is a technique to study uni- or multivariate, stochastic systems in discrete time, which may be linear or nonlinear.

18. Autoregressive models at-2 at-1 at at+1 at+2 xt-2 xt-1 xt xt+1 xt+2 yt-2 yt-1 yt yt+1 yt+2 ut-2 ut-1 ut ut+1 ut+2

19. Time series Unrelated series: first series contains autocorrelation second series is white noise Two related series: first contains positive autocorrelation second contains negative autocorreclation

20. Stationarity We can distinguish between two kinds of processes: • stationary processes: variability but no structural changes • nonstationary processes: sudden or less sudden changes, which may be reversible or not

21. Outline History Problem Time series analysis Examples: - academic performance - extraversion & neuroticism states - dyadic interaction Discussion

22. Example 1

23. Academic performance Schmitz & Skinner (1993) investigated academic performance of children. effort + + control performance + + evaluation

24. Child 1 Lag 0: eff per eva con eff - R = per .08 - eva -.17 .57* - con .03 .11 .22 - Lag 1: eff per eva con eff .22 .20 -.49* .27*  = per - -.15 .18 .38* eva - - .23 .32* con - - - .32* eff + - + con per + + eva

25. Child 2 Lag 0: eff per eva con eff - R = per .42* - eva .53* .96* - con .30* .24 .33* - Lag 1: eff per eva con eff -.18 .09 -.13 .12  = per - -.07 .10 -.25 eva - - .12 -.16 con - - - .49* eff + + con per + + + eva

26. Example 2

27. Daily measures of E & N 90 repeated measures in 22 subjecten Neuroticism items Extraversion items total variance state variance trait variance

28. The model et-1 et-1 et-1 et-1 et-1 et-1 et et et et et et et+1 et+1 et+1 et+1 et+1 et+1 yt-1 yt-1 yt-1 yt-1 yt-1 yt-1 yt yt yt yt yt yt yt+1 yt+1 yt+1 yt+1 yt+1 yt+1 Et-1 Et Et+1 at-1 at at+1 et cetera et cetera ut-1 ut ut+1 Nt-1 Nt Nt+1 yt-1 yt-1 yt-1 yt-1 yt-1 yt-1 yt yt yt yt yt yt yt+1 yt+1 yt+1 yt+1 yt+1 yt+1 et-1 et-1 et-1 et-1 et-1 et-1 et et et et et et et+1 et+1 et+1 et+1 et+1 et+1

29. Results 1. Does every one have the same 2-factor structure? - 3 persons out of 22 not - only small groups with same factor loadings 2. Are there similarties in dynamics? + Et-1 Et - at-1 at - - + ut-1 ut + Nt-1 Nt

30. Example 3

31. Dyadic interaction Gottman and Murray study spousal interaction • 15 minutes • code affect (sum 6 seconds): -24 to +24 • bivariate timeseries of 150 points   W1 W2 W3 f(W2) f(W1) f(H2) f(H1) H1 H2 H3  

32. Scores of W and H against time

33. State space and null clines W 2 1 4 3 H 5

34. State space and null clines W H

35. Influence function Wt+1 negatieve threshold Ht positieve threshold

36. Finding the steady states W H

37. A less happy couple W H

38. And next... W H

39. Simulation results

40. Outline History Problem Time series analysis Examples: - academic performance - extraversion & neuroticism states - dyadic interaction Discussion

41. There is more… What we saw: • vector autoregressive models (Examples 1&2) • threshold autoregressive models (Example 3) Other possibilities: • deterministic trends/cycles • difference scores • intervention analysis • latent regime switching • ordinal data

42. In sum Time series analysis is a powerful tool to study processes at the level of the individual (or dyad). There are different ways of combining the information obtained from multiple subjects: - can parameters be constrained across individuals? - individual parameters can be used to compare individuals In this way time series analysis can also contribute to nomothetic knowledge.

43. Was it all for nothing? Populations do not change: individuals do Thelen & Smith, 1994 So change at the level of the population must imply at leastone individual changed. BUT… beware of the generalization trap!

44. Thank you email: e.l.hamaker@fss.uu.nl