Training-induced compensation versus magnification of individual differences in memory performance.

Abstract

Do individuals with higher levels of task-relevant cognitive resources gain more from training, or do they gain less? For episodic memory, empirical evidence is mixed. Here, we revisit this issue by applying structural equation models for capturing individual differences in change to data from 108 participants aged 9-12, 20-25, and 65-78 years. Participants learned and practiced an imagery-based mnemonic to encode and retrieve words by location cues. Initial mnemonic instructions reduced between-person differences in memory performance, whereas further practice after instruction magnified between-person differences. We conclude that strategy instruction compensates for inefficient processing among the initially less able. In contrast, continued practice magnifies ability-based between-person differences by uncovering individual differences in memory plasticity.

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ORIGINAL RESEARCH ARTICLE
published: 15 May 2012
doi: 10.3389/fnhum.2012.00141
Training-induced compensation versus magnification
of individual differences in memory performance
Martin Lövdén1,2,3*, Yvonne Brehmer1,3, Shu-Chen Li1and Ulman Lindenberger1
1Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany
2Department of Psychology, Lund University, Lund, Sweden
3Aging Research Center, Karolinska Institutet, Stockholm, Sweden
Edited by:
Julia Karbach, Saarland University,
Germany
Reviewed by:
Lars Nyberg, Umeå University,
Sweden
Marion Spengler, Saarland
University, Germany
*Correspondence:
Martin Lövdén, Aging Research
Center, Karolinska Institutet,
Gävlegatan 16, 113 30 Stockholm,
Sweden.
e-mail: martin.lovden@ki.se
Do individuals with higher levels of task-relevant cognitive resources gain more from
training, or do they gain less? For episodic memory, empirical evidence is mixed. Here,
we revisit this issue by applying structural equation models for capturing individual
differences in change to data from 108 participants aged 9–12, 20–25, and 65–78
years. Participants learned and practiced an imagery-based mnemonic to encode and
retrieve words by location cues. Initial mnemonic instructions reduced between-person
differences in memory performance, whereas further practice after instruction magnified
between-person differences. We conclude that strategy instruction compensates for
inefficient processing among the initially less able. In contrast, continued practice
magnifies ability-based between-person differences by uncovering individual differences
in memory plasticity.
Keywords: memory plasticity, magnification, amplification, compensation, associative memory, aptitude by
treatment interactions
INTRODUCTION
A long-standing debate in psychometrically oriented develop-
mental and non-developmental intelligence research deals with
the issue of whether intelligence equals learning efficiency (e.g.,
Sternberg and Detterman, 1986; Neisser et al., 1996; Garlick,
2002) and with the related issue of aptitude by treatment inter-
actions (e.g., Ferguson, 1956; Cronbach, 1957; Sullivan, 1964).
In other words, do individuals with higher levels of task-relevant
cognitive resources gain more from training? For the cognitive
ability focused on in this article, episodic memory, the empirical
evidence is still mixed: while positive correlations between cogni-
tive ability and gains from instructions and practice on cognitive
tasks have been reported (e.g., Kliegl et al., 1990; Verhaeghen and
Marcoen, 1996; Kwon and Lawson, 2000), negative correlations
are also common (e.g., Gaultney et al., 1996; Cox, 2001). These
different findings have consequently given rise to competing
views on interindividual differences in training gains, which are
mostnotablyrepresented bythemagnificationandcompensation
accounts.
The magnification view is prominent for interpreting the
increase in adult age differences after mnemonic training, such as
after instructions and practice in the Method of Loci (Kliegl et al.,
1990; Verhaeghen and Marcoen, 1996). In adult lifespan samples,
both cognitive abilities (Schaie, 1996; Li et al., 2004; Rönnlund
et al., 2005) and gains from mnemonic training (Verhaeghen
etal.,1992)declinewithage.Moreover,cognitiveabilitiesareusu-
ally positively related to gains from mnemonic training (Kliegl
et al., 1990; Lindenberger et al., 1992; Verhaeghen and Marcoen,
1996). This pattern of findings suggests that individual and
age-related differences in gains from cognitive training can be
explained by initial differences in cognitive resources available
to acquire, implement, and sharpen effortful cognitive strategies.
The magnification account comes with three predictions. First,
group differences should be magnified after training, in the sense
that groups starting out higher will gain more. Second, within
groups, gains from cognitive training should correlate positively
with cognitive abilities as well as with initial performance. Third,
the magnitude of interindividual differences should increase as
a function of training because differences between the high-
and low-performing individuals should be greater after training
than at baseline assessment. The magnification view has gained
widespread acceptance in the cognitive aging community (e.g.,
Kramer and Willis, 2002; Baltes et al., 2006; for reviews see
Verhaeghen et al., 1992; Verhaeghen and Kliegl, 2000, see also
Bjorklund et al., 1997).
In contrast, the basic reasoning in favor of the competing
compensation account is that individuals with good assets are
already functioning at optimal levels and thus have less room
for improvement. In the case of mnemonic strategy training, for
example, individuals who already apply an efficient and honed
mnemonic strategy that yields good memory might gain lit-
tle from being taught another efficient strategy, as compared
to individuals who apply an inefficient or no strategy. Thus,
the compensation account predicts that gains from cognitive
training correlate negatively with cognitive abilities and initial
performance, and that age differences, and other interindividual
differences, are reduced after training. Notably, supporting data
for the compensation model appears to be more prevalent in the
literature on child development (e.g., Gaultney et al., 1996; Cox,
2001; see also Bjorklund and Douglas, 1997; Schneider, 2012).
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Lövdén et al.Compensation versus magnification
Though both the magnification and the compensation views
make clear and competing predictions, their simultaneous
presence also gives room for post-hoc explanations of empirical
observations because neither account includes predictions for the
conditions under which it may or may not be applicable. Here,
werely onthe recently introduced theoretical distinction between
flexibility and plasticity (Lövdén et al., 2010; see also Baltes, 1987;
Will et al., 2008) to arrive at such discriminating predictions, and
then test our predictions in a sufficiently large data set on lifespan
differences in memory plasticity.
AccordingtoLövdénetal.(2010),flexibilitydenotesthecapac-
ity to optimize performance within the limits of the brain’s
currently imposed structural constraints. That is, the cogni-
tive system is characterized as having a range of existing (i.e.,
previously formed) representational states available, and to con-
stantly adapt to environmental demands by assuming such states.
This notion of a range of performance and function is similar
to the concept of baseline reserve capacity (e.g., Baltes, 1987),
and points to the malleability of cognitive performance through
environmental support (e.g., instructions). In contrast, plastic-
ity denotes the capacity for changes in the possible range of
cognitive performance enabled by flexibility (cf. Baltes, 1987;
Baltes et al., 2006). In other words, adaptations of the brain
to environmental changes do not uniquely define plasticity, but
rather constitute a fundamental property of experience and a
starting point of plasticity. Whereas flexibility refers to the adap-
tation of a pre-existing behavioral repertoire, plasticity refers
to the expansion of this repertoire following structural cerebral
change.
We propose that the distinction between flexibility and plas-
ticity permits predictions about the empirical conditions under
which compensation or magnification are more likely to occur.
First, performance gains primarily acquired by making use of
flexibility are likely to display a pattern consistent with the
compensation model. If the brain’s performance for a partic-
ular task is already optimized within current structural con-
straints, then nothing can be gained from altering the way
that a task is executed, be it through instructions or through
some other means. Hence, within the range of performance
covered by flexibility, better performing individuals will gain
less. In contrast, the situation is radically different if extensive
practice pushes individuals beyond the current range of per-
formance, thereby inducing plastic changes. In this case, the
prevailing empirical pattern should be magnification because
individual differences in baseline levels of performance and cog-
nitive resources are, at least in part, a reflection of past manifesta-
tions of plasticity. Under such conditions, we expect that baseline
performance will correlate positively with intervention-induced
training gains.
To address this set of predictions, we reanalyzed data from
a study previously reported by Brehmer et al. (2007; see also
Brehmer et al., 2008). In this study, children, younger adults,
and older adults were first taught and then allowed to practice
memory performance with an interactive imagery mnemonic,
akin to the Method of Loci (Bower, 1970). The mnemonic
used is well suited for encoding and retrieving location-word
paired-associates, which were the target of training. After
initial assessment of performance, instruction sessions, and a
post-instruction assessment of performance, an adaptive proce-
dure, involving individual adjustment of presentation times, was
used to producea measurement spacecovering all agegroups and
the total practice phase (for details, see Brehmer et al., 2007).
In addition, to assess baseline cognitive resources, Brehmer and
colleagues (2007) also administered a psychometric battery of
tasks measuring four cognitive abilities: perceptual speed, rea-
soning, episodic memory, and verbal knowledge. The present
reanalysis goes beyond Brehmer and colleagues (2007, 2008) by
addressing the predictions from the compensation and magni-
fication views, and by applying statistical techniques (structural
equation modeling; SEM) suitable for analyzing interindivid-
ual differences in performance changes as well as correlations
between initial level and change. In contrast, previous reports
of this data focused on age group differences (Brehmer et al.,
2007) and maintenance (Brehmer et al., 2008) of mean perfor-
mance.
To summarize, we assume that gains due to instructions in the
mnemonic technique are primarily acquired through flexibility,
as they recruit and configure existing resources, such as knowl-
edge about memory strategies. In contrast, performance gains
produced through subsequentpractice primarilyreflect plasticity.
Specifically, during practice, all individuals are likely to per-
form the task in a qualitatively similar fashion, and performance
improvements reflect changes in the possible range of cognitive
performance. Based on these considerations, we hypothesized
that instruction gains follow the prediction from the compensa-
tion view whereas practice gains follow the prediction from the
magnification model.
MATERIALS AND METHODS
PARTICIPANTS
The sample consisted of 50 children aged 9–12 years (Mage=
11.0; SDage= 1.2; 24 girls), 29 younger adults aged 20–25
years (Mage= 22.5; SDage= 0.6; 15 women), and 29 older
adults aged 65–78 years (Mage= 66.9; SDage= 3.7; 14 women).
Children either had received the elementary school’s recom-
mendation to attend, or were attending the German school
type with the highest entry requirements after completion
of elementary school (i.e., Gymnasium). Younger adults were
students at Saarland University, Saarbrücken, Germany. Older
adults were either auditors at Saarland University, participants
in other continuing education programs, or both. All partic-
ipants had normal, or corrected to normal, vision, and hear-
ing. Participants were paid 7.5 Euro for each full hour of
testing.
Table 1 summarizes scores on four cognitive composites rep-
resenting performance onpsychometric tests ofperceptual speed,
episodic memory, reasoning, and verbal knowledge as a func-
tion of age group. For a detailed description of these composites,
seeBackgroundassessment.Importantly,thecognitivecharacteris-
tics display the typical developmental dissociation of an inverted
U-shape for the measures of broad fluid abilities (memory, per-
ceptual speed, and reasoning), and a continuous age-related
increase in verbal knowledge (e.g., Li et al., 2004). Thus, although
the overall sample is positively selected (see Brehmer et al., 2007
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Lövdén et al.Compensation versus magnification
Table 1 | Cognitive characteristics of the age groups.
VariableChildren Younger adultsOlder adults
M SDM SDM SD
Perceptual speed
Paired-associates
Reasoning
Verbal knowledge
44.8
49.9
46.4
40.5
5.0
10.4
7.5
5.1
63.3
55.2
59.7
57.5
6.0
7.8
8.3
4.2
45.8
45.1
46.4
58.9
7.2
9.0
9.0
4.2
Note: Perceptual speed = unit-weighted composite of Digit Symbol Substitution
(Wechsler, 1958) and Digit Letter; Reasoning = unit-weighted composite of
Figural Analogies, Letter Series, and Practical Problems; Verbal knowledge =
unit-weighted composite of Spot-a-Word and Vocabulary. All variables were
scaled to the T-metric (M = 50; SD = 10), with the total sample providing
reference values.
for details), it constitutes a satisfactory approximation of lifespan
population trends in cognitive functioning.
MEMORY TASK
Materials
Every study list consisted of 16 location-word pairs. Sixteen
generic common city locations (e.g., bakery and train station)
wereused.The16locationswererecycled acrossthedifferentlists.
The presentation order of the location cues was separately ran-
domized at encoding and retrieval, for each list in a new random
order.
A total of 413 highly imaginable and concrete nouns were
selected asmemorymaterialsfromapoolof1,200wordsrecorded
by a professional radio speaker. Selection was based on a rat-
ing study with 10 children (7–9 years old) to reduce a possible
confound of age differences in word knowledge (Brehmer et al.,
2004). No word was administered more than once within a given
session. Words were recycled over sessions with the following
three constraints: (a) A word presented at a given session did not
reappear in the next session; (b) within each list, the first three
letters of all 16 words were different from each other to avoid
errors during response entry; and (c) words presented at the pre-
instruction, post-instruction and posttest assessments were not
presented in any other sessions.
Experimental paradigm
During the encoding phase, the words constituting location cues
were presented visually on a monitor, and to-be-learned words
were presented over headphones. First, a blank screen was pre-
sented. Second, the location cue was presented. Third, the loca-
tion cue was replaced by a fixation cross, and the to-be-learned
word was presented. The time for the third phase was set to 10s
for pre-instruction and post-instruction sessions. For the prac-
tice sessions, an adaptive algorithm dynamically set the encoding
time for each participant individually for each list. At the final
session for each individual, memory performance was assessed
at a fixed (across lists), but individualized, presentation rate (see
Individually Adaptive Practice).
After all 16 location-word pairs had been presented partic-
ipants started the recall phase by pressing the space bar. After
that, an empty screen appeared for 0.5s, followed by a location
cue, which was presented for 5s. After another 5s, a rectangle
appeared on the screen to signal the participants that responding
was possible. Participants made their responses by entering the
first three letters of the corresponding word. The response time
window was 90s. Participants went to the next location cue by
pressing the enter bar. After recall of each list, participants were
given feedback on their level of recall performance.
PROCEDURE
The general procedures can bedived into five phases: background
assessment, baseline assessment, mnemonic instruction, post-
instruction assessment, and individually adaptive practice, which
ranged from 3 to 7 sessions (see Table 2 for an overview of the
study design).
Background assessment
Inthefirstsession, participants wereadministered ademographic
questionnaire, tests of sensory acuity, and a psychometric battery
of tests assessing perceptual speed, reasoning, paired-associates
(episodic memory), and verbal knowledge (Lindenberger et al.,
1993; see also Lövdén et al., 2004). A Macintosh SE30 computer
equipped with a touch-sensitive screen was used for cognitive
testing.
Table 2 | Outline of study design.
Phase of studyNumber of sessionsDescription Lists observedLists used
Background assessment1 Demographic questionnaire, psychometric battery of intellectual
abilities, visual and auditory acuity
Baseline assessment1 Cued recall of four word lists: first two lists with number cues,
second two with location cues
1–43 + 4
Mnemonic instruction2Introduction to a variant of interactive imagery, followed by
individualized instruction and initial training
Post-instruction assessment1Cued recall of six word lists using interactive imagery without
assistance
5–107 + 8
Individually adaptive practice 3–7Maximum of 36 lists (= 6 lists x 6 sessions) of adaptive practice
to adjust individuals performance to a pre-fixed performance
criterion, followed by six lists after reaching the performance
criterion
11–5211–52
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Lövdén et al.Compensation versus magnification
Verbal knowledge. Two tests, Spot-a-Word and Vocabulary,
formed a unit-weighted composite representing verbal knowl-
edge. The composite was scaled to the T-metric (M = 50;
SD = 10) with the total sample providing reference values. For
the Spot-a-Word test, 35 items containing one word and four pro-
nounceable non-words were presented successively on the screen.
Participants were asked to select the word without any time pres-
sure. Number of correct responses was the dependent variable.
For the Vocabulary test, 16 words were presented one-by-one on
the screen. Participants produced definitions for each item that
were coded by two independent raters. Each response received a
score of 0 (wrong), 1 (partially correct), or 2 (correct). The sum
of the 16 scores was the dependent variable. Testing time was
unlimited.
Paired-associates. As a marker of episodic memory we used
Paired-associates. Eight pairs of nouns were presented twice at a
rate of 5s per pair. After each of two presentations, the first noun
of each pair was presented as a recall cue. The dependent variable
was the total number of correctly remembered items across the
two lists, scaled to the T-metric.
Reasoning. The T-scaled unit-weighted composite representing
reasoning was composed of three tasks, Figural Analogies, Letter
Series, and Practical Problems. In all three tasks the test phase was
terminated when subjects madethree consecutive false responses,
when they reached the maximum time limit (15min), or after
theyhadansweredthelastitemofthetest. IntheFiguralAnalogies
test, items followed the format “A is to B as C is to?”. Participants
chose one of five alternative answers to complete the open fig-
ure analogy. The number of correct responses was the dependent
variable. For each item of the Letter Series test, a series of five let-
ters followed by a question mark was presented. Participants had
to choose the right letter out of five alternatives that logically fol-
lowed the underlying rule of the letter series used in each item.
The dependent variable was the number of correct responses. In
the Practical Problems task, participants solved everyday prob-
lems, such as the hours of a bus schedule, instruction of medi-
cation as well as other forms and tables. Answers were given by
choosing one of five alternatives and the dependent variable was
the number of correct responses.
Perceptual speed. Two tests, DSS and Digit Letter, formed a
T-scaled unit-weighted composite representing perceptual speed.
For the DSS test, the Wechsler (1958) version of the test was used.
Participants had 90s to write as many symbols as possible. The
number of correctly written symbols was the dependent vari-
able. The Digit Letter test closely resembles the DSS test except
that subjects had to name letters instead of writing symbols with
respect to corresponding digits. The dependent variable was the
total number of correct responses after 3min.
Baseline assessment
In the second session, individuals were asked to encode and recall
four lists of 16 words each. The first two lists involved numbers
ranging from 1 to 16 as cues. The 16 locations were used for the
last two lists as well as for the rest of the experiment.
Mnemonic instruction
In the next two sessions, participants were introduced to a mod-
ified interactive-imagery version of the Method of Loci. The first
session took place in age-homogeneous groups of 3–4 individ-
uals. After introducing the participants to the historical origins
of the method, the principles of the method were explained by
giving concrete examples. The instruction emphasized the gen-
eration of interactive images that associate the location cue with
the to-be-learned word.Participants then practiced the technique
withtwowordlists.Instructionandsupervisedtrainingwerecon-
tinued individually with six word lists in the second instruction
session. Supervised training included prompts to verbalize and
discuss all aspects of image formation and image retrieval, col-
laborative image generation, assistance during recall, repetition
and elaboration of instructions, as well as various other forms of
encouragement.
Post-instruction assessment
In this session, and all further sessions, six lists of location-word
pairs were presented sequentially for encoding and retrieval. No
assistance in using the mnemonic technique was provided.
Individually adaptive practice
This phase of individual practice sessions used adaptive adjust-
ment of encoding times (cf. Kliegl and Lindenberger, 1993) to
control task difficulty individually. For each participant, this part
of the study lasted between three and seven sessions, depending
on the number of sessions needed to reach stable levels of mem-
ory performance as defined by the adaptive practice procedure
(see below). Individuals participated in one or two sessions per
week, with a minimum of 2 days between sessions.
For each individual, an adaptive algorithm determined the
amount of encoding time per word for the next list by three vari-
ables: encoding time of the current list, the current step width of
adjustment, and the alteration, which is a variable that indicate
the direction (i.e., increased, decreased, or equal) of the previous
adjustment (for details and a numerical example, see Brehmer
et al., 2004). During practice, the values of all three variables
were updated after each list to maximize the likelihood that a
given individual would correctly recall 10 out of 16 words in the
next list. When the step width for the next list was lower than
0.08sorwhensix practicesessions werecompleted, afinalsession
was completed. Depending upon the speed with which the adap-
tive practice algorithm converged, the final session was scheduled
after the third to the seventh practice session. In this final ses-
sion, encoding time was adjusted to fix each individual’s level of
performance to 50% correct and was held constant across the six
lists given to participants in this session. This time-relative crite-
rionofcorrectperformancewaschosenbecauseofconsiderations
for subsequent memory analyses using electroencephalography,
which are not reported here. For motivational reasons, the crite-
rion was higher (i.e., 10 out of 16 word, or 62.5% correct) during
practice.
DATA ANALYSIS
The dependent variable: timed recall score
In this study, information regarding memory performance comes
from both encoding times and number of correctly recalled
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Lövdén et al. Compensation versus magnification
items. Thus, both pieces of information must be taken into
account. Typically, the function relating encoding time to the
number of words recalled approximates a logarithmic function
(e.g., Kliegl et al., 1994). Therefore, we divided the number of
correctly recalled items by the log of the associated encoding
time to produce a single dependent variable (henceforth, Timed
Recall Score; see also Brehmer et al., 2007). We also scaled up
this score by a factor of 10 to produce a variance of approxi-
mately the same magnitude as the T-scaled cognitive background
composites.
Modeling instruction gains
To analyze instruction gains (i.e., the difference between base-
line and post-instruction assessments; see Table 2) we fitted a
confirmatory two-factor model to the data from the baseline
assessment and the post-instruction assessment (see Figure1A).
That is, we assumed a latent unobserved variable representing
an individual’s latent error-free baseline performance score (BP)
before introduction to the mnemonic technique anda latent vari-
able representing an individual’s score after instruction (Post).
The latent BP score is defined as a unit-weighted factor of two
observed variables [list 3 (l3) and list 4 (l4)], representing per-
formance on the first and second lists using landmark cues in
the baseline assessment (the first two lists had numbers as cues),
respectively. The latent post-score is defined as a unit-weighted
factor of two other observed variables (l7 and l8), representing
performance on the third and fourth lists presented to partici-
pants in the post-instruction assessment. The reason for includ-
ing only two lists from the post-instruction assessment was to
match the list-order of the lists tapping baseline performance. We
simultaneously and freely estimate the error variances (σ2
σ2e7, and σ2
ρe4,e8), and the mean difference between the lists used as indi-
cators of baseline and post-instruction performance (μlistdiff). Of
particular interest, we simultaneously estimate the mean of base-
line performance (μBP), interindividual differences in baseline
performance (σBP), the mean of the latent post-instruction per-
formance (μpost), interindividual differences in post-instruction
performance (σpost), and the correlation between baseline per-
formance and post-instruction performance (ρBP,post). We also
included the cognitive composites of perceptual speed, episodic
memory, reasoning, and verbal knowledge as observed variables,
and allowed these to freely covary among themselves and with
latent baseline performance and post-instruction performance
(not shown in Figure1A)1. In order to compare the estimates
across age groups, we estimated this model as a multigroup
model (children, younger adults, and older adults). In the start-
ing model, no across-group constraints were applied. With this
model, we can inspect the standard deviations of the latent fac-
tors, baseline performance, and post-instruction performance,
e3, σ2
e4,
e8), the autocovariances between the errors (ρe3,e7and
1In all models applied in this paper the psychometric composites were
included as a single indicator of a latent variable with a variance of one and
thepath(now representing thestandard deviation ofthecognitive composite)
aswellastheintercept freely estimated.The latent variable wasallowedto cor-
relate with other variables. This implementation allows for direct estimation
and comparison of standardized covariances (i.e.,correlations) in themodels.
and test for the effects of training on between-person differences
expected from the compensation and magnification views.
Next, we reformulated the confirmatory factor model into a
latent difference model (LDM; McArdle and Nesselroade, 1994).
Figure1B displays a graphical representation of the LDM as
we implement it here. In this model, the latent post-scores are
defined as the unit-weighted sum of the latent pre-score plus a
latent difference score (Gain), so that the Gain factor is inter-
preted as the latent difference (reliable gain) from the base-
line to the post-instruction assessment. Thus, this gain factor
reflects instruction gains. This latent difference approach atten-
uates problems related to unreliability of raw difference scores
by estimating the mean and variance of differences separately
from error variance. Of particular interest, this models allows
for simultaneously estimating the mean of baseline performance
(μBP), interindividual differences in baseline performance (σBP),
the mean of the latent gain scores (μgain), interindividual dif-
ferences in gain (σgain), and the correlation between baseline
performance and gain (ρBP,gain). Thus, with this model we can
examine the prediction that magnification and compensation
views have regarding the correlations between initial level of
performance and gains from instruction in a methodologically
rigorous manner.
Modeling practice gain
We analyzed practice gains with a latent curve model (LCM;
e.g., Bryk and Raudenbush, 1987; McArdle and Epstein, 1987;
Meredith and Tisak, 1990; McArdle, 2006). Figure2 displays
a graphical representation of the LCM implemented here. The
observed variables, l11–l52, emanate from the seven sessions in
the phase of individually adaptive practice, each session includ-
ing the presentation of six location-word lists. In a linear LCM,
two latent variables, the intercept IC and the linear slope S, are
proposed to account for the time series information. The linear
slope S represents linear gain from practice by constraining the
42 loadings oftheobservedvariablesonSto increaselinearly. The
intercept IC represents an individual’s latent score at the end of
the time series (i.e., at l52) by setting the factor loading of the
observed variable l52 on S to zero (i.e., l11 has a −41 loading
on S, l12 has a −40 loading, etc.; see the loading matrix (?) in
Figure2). The intercept and the linear slope factors are estimated
at the mean level (i.e., their means μICand μSare estimated),
they both allow forinterindividual differences (i.e., their standard
deviations σICand σSare estimated), and they may covary ρIC,S.
The error variance σ2
eis commonly assumed to have a mean of
zero and to neither correlate nor change over time. Estimating
the six parameters mentioned so far (μIC, μS, σIC, σS, ρIC,S,
σ2
e) corresponds to estimating a classic linear LCM. We included
an additional factor representing the orthogonal quadratic effect
(S2). For these factors, preliminary analyses showed no signifi-
cant interindividual differences (i.e., standard deviations) for any
of the age groups. Therefore, we did only estimate the mean μS2
and not the standard deviation.
In addition to the standard modeling of the time series with
polynomials, we included session-wise factors representing the
uniquelinear slope within a session. The loadings of the observed
variables(six location-wordlists foreach ofthe sevensessions)on
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Lövdén et al.Compensation versus magnification
FIGURE 1 | Graphical representation of the confirmatory factors model
(A) and the latent differences score model (B) used to estimate
gains from mnemonic instruction (baseline plasticity). Observed variables
are represented by squares, latent variables by circles, regression
weights by one-headed arrows, and variances and covariances by
two-headed arrows. The triangle indicates means. Unlabeled parameters
are fixed to 1. BP , baseline performance; POST, post-instruction
performance; l, list.
the session-wise slope factors (SS1–SS7) were defined as linearly
increasing across lists within a session. The session-wise slope
factors were included because we expected proactive interference
fromthepreceding lists (e.g., Kliegl andLindenberger, 1993)and,
to some extent, other reactive effects related to list-order (e.g.,
fatigue) to reduce practice-related gains on performance within
sessions. We freely estimated the means of the session-wise slope
factors (μSS1–μSS7) but fixed their standard deviations to zero.
The assumption that the session-wise reactive effects took on a
linear form without interindividual differences were based on
visual inspection of the data. Specifically, we averaged the Timed
Recall Score over sessions by list position within a session for each
individual.Separatelyfortheagegroups,theindividualmeansare
displayed as a function of list position in Figure3, which clearly
suggests an approximately linear decrease as a function of list
position for most of the individuals. Furthermore, individual dif-
ferences in the slopes appeared to be limited. Indeed, preliminary
analyses allowing the variances for the session-wise slopes to be
estimated did not result in an increase in fit, further bolstering
the decisions to model these session-wise slopes without allowing
for interindividual differences.
In analogyto the analyses ofthe instruction gains, we included
the cognitive composites (not shown in Figure2) as observed
variables, and allowed these to freely covary among themselves
as well as with the intercept and the linear slope. In addition, we
estimated the model as a multigroup model (children, younger
adults, and older adults). In the starting model, no across-group
constraints were applied.
Handling missingness
Not all individuals contributed data to all variables. For the
analyses of instruction gains with the LDM, the number of
missing values was limited (a few missing values owing to tech-
nical problems and deletion of outliers). For practice gains, the
number of missing values was dramatically higher, reflecting
planned missingness due to the termination rule of the adap-
tive training procedure (see General Procedures; cf. McArdle,
1994). Specifically, all individuals provided scores in the first
three sessions (l11–l34), but thereafter data become more and
more sparse. Planned missingness was handled by taking the
scores from each participant’s final session and imputing these
scores through the rest of the time series. This procedure
assumes that the last completed session provides an accurate
description of asymptotic performance, both with respect to
the overall time series as well as to the session-wise reac-
tive effects. Previous analyses suggested that a step width
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Lövdén et al.Compensation versus magnification
FIGURE 2 | Graphical representation of the latent growth curve
model implemented here. Observed variables are represented by
squares, latent variables by circles, regression weights by one-headed
arrows, and variances and covariances by two-headed arrows.
The triangle indicates means. Unlabeled parameters are fixed to the values
displayed in the matrix of loadings. IC, intercept, reflecting post-training
performance; S, linear slope; S2, quadratic slope; SS1–7 , session-wise linear
slopes; l, list.
below 0.08 is conservative enough for making this assumption
(Brehmer et al., 2007).
Remaining instances of missingness (due to technical prob-
lems and deletion of outliers) were accommodated by estimating
the model with Full Information Maximum Likelihood (FIML;
Finkbeiner, 1979; Arbuckle, 1996; Duncan et al., 1998; Wothke,
2000; Enders, 2001; Schafer and Graham, 2002). The FIML algo-
rithm does not result in imputed values but uses the information
in the complete data for estimating parameters that involve miss-
ing values. The FIML algorithm and related approaches generate
more precise and less biased population estimates than other
widespread procedures dealing with missing values (e.g., listwise
deletion, regression imputation, mean imputation; e.g., Wothke,
2000; Schafer and Graham, 2002). The FIML algorithm operates
under theassumptionofMissing-at-Random (MAR;Rubin,1976;
see Schafer and Graham, 2002, for a non-technical treatment),
which means that the probability that a score on variable X is
missing may depend on other variables in the model, but not on
X itself. Note also that under the MAR assumption a relationship
between missingness and X produced by the mutual association
to the other variables in the model is allowed, but there must
be no residual relationship between missingness and X once the
other variables are taken into account.
General statistical considerations
We note that our sample size is small for SEM. Some method-
ological limitations associated with small sample sizes are, for
example, potential violations ofmultivariate normality, problems
withimpropersolutions,andlowpower.Toaddresspotential vio-
lations of multivariate normality, we devoted considerable atten-
tion to the screening of variables. Wedetected five outliers among
the post-instruction lists, seven outliers among the practice lists,
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Lövdén et al.Compensation versus magnification
FIGURE 3 | Timed Recall Scores averaged over sessions by list position
within a session for each individual in the group of children (A),
younger adults (B), and older adults (C). Each line represents the scores
for one individual.
one outlier for reasoning, and two outliers for perceptual speed.
After deletion of the outlier scores, skewness, and kurtosis were
within an acceptable range for all variables (rangeskewness= −2.5
to 1.7; rangekurtosis= −1.7 to 8.3), indicating satisfactory uni-
variate normal distributions (e.g., Kline, 1998). Satisfactory
univariate distributions also reduce the risk for violations of
multivariate normality. The only variable bordering to devia-
tions from normal distribution was the second list (l8) indicating
post-instruction performance for the group of younger adults
(skewness = −2.5; kurtosis = 8.3), which reflected a tendency
for ceiling effects. This tendency arose because encoding time
was fixed across all individuals at 10s for the baseline and post-
instruction assessments. In addition to univariate screening, we
visually inspected the graphed time series of each individual for
atypical patterns. No individual time series was judged to consti-
tute amultivariate outlier. Insummary, wefound no violations of
multivariate normality in the final data set. In addition, we note
that minimum was achieved without problems and no improper
solutions were obtained. Finally, the power of the present statisti-
cal approachis, inthe caseofthe LCM, boosted by the abundance
of variables from which relatively few substantively important
parameters are extracted (e.g., Hertzog et al., 2008). Nonetheless,
the LCM applied is quite complex considering the limited sam-
ple size, and we, therefore, also did follow-up analyses applying
the LDM to the analyses of practice gains (see Results for a more
detailed description).
WeutilizedAMOS5.0forallcomputations.Modelfitwaseval-
uated with the χ2statistic and associated p-value, the normed
χ2(χ2/df), the Comparative Fit Index (CFI), and the Root Mean
Square Error of Approximation (RMSEA). A χ2/df below 2, a CFI
above 0.90, and a RMSEA below 0.08 indicate acceptably fitting
models (Arbuckle and Wothke, 1999). The likelihood ratio test
(difference in χ2; ?χ2) was used for comparing nested models.
The level for all statistical decisions was 0.05.
RESULTS
BASELINE PERFORMANCE AND INSTRUCTION GAINS
First we estimated the confirmatory two-factor model of base-
line and post-instruction performance displayed in Figure1A as
a multigroup model (children, younger adults, and older adults)
while including the cognitive composites of perceptual speed,
episodic memory, reasoning, and verbal knowledge as observed
variables. This starting model had an acceptable fit, χ2= 39.46,
df = 30, p = 0.116, CFI = 0.946, RMSEA = 0.055. Inthis model
we tested the compensation view’s prediction that interindividual
differences inperformancedecreaseafter instructions bycompar-
ing the starting model with a model assuming that the standard
deviations of the two latent factors were equal across time for
all groups. This model produced a decrease in fit, ?χ2= 57.52,
df = 2, p < 0.001. Fixing the standard deviation to equal across
time separately for the young children, young adults, and older
adultsresulted indecreasesinfitforallthesethreemodelsincom-
parison with the starting model, ?χ2= 12.49, df = 1, p < 0.001
for children, ?χ2= 34.84, df = 1, p < 0.001 for younger adults,
and ?χ2= 10.20, df = 1, p < 0.001 for older adults. The stan-
dard deviations decreased after instruction for all groups.
Next we estimated the LDM of instruction gains shown in
Figure1B. The starting model had a fit identical to the confir-
matory factor model reported above. We started by examining
the compensation view’s prediction that groups starting out
lower would gain more from instruction. The means at base-
line and post-instruction assessments (predicted from the mean
gain) are displayed as a function of age group in Figure4. An
inspection of this figure suggests age-group differences in base-
line performance. Estimating the means of baseline performance
to be equal across age groups, as an omnibus test of group
differences, yielded a reliably less well fitting model than the
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Lövdén et al. Compensation versus magnification
FIGURE 4 | Baseline performance and gains from instruction. Mean
performance (Timed Recall Score) at baseline and post-instruction
assessment for children, younger adults, and older adults, as predicted
from baseline performance and instruction gain.
starting model, ?χ2= 40.79, df = 2, p < 0.001. Univariate tests
showed that younger adults (μpre= 13.25) performed signifi-
cantly better than both children (μpre= 7.74), ?χ2= 35.53,
df = 1, p < 0.001, and older adults (μpre= 7.09), ?χ2= 32.81,
df = 1,p < 0.001.Childrenandolderadultsdidnotdiffersignifi-
cantly in baseline performance, ?χ2= 0.53, df = 1, p > 0.467.
All groups gained reliably from instruction. Children gained
on average 3.21 scores (z = 6.60), younger adults gained 1.97
scores (z = 3.20), and older adults gained 5.38 scores (z =
7.22). The omnibus test involving average gains from instruc-
tion indicated significant age-group differences, ?χ2= 10.93,
df = 2, p < 0.004. Univariate tests showed that the group of
older adults gained significantly more than both children,
?χ2= 5.22, df = 1, p < 0.022, and younger adults, ?χ2=
10.73, df = 1, p < 0.001. Note, however, that there was a ten-
dency for ceiling effects at post-instruction assessment for the
younger adults, which probably reduced the mean gains for
this group.
Next we addressed the predicted negative correlation between
baseline performance and gains from instruction. All variances
and standard deviations were significant. Figure5 displays indi-
vidual baseline and post-instruction performances (average of
the two lists at each assessment) separately for the children
(a), younger adults (b), and older adults (c). An inspection
of Figure5 reveals pronounced between-person differences in
instruction gains: within age groups, individuals differed in how
much they gained in memory performance from mnemonic
instruction. Table 3 displays the correlations among baseline
memory performance, gains from mnemonic instruction, and
the cognitive composites, separately for the three age groups.
The most salient finding reported in Table 3 is the strong
negative correlations between baseline performance and instruc-
tion gain observed in all age groups, indicating that individ-
uals entering the study with low memory performance gained
more from instruction than those who entered the study with
FIGURE 5 | Individual baseline performance and gains from
instruction. Performance at baseline and post-instruction assessments for
each individual in the group of children (A), younger adults (B), and older
adults (C). The scores at baseline and post-instruction assessments are
unit-weighted composites of the two lists indicating performance at each
assessment, respectively. To plot all scores on the positive axis, a constant
of 10 has been added to all scores.
good memory performance (see also Figure5). Caution is, how-
ever, warranted when interpreting this finding for the group
of younger adults because their tendency for a ceiling effect
at post-instruction assessment may contribute to the nega-
tive correlation. Likewise, correlations between the cognitive
composites and instruction gain indicated that Paired-associates
performance was negatively related to instruction gain in the two
adult groups.
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Lövdén et al. Compensation versus magnification
Table 3 | Correlations among cognitive composites, baseline memory performance, and gain in memory performance from baseline to
post-instruction assessments (instruction gain) separately for the age groups.
Instruction gainPaired-associates Perceptual speedReasoning Verbal knowledge
CHILDREN
Baseline performance
Instruction gain
YOUNGER ADULTS
Baseline performance
Instruction gain
OLDER ADULTS
Baseline performance
Instruction gain
−0.85∗
—
0.35∗
0.01
0.00
0.29
0.22
−0.23
0.24
0.10
−0.99∗
—
0.39∗
−0.37∗
0.15
−0.15
0.11
−0.04
−0.02
0.06
−0.90∗
—
0.66∗
−0.56∗
0.20
−0.01
0.44∗
−0.19
0.11
0.10
Note: Perceptual speed = Unit-weighted composite of Digit Symbol Substitution (Wechsler, 1958) and Digit Letter; Reasoning = Unit-weighted composite of Figural
Analogies, Letter Series, and Practical Problems; Verbal Knowledge = Unit-weighted composite of Spot-a-Word and Vocabulary.∗p < 0.05.
Tosumup,theanalysesofinstruction gainsrevealanempirical
pattern consistent with the compensation account: interindi-
vidual differences in memory performance are reduced after
instructions, group mean differences are reduced, and baseline
performance correlates negatively with gains from instructions
within the groups.
BASELINE PERFORMANCE AND PRACTICE GAINS
To address the predictions regarding practice gains, we simul-
taneously estimated the LDM of instruction gains and a LCM
of the practice gains. This model was estimated as a multi-
group model (children, younger adults, and older adults) while
allowing the cognitive composites to freely covary among them-
selves and with baseline performance, instruction gain, lin-
ear practice gain, and post-training performance. The starting
model estimated 171 parameters with a log-likelihood function2
of 21,750.47.
We first tested the magnification view’s prediction that
interindividual differences in performance increase from training
by comparing the starting model with a model assuming that the
standard deviations of the baseline assessment and post-practice
performance were equal across time for all groups. This model
produced a decrease in fit, ?χ2= 57.88, df = 3, p < 0.001.
The standard deviations increased from baseline assessment to
post-practice assessment for the groups of children (3.39–8.23),
?χ2= 33.31,df = 1,p < 0.001,andyoungeradults(2.83–8.22),
2With FIML, the overall log-likelihood fitting function for a model is the sum
of the casewise likelihoods. The chi-square statistic and derivate indices are
calculated from the difference between the log-likelihood fitting functions of
the saturated (unrestricted) model and the restricted model (e.g., the applied
LCM) with the degrees of freedom equal to the difference in the number
of estimated parameters between the models. This calculation was done for
the LDM applied to the instruction gains. However, not enough informa-
tion was available in the data set to fit the saturated model for the LCM.
Thus, we report only the minimum value of the function of log-likelihood for
the restricted model (i.e., the applied LCM). The lack of the conventional fit
indices for theLCM isnot problematic because thefit of themodel is not crit-
ical per se; rather, the major focus is on the parameter estimates, differences
in the estimates across age groups, and thus differences between alternative
models.
?χ2= 24.52, df = 1, p < 0.001, but not for the group of older
adults (3.53–3.69), ?χ2= 0.05, df = 1, p > 0.816.
Next, we examined the means predicted from the estimates
of the intercept, linear slope, and quadratic slope of the practice
period (see Figure6). All groups gained in memory performance
from practicing. Children had a linear mean gain (μS) of 0.17
(z = 8.31), younger adults gained 0.35 scores (z = 10.32), and
older adults gained 0.04 scores (z = 3.70) per practiced list.
The omnibus test indicated significant age-group differences,
?χ2= 52.51, df = 2, p < 0.001. Pairwise comparisons showed
that younger adults gained significantly more than children,
?χ2= 17.37, df = 1, p < 0.001. In turn, children gained more
than older adults, ?χ2= 21.16, df = 1, p < 0.001.
Figure6 suggests that the practice-related improvements in
memory performance took on a quadratic shape for children and
younger adults. In fact, the quadratic mean slope (μS) was sig-
nificant for children (−0.004; z = 4.62) and younger adults only
(−0.015; z = 9.35). Note that follow up analyses showed that the
FIGURE 6 | Practice gains. Mean performance (Timed Recall Score) during
the practice phase as predicted from the parameter estimates of the
intercept, linear slope, and quadratic slope as a function of list number and
age group.
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Lövdén et al.Compensation versus magnification
apparent tendency for declining performance for younger adults
toward the end of the time series could be partially removed by
adding a cubic trend. However, this trend did not reach signifi-
cance (p > 0.13) and we thus decided against including it in the
final models.
Finally, we addressed the predicted positive correlation
betweenbaseline performance and gains from practice.
Importantly, all estimated variances and standard deviations,
including the linear practice gains, were statistically reliable.
Table 4 displays the correlations among post-training memory
performance, practice gain, and the cognitive ability composites.
The most salient finding is the uniformly strong and positive
correlations between post-training performance and practice
gains, indicating that the magnitude of practice-related gains
for an individual was strongly determining the individual’s rank
order at the end of training. All cognitive composites showed
some significant and positive associations with post-practice
performance and with linear practice gains, but it is difficult to
discern any consistent and salient pattern within or across age
groups for these correlations.
Table 5 presents the correlations, separately for the three age
groups, among all the estimated components of the training
curve.The new informationinthis tableisa weakpatternofposi-
tive correlations between baseline performance and post-practice
performance. In addition, for children, baseline performance
correlates positively with practice gains.
Because the main take-home messages from these analyses are
based on a quite complex model fitted to a relatively small sam-
ple, we also double-checked these results in a simplified model of
practice gains. In this model, fitted as a multigroup model (chil-
dren, younger adults, and older adults), the practice gains were
modeled in a similar way as the instruction gains, with a latent-
difference score model. For the practice gains, a pre-practice
factor was formed by the six first lists of the practice phase and a
post-practice factor was formed by the last six lists completed by
each participant. Initial analyses of these factors confirmed that
Table 4 | Correlations among cognitive composites, post-training memory performance (IC), and linear gain in memory performance from
practice (S) separately for the age groups.
Practice gain (S)Paired-associates Perceptual speedReasoning Verbal knowledge
CHILDREN
Post-training (IC)
Practice gain (S)
YOUNGER ADULTS
Post-training (IC)
Practice gain (S)
OLDER ADULTS
Post-training (IC)
Practice gain (S)
0.87∗
—
0.38∗
0.12
0.40∗
0.42∗
0.23
0.05
0.40∗
0.18
0.91∗
—
0.20
0.13
0.14
0.02
0.34∗
0.33
0.28
0.22
0.76∗
—
0.19
−0.16
0.29
0.03
0.54∗
0.23
0.31
0.11
Note: Perceptual speed = Unit-weighted composite of Digit Symbol Substitution (Wechsler, 1958) and Digit Letter; Reasoning = Unit-weighted composite of Figural
Analogies, Letter Series, and Practical Problems; Verbal Knowledge = Unit-weighted composite of Spot-a-Word and Vocabulary.∗p < 0.05.
Table 5 | Correlations among baseline memory performance, instruction gain, gain from practicing (S), and post-training performance (IC)
separately for the age groups.
Baseline performanceInstruction gain Practice gain (S)Post-training (IC)
CHILDREN
Baseline performance
Instruction gain
Practice gain (S)
Post-training (IC)
YOUNGER ADULTS
Baseline performance
Instruction gain
Practice gain (S)
Post-training (IC)
OLDER ADULTS
Baseline performance
Instruction gain
Practice gain (S)
Post-training (IC)
—
−0.85∗
0.33∗
0.46∗
—
−0.05
−0.05
—
0.87∗
—
—
−0.99∗
−0.02
0.11
—
0.13
0.03
—
0.98∗
—
—
−0.90∗
−0.09
0.31
—
0.18
0.02
—
0.76∗
—
Note:∗p < 0.05.
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Lövdén et al. Compensation versus magnification
within-group interindividual differences increased for children
and younger adults. That is, the standard deviations increased
from baseline assessment to post-practice assessment for the
groupsofchildren,?χ2= 22.09,df = 1,p < 0.001,andyounger
adults, ?χ2= 19.91, df = 1, p < 0.001. When these factors were
reformulated as latent-difference score model, we could confirm
thatyoungeradultsincreasedonaveragemoreinmemoryperfor-
mance than children, ?χ2= 13.47, df = 1, p < 0.001 and that
children increased more than older adults, ?χ2= 12.89, df = 1,
p < 0.001. Finally, the correlation between baseline performance
and practice gains was significant in the group of children, r =
0.53, p = 0.010.
In summary, the main message from these analyses are that
practice-related changes in memory performance partly follows
a pattern consistent with the predictions from the magnification
model: relative to baseline performance, age-group differences
increased after practice; for children and younger adults, within-
group interindividual differences increased after practice; and
in children, baseline performance as well as cognitive abilities
assessed before the intervention tended to bepositively associated
with practice gains.
DISCUSSION
This article reports that between-person differences in associative
memory performance are reduced after mnemonic instructions
and that baseline performance within age groups correlates nega-
tively with instruction gains. In contrast, age-group differences,
and between-person differences among children and younger
adults, increaseas a function of extended adaptivepracticing, and
baseline performance and cognitive abilities tends to be weekly
positively associated with practice gains for the group of chil-
dren. Thus, the compensation view fit the pattern of instruction
gains nicely, while the magnification model fit the interindividual
differences in practice gains better than the compensation model.
Clearly, the present results are consistent with the distinction
between flexibility and plasticity (Lövdén et al., 2010). Flexibility,
in our view, denotes the capacity to optimize the brain’s perfor-
mance within current structural constraints, using the available
range of existing representational states. In contrast to flexibility,
plasticity denotes the capacity for changes in the possible range
of cognitive performance enabled by flexibility. Instruction gains
may be primarily acquired through flexibility, and if the brain’s
functioning is already appropriate for handling the task at hand,
then little can be gained by altering the way a particular task is
executed, and thus better performing individual will gain less.
In contrast, gains primarily acquired through adaptive practice
may reflect plasticity and extend the possible range of perfor-
mance, possibly by boosting associative potential (Brehmer et al.,
2007; Shing et al., 2008, 2010). Initial performance should then
correlate with individual differences in plasticity because initial
performance can be viewed as a reflection of past manifestations
of plasticity.
These theoretical notions also help to explain why older adults
gained more from instructions than children, whereas children
gained more from practicing than older adults, despite the fact
that both groups were performing similarly at baseline and on
measures of fluid cognitive ability (see also Brehmer et al., 2007).
Specifically, older adults may, perhaps due to their larger knowl-
edge base, possess better possibilities to rapidly shift to a more
effective mnemonic strategy, while children may possess a more
plastic associative memory system (Werkle-Bergner et al., 2006;
Shing et al., 2008, 2010).
This study has several benefits. One positive characteristic of
the study is the lifespan sample, which gave us the opportunity
to examine the validity of the magnification and compensation
views across the lifespan and for both instructions and prac-
tice gains. Another advantage is the inclusion of an extensive
training program using an adaptive procedure to encompass the
wide measurement space. The adaptive procedure also ensured
that all participants faced equally demanding conditions during
training, thus minimizing confounding between-person differ-
ences in the impetus for change in performance (Lövdén et al.,
2010). Finally, our use of modern statistical procedures appropri-
ate for the explicit estimation of change provides an important
addition to past research in this area and circumvents several of
the methodological problems discussed in the psychometric lit-
erature on relations between initial performance and subsequent
change (Jin, 1992). These methodological improvements gave us
the opportunity to, in a rigorous manner, extend the evaluation
of the magnificationand compensation models to interindividual
differences.
A number of limitations should be noted as well. First, gen-
eralization from the specific context in which this study was
conducted to other forms of training is not straightforward.
In particular, the present target task of training deviates some-
what from past studies on memory plasticity with the method
of loci (e.g., Kliegl et al., 1990; Lindenberger et al., 1992; Kliegl
and Lindenberger, 1993). In the present task, location cues were
not presented in a fixed serial order but randomized at each
list. Hence, the current task was less strategic but loaded more
on the associative component of episodic memory (e.g., Shing
et al., 2010). It is possible that this feature enhanced the compen-
satory pattern found for baseline plasticity. Specifically, encoding
and retrieval strategies such as imagery might be relatively stan-
dard ways of dealing with to-be-learned materials whereas full
application of the method of loci mnemonic may not. Thus, a
subset of participants in this study may have applied some form
of interactive-imagery strategy at baseline (cf. Dunlosky et al.,
2005). Another issue is the ceiling effect of younger adults in the
post-instruction session. Although we caninterpret young adults’
baseline performance, practice gains, and overall training gains,
this ceilingeffectrendersitimpossibletointerpretyoungeradults’
gains from instructions.
We also note that the key dependent variable was a com-
posite score of presentation time and the number of correctly
recalled items. The underlying assumption of this Timed Recall
Score is that a reduction in processing time increases the effort
for the participant to form a quick and effective association and
that this mechanism is functionally equivalent across age groups.
Previous age-comparative memory research in the field of cogni-
tive aging supports these assumptions (Kliegl and Lindenberger,
1993;Kliegletal.,1994),andlifespancomparisonsinthedomains
of working memory and inductive reasoning have successfully
used similar procedures (Mayr et al., 1996). Nevertheless, further
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Lövdén et al. Compensation versus magnification
methodological workontheissueofageequivalenceofthe Timed
Recall Score is desirable. It should also be noted that our over-
all sample is positively selected (see Brehmer et al., 2007 for
details), limiting generalizability to lower performing segments
of the population. Finally, and most importantly, we note that the
sample size was relatively small, especially considering the com-
plex latent-growth curve approach to analyzing practice gains.
Though follow-up analyses applying the less complex latent dif-
ference score model to this data delivered results that confirmed
the main analyses, we acknowledge that the statistical power for
addressing these research questions is limited. Due to this fact,
we run a higher risk than usual of missing important effects and
of reporting false alarms. In addition, we note that the proce-
dure of imputing data missing due to the termination rule of the
adaptive training procedure assumes that the last completed ses-
sionprovides anaccuratedescriptionofasymptotic performance.
The validity of this assumption is unknown. There is, therefore, a
risk that the true shape of the mean practice gains looks differ-
ent than the one we reported in Figure6. Nevertheless, the main
conclusionconcerning the individual differences in practice gains
remains valid regardless of the true shape of this learning process.
This has been shown by the follow-up analyses, which only relies
on the difference between initial and final performance of the
practicephase.Overall,consideringtheselimitations, futurestud-
ies mustconfirmthe present results beforestrong claimsbased on
these results can be made.
Despite these limitations, the findings of this study suggest a
resolution to the long-standing debate on the presence, direc-
tion, and meaning of aptitude by treatment interactions. In line
with the conceptual distinction between flexibility and plastic-
ity, we found that mnemonic instructions have compensatory
effects, whereas subsequent practice magnifies between-person
differences in memory performance. Future research needs to
examine whether the explanatory framework introduced in this
article is also helpful to interpret results from other data set with
larger samples and whether it also helps to clarify the relation
among initial performance, cognitive resources, and performance
gains in cognitive domains other than memory. With educational
issues in mind, it is clear that understanding the mechanisms that
reduce and magnify between-person differences in performance
is important, and may have practical and societal implications.
ACKNOWLEDGMENTS
This study was carried out in the context of the Research
Group, “Binding: functional architecture, neuronal correlates,
and ontogeny,” funded by the German Research Foundation
(DFG FOR 448). The authors thank Michael Schellenbach for
technical assistance, the research assistants at Saarland University
for their help in collecting the data, and the participants for their
cooperation and endurance. Thanks also go to Lars Bäckman,
Chris Hertzog, Viktor Müller, Timo von Oertzen, and Florian
Schmiedek for productive discussions.
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Conflict of Interest Statement: The
authors declarethat
was conducted in the absence of any
commercial or financial relationships
that could be construed as a potential
conflict of interest.
theresearch
Received: 14 February 2012; accepted:
02 May 2012; published online: 15 May
2012.
Citation: Lövdén M, Brehmer Y, Li S-C
and Lindenberger U (2012) Training-
induced compensation versus magnifica-
tion of individual differences in mem-
ory performance. Front. Hum. Neurosci.
6:141. doi: 10.3389/fnhum.2012.00141
Copyright © 2012 Lövdén, Brehmer,
Li and Lindenberger. This is an open-
access article distributed under the terms
of the Creative Commons Attribution
Non Commercial License, which per-
mits non-commercial use, distribution,
and reproduction in other forums, pro-
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