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Time series analysis and the individual in psychological research. Ellen Hamaker Methods and Statistics Faculty of Social Sciences Utrecht University. Outline. History Problem Time series analysis Examples: - academic performance - extraversion & neuroticism states

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time series analysis and the individual in psychological research

Time series analysisand the individual inpsychological research

Ellen Hamaker

Methods and Statistics

Faculty of Social Sciences

Utrecht University

outline
Outline

History

Problem

Time series analysis

Examples: - academic performance

- extraversion & neuroticism states

- dyadic interaction

Discussion

the subject of psychological research
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

general and differential psychology
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

how did it all start
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

variation in the population
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.

other important eugenicists
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…

mathematical statistics
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

outline1
Outline

History

Problem

Time series analysis

Examples: - academic performance

- extraversion & neuroticism states

- dyadic interaction

Discussion

psychological processes
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.

what is the problem
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
e g correlation
E.g., correlation

interindividual

intraindividual

mistakes

mistakes

words per

minute

words per

minute

who makes this mistake
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

questions about processes
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?

outline2
Outline

History

Problem

Time series analysis

Examples: - academic performance

- extraversion & neuroticism states

- dyadic interaction

Discussion

dynamic system
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.

autoregressive models
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

time series
Time series

Unrelated series:

first series contains autocorrelation

second series is white noise

Two related series:

first contains positive autocorrelation

second contains negative autocorreclation

stationarity
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

outline3
Outline

History

Problem

Time series analysis

Examples: - academic performance

- extraversion & neuroticism states

- dyadic interaction

Discussion

academic performance
Academic performance

Schmitz & Skinner (1993) investigated academic performance of children.

effort

+

+

control

performance

+

+

evaluation

child 1
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

child 2
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

daily measures of e n
Daily measures of E & N

90 repeated measures in 22 subjecten

Neuroticism items

Extraversion items

total variance

state variance

trait variance

the model
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

results
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

dyadic interaction
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

influence function
Influence function

Wt+1

negatieve

threshold

Ht

positieve

threshold

outline4
Outline

History

Problem

Time series analysis

Examples: - academic performance

- extraversion & neuroticism states

- dyadic interaction

Discussion

there is more
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
in sum
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.

was it all for nothing
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!

thank you
Thank you

email: e.l.hamaker@fss.uu.nl