Individual Differences and Reliability of Paired Associates
Learning in Younger and Older Adults
Philippe Rast and Daniel Zimprich
University of Zurich
The authors modeled individual nonlinear trajectories of learning using structured latent growth curves
based on an exponential function with 3 parameters: initial performance, learning rate, and asymptotic
performance. The 3 parameters showed reliable individual differences and the between-parameter
correlations indicated that participants with high learning rates recalled more items initially. The
asymptotic performance was unrelated to the learning rate and the initial performance. In addition, age and
speed of information processing were included in the analyses. Age mainly affected negatively the
asymptotic and the initial performance whereas speed of information processing affected the learning rate
positively. Reliability estimates based on 2 similar learning conditions were moderate overall.
Keywords: individual differences, age differences, learning, reliability
Supplemental materials: http://dx.doi.org/10.1037/a0016138.supp
Learning typically follows a nonlinear trajectory: If perfor-
mance is diagrammed as a function of the number of practice
repetitions, the so-called learning curve emerges, which follows a
gradually increasing, albeit negatively accelerated, trajectory (cf.
Ritter & Schooler, 2001). Although the bulk of learning research
has focused on group-based data and thus on an average learning
curve, little is known about individual differences in verbal learn-
ing and factors that influence these between-person differences.
The paired associates (PA) learning task has been prototypal for
investigating individual differences in associative learning. PA
tasks are structured in terms of stimulus and response items that
are presented contemporarily, with the task being to learn to
respond with the response element when the stimulus is presented
(e.g., Nelson & Dunlosky, 1994). Ideally, in a PA procedure
participants start with no knowledge of the stimulus–response
association and finish with these pairs coded in associative mem-
ory (cf. Cerella, Onyper, & Hoyer, 2006). Comparable to other
memory-related domains, associative learning appears to decline
from adulthood into old age. On average, older adults show lower
learning rates and lower recall performance compared with
younger adults (Cerella et al., 2006; Kausler, 1991, 1994; Salt-
house, 1994; Winn, Elias, & Marshall, 1976). There is evidence
that the PA task tends to make these age differences more pro-
nounced, due to older adults’ difficulties in merging unrelated
attributes (Naveh-Benjamin, 2000).
Many learning processes can be described by three prominent
characteristics (cf. Meredith & Tisak, 1990): They have an initial
level; they reach a plateau where learning has an upper asymptote;
and they incorporate a rate of learning, a nonlinear slope that
describes the speed with which the asymptote is reached, starting
from the initial level. Learning curves usually are inherently non-
linear, which renders standard—that is, linear or quadratic—
growth models inappropriate.
1
In contrast to polynomial functions
(McCullagh & Nelder, 1989), nonlinear functions fit the data
adequately when limiting behavior is expected. On the basis of
earlier work (Browne & Du Toit, 1991), Browne (1993) suggested
applying “structured latent curve models” for learning data, which
impose specific nonlinear constraints on the pattern matrix of
otherwise standard latent growth curve models.
Zimprich, Rast, and Martin (2008) followed this approach to
model individual differences at the initial level, the asymptotic
performance, and the rate of verbal learning in a representative
sample of 364 older adults between 65 and 80 years of age. The
authors used data from a verbal learning test comprising five
learning and recall trials of 27 unrelated words administered in
the first wave of the Zurich Longitudinal Study on Cognitive
Aging (Zimprich, Martin, et al., 2008). The variances in the verbal
learning parameters were all large compared with their standard
errors, implying that there were reliable individual differences with
respect to the means of the three learning parameters. The authors
argued that individual learning trajectories should not be collapsed
across individuals, because this would discount relevant informa-
tion. In addition, asymptotic performance and learning rate were
significantly but negatively correlated, showing that those with a
higher asymptotic performance tended to have a slower rate of
1
In polynomial functions, all parameters enter the equation linearly, and
the curvature is achieved by adding or subtracting polynomials from each
other or from constants. Higher order polynomials follow the observed data
closely but often fit badly at the extremes of the observed range of the axis
of abscissa, even more so for values which are beyond the observed range
(Royston & Altman, 1994).
Philippe Rast and Daniel Zimprich, Department of Psychology, Univer-
sity of Zurich, Zurich, Switzerland.
The research described in this article was supported by a grant from the
University of Zurich (Forschungskredit 2004) to Daniel Zimprich.
Correspondence concerning this article should be addressed to Philippe
Rast, Department of Psychology, University of Zurich, CH-8050 Zurich,
Switzerland. E-mail: p.rast@psychologie.uzh.ch
Psychology and Aging © 2009 American Psychological Association
2009, Vol. 24, No. 4, 1001–1006 0882-7974/09/$12.00 DOI: 10.1037/a0016138
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