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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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Ellen Hamaker
Methods and Statistics
Faculty of Social Sciences
Utrecht University
History
Problem
Time series analysis
Examples:  academic performance
 extraversion & neuroticism states
 dyadic interaction
Discussion
Psychological research is often nomothetic, i.e., based on studying characteristics of the population.
We may distinguish between:
general psychology
and
differential psychology
General psychology concerns means
ttest
ANOVA
MANOVA
Differential psychology concerns covariance structure
correlation
regression analysis
factor analysis
path analysis
Means and covariance structures combined in SEM
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
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.
Pearson follower of Galton, and inventor of the productmoment 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, nullhypothesis testing, Ftest, Fisher information, nonparameteric statistics, et cetera, et cetera…
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 traitlike variables, not processes
History
Problem
Time series analysis
Examples:  academic performance
 extraversion & neuroticism states
 dyadic interaction
Discussion
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.
Our standard techniques focus on characteristics of the population: means, correlations, and proportions.
Results are not always generalizable to the individual.
For instance:
Personality processes, by definition, involve some change in thoughts, feelings and actions of an individual; all these intraindividual changes seem to be mirrored by interindividual differences in characteristic ways of thinking, feeling and acting.
McCrae & John (1992)
shy
sociable
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?
History
Problem
Time series analysis
Examples:  academic performance
 extraversion & neuroticism states
 dyadic interaction
Discussion
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:
Time series analysis is a technique to study uni or multivariate, stochastic systems in discrete time, which may be linear or nonlinear.
Unrelated series:
first series contains autocorrelation
second series is white noise
Two related series:
first contains positive autocorrelation
second contains negative autocorreclation
We can distinguish between two kinds of processes:
variability but no
structural changes
sudden or less sudden
changes, which may be
reversible or not
History
Problem
Time series analysis
Examples:  academic performance
 extraversion & neuroticism states
 dyadic interaction
Discussion
Schmitz & Skinner (1993) investigated academic performance of children.
effort
+
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control
performance
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evaluation
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
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
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+
+
eva
90 repeated measures in 22 subjecten
Neuroticism items
Extraversion items
total variance
state variance
trait variance
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1. Does every one have the same 2factor structure?
 3 persons out of 22 not
 only small groups with same factor loadings
2. Are there similarties in dynamics?
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Gottman and Murray study spousal interaction
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History
Problem
Time series analysis
Examples:  academic performance
 extraversion & neuroticism states
 dyadic interaction
Discussion
What we saw:
Other possibilities:
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.
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!
email: e.l.hamaker@fss.uu.nl