jung, 2013 efa with small sample sizes
Post on 02-Jun-2018
214 Views
Preview:
TRANSCRIPT
-
8/10/2019 Jung, 2013 EFA With Small Sample Sizes
1/6
Behavioural Processes 97 (2013) 9095
Contents lists available at SciVerse ScienceDirect
Behavioural Processes
j ournal homepage: www.elsevier .com/ locate /behavproc
Exploratory factor analysis with small sample sizes:A comparison ofthree approaches
SunhoJung
School of Management, Kyung HeeUniversity, 1 Hoegi-dong, Dongdaemon-gu, Seoul, 130-872, Republic of Korea
a r t i c l e i n f o
Article history:
Received 23 February 2012
Received in revised form 13 August 2012Accepted 29 November 2012
Keywords:
Exploratory factor analysis
Small sample size
Regularized exploratory factor analysis
Generalized exploratory factor analysis
Unweighted least-squares
a b s t r a c t
Exploratory factor analysis (EFA) has emerged in the field ofanimal behavior as a useful tool for deter-
mining and assessing latent behavioral constructs. Because the small sample size problem often occurs in
this field, a traditional approach, unweighted least squares, has been considered the most feasible choice
for EFA. Two new approaches were recently introduced in the statistical literature as viable alternatives
to EFA when sample size is small: regularized exploratory factor analysis and generalized exploratory
factor analysis. A simulation study is conducted to evaluate the relative performance of these three
approaches in terms of factor recovery under various experimental conditions of sample size, degree
of overdetermination, and level of communality. In this study, overdetermination and sample size are
the meaningful conditions in differentiating the performance ofthe three approaches in factor recovery.
Specifically, when there are a relatively large number offactors, regularized exploratory factor analysis
tends to recover the correct factor structure better than the other two approaches. Conversely, when
few factors are retained, unweighted least squares tends to recover the factor structure better. Finally,
generalized exploratory factor analysis exhibits very poor performance in factor recovery compared to
the other approaches. This tendency is particularly prominent as sample size increases. Thus, generalized
exploratory factor analysis may not be a good alternative to EFA. Regularized exploratory factor analysis
is recommended over unweighted least squares unless small expected number offactors is ensured.
2013 Elsevier B.V. All rights reserved.
1. Introduction
Exploratory factoranalysis (EFA) is a basic tool in the behavioral
sciences. Theattractionof EFAis its ability to investigatethe nature
of unobservable behavioral constructs (often called latent vari-
ables) that account for relationships among measured variables.
Traditionally, unweighted least squares (ULS) and maximum like-
lihood(ML)havebeen two of themostpopular estimation methods
in EFA (e.g., Fabrigar et al., 1999). Despite the popularity of ULS and
ML, the development of a new factor analysis procedure continues
to be actively studied (e.g., Bentler and de Leeuw, 2011). Recently,
two new approaches have been published in the statistical litera-
ture as viable alternatives to EFA in small sample size situations:One is regularized EFA (REFA) (Jung and Lee, 2011), and the other
is generalized EFA (GEFA) (Trendafilov and Unkel, 2011).
Researchers in animal behavior have long recognized the bene-
fit of studying an underlying latent variable and the importance of
EFA. However, the small sample size problem often limits the gen-
eral applicability of EFA in animal behavior studies (e.g., Budaev,
2010). Both REFA and GEFA are shown to perform well particularly
when sample sizes are small (Jung and Lee, 2011; Trendafilov and
E-mail address: sunho.jung@khu.ac.kr
Unkel, 2011). Thus, use of these approaches can be valuable in ani-
mal behavior research. In fact, our review found one instance of
an application of REFA in the study of animal personality (Konecn
et al., in press). However, the new approaches may still be novel to
researchers in animal behavior. Moreover, previous research has
not compared the performance of the new approaches to that of
traditional approach. It would be useful to know under what cir-
cumstances the new approaches are preferable to the traditional
approach. The objective of this article, therefore, is to make the
new approaches more accessible to researchers in animal behav-
ior, and to evaluate the traditional and new approaches in terms of
factor recovery capability using a Monte Carlo simulation study.
The article is organized as follows. We offer a general overviewpointing to the relative strengths and weaknesses of the traditional
andnew approaches. Then, we describethedesignofthesimulation
study and report results. An empirical study is conducted as well,
to investigate factor recovery in a more realistic context. Finally,
we discuss the implications of the study and also offer recommen-
dations based on the factor recovery capability.
2. Background
In animal behavior research, small sample sizes may be rule
rather than the exception (e.g., Havstad and Olson-Rutz, 1991). The
0376-6357/$ seefrontmatter 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.beproc.2012.11.016
http://localhost/var/www/apps/conversion/tmp/scratch_6/dx.doi.org/10.1016/j.beproc.2012.11.016http://localhost/var/www/apps/conversion/tmp/scratch_6/dx.doi.org/10.1016/j.beproc.2012.11.016http://www.sciencedirect.com/science/journal/03766357http://www.elsevier.com/locate/behavprocmailto:sunho.jung@khu.ac.krhttp://localhost/var/www/apps/conversion/tmp/scratch_6/dx.doi.org/10.1016/j.beproc.2012.11.016http://localhost/var/www/apps/conversion/tmp/scratch_6/dx.doi.org/10.1016/j.beproc.2012.11.016mailto:sunho.jung@khu.ac.krhttp://www.elsevier.com/locate/behavprochttp://www.sciencedirect.com/science/journal/03766357http://localhost/var/www/apps/conversion/tmp/scratch_6/dx.doi.org/10.1016/j.beproc.2012.11.016 -
8/10/2019 Jung, 2013 EFA With Small Sample Sizes
2/6
S. Jung / Behavioural Processes97 (2013) 9095 91
potential application of EFA in this research even involves those
cases where the number of variables exceeds the sample size (e.g.,
Liu and Gershenfeld, 2003). In general, MLis most frequently rec-
ommended for use in EFA (e.g., Fabrigar et al., 1999). However,
ML requires large sample sizes to yield reliable and stable solu-
tions (e.g., MacCallum et al., 1999). Previous research has shown
that ULS can yield high quality solutions with small sample sizes
(below 50) under ideal conditions of few factors, highly reliable
data, andhigh communalities(e.g., Preacherand MacCallum, 2002).
Although these conditions often fail in practice, ULS has been the
most feasible option for EFA in animal behavior research (Budaev,
2010). Here, only ULS is considered the traditional approach (here-
after referred to as ULSFA).
ULSFA, REFA, and GEFA are based on a common factor model.
This model partitions variance of each measured variable into
two parts: unique variance (uniqueness) due to a unique factor
and common variance (communality) due to the common factors.
Unique factors represent latent variables specific to only one mea-
sured variable, whereas common factors are shared among two
or more measured variables and represent latent variables that
can explain relationships among measured variables. Thus, factor
analysis concerns only common variance to derive the patterns of
relations between the commonfactors and the measured variables
(i.e., factor loadings). However, this requires the computation ofunique variances in some way. Broadly speaking, REFA and GEFA
differ from ULSFA in that estimation of unique variances is sep-
arated from estimation of factor loadings. In REFA, only a single
parameter needs to be determined to obtain estimates of unique
variances. GEFA first derives unique factor scores and then uses
them to estimate unique variances.
Compared to ULSFA, REFA and GEFA have several advantages.
ULSFA relies on complicated iterative algorithm, whereas REFA
and GEFA simplify the estimation of parameters in the model.
REFA assumes that the true unique variances are proportional
to their tentative estimates. That is, REFA involves estimating a
single parameter representing proportion. Unique variances are
estimated by multiplying their tentative quantities by an esti-
mate of the proportion. After unique variance estimates have beenobtained, factor loadings are then computed by a closed-form for-
mula (e.g., Jreskog, 1977). On the other hand, GEFA first derives
the common and unique factor scores for each observation. For
these latent variable scores, factor loadings and unique variances
are then found respectively using separate linear regression anal-
yses.
Another advantage results from the piece-by-piece approach
that REFA and GEFA take to estimate parameters in the model.
Data sets with small samples and many measured variables are
common in behavioral research. With many parameters relative
to sample size, iterative numerical methods would be feasible but
computationally demanding. The implementation of these meth-
ods may present numerical difficulties (e.g., nonconvergence). To
deal with this problem, methodologists have advocated subdivid-ing the parameters into several subsets (e.g., Bollen, 1996).
However, compared to ULSFA, REFA and GEFA also have several
limitations.For EFA, an overall model fit index can be used in deter-
mininghowwellthe model fits a sampleas a whole. ULSFAprovides
indices to assess the models goodness of fit and also permits sta-
tistical significance testing (Browne, 1984). However, no overall fit
indices are available for these two new approaches. Another limi-
tation is the absence of software programs for implementation of
the new approaches. The lack of statistical software could make
applied researchers less motivated to understand and implement
the new approaches. In contrast, ULSFA are readily implemented
and available in many software programs, including SPSS, SAS,
Mplus (Muthn and Muthn, 2006), CEFA (Browne et al., 1998),
FACTOR (Lorenzo-Seva and Ferrando, 2006).
Beyond the theoretical characteristics among the three
approaches we have discussed, theutility of a factoranalysis proce-
dure depends heavily on its ability to recover the underlying factor
structure, which is required for good interpretation and inference.
In thenext section,we present a simulation studythat evaluatesthe
performance of REFA and GEFA relative to ULSFA in terms of factor
recovery. Based on our findings, we provide guidelines in the Dis-
cussion and recommendations section for choosing between the
three approaches.
3. Simulation design
In the present simulation study, we investigate the capability
of the three approaches in population factor recovery under sev-
eral experimental conditions of sample size, communality, and
overdetermination. These conditions are commonly encountered
in simulations based on exploratory factor analysis (e.g., Hogarty
et al., 2005). Prior research has shown that level of commu-
nality moderates the impact of sample size on factor recovery
(e.g., MacCallum et al., 1999). Degree of overdetermination was
shown to greatly influence the quality of factor solutions, partic-
ularly with small samples (e.g., Preacher and MacCallum, 2002).
Overdetermination is defined as the ratio of factors to measured
variables. If the number of observed variables (p) is held con-stant, varying the number of factors (f) leads to different degrees
of overdetermination. Fewer factors indicate higher degree of
overdetermination. Withp held constant (p= 20), the Monte Carlosimulations involved manipulating four experimental conditions
as follows.
1 Approach: REFA, GEFA, and ULSFA.
2 Sample Size: N=5, 10,20, 30,and 50.
3 Communality: High (0.60.7), Low (0.20.4), and Wide (0.20.8).
4 Overdetermination: High (f=3) and Low (f=7).
Using a method developedby Tuckeret al.(1969), six population
correlation matrices were generated to correspond to the six com-
binations of communality and overdetermination. Individual-levelmultivariate normal data were drawn from N(0,), where is the
population covariance matrix, using the Cholesky decomposition
(Wijsman, 1959). One hundred samples were generated for each
level of the experimental conditions resulting in 3000 samples for
each approach (5 Sample Sizes3 levels of communality2 degrees
of overdetermination100 Replications). All sample matrices were
factor analyzed using each of the three approaches. All simulations
were carried out using MATLAB (R2010a).
4. Simulation results
To assess the degree of factor pattern recovery under the
three approaches, we computed the root mean squared deviation
(denoted asg) (Velicer and Fava, 1998) as follows:
g=
trace
( )
( )
pf
1/2
. (1)
This index represents the average difference between sample
loadings andtheir correspondingpopulation loadings. In thisstudy,
thevalueofgwascomputed after the sign of loading estimates was
recovered usinga procedure suggested by Cliff (1966). Because this
value can be affected by the rotational indeterminacy, the loadings
produced by each of the three approaches were not submitted to
the rotation method.
An ANOVA test was performed using the root mean squared
deviation g as the dependent variable and the four experimental
-
8/10/2019 Jung, 2013 EFA With Small Sample Sizes
3/6
92 S. Jung / Behavioural Processes97 (2013) 9095
Table 1
The results of an ANOVA testfor the root mean squared deviation (g) (Sig.= significance, 2 = effect size).
Source SS DF F Sig. 2
Approach (A) 1,020,833 2 23806 0.00 0.84
Communality (C) 1205 2 28 0.00 0.01
Overdetermination (O) 25576 1 1192 0.00 0.12
Sample size (N) 56418 4 657 0.00 0.23
A*C 3044 4 35 0.00 0.02
A*O 33353 2 111 0.00 0.15
A*N 270325 8 1576 0.00 0.59C*O 1582 2 36 0.00 0.01
C*N 2711 8 15 0.00 0.01
O*N 1530 4 17 0.00 0.01
A*C*O 3005 4 35 0.00 0.02
A*C*N 6902 16 20 0.00 0.04
A*O*N 7500 8 43 0.00 0.04
C*O*N 2266 8 13 0.00 0.01
A*C*O*N 2266 16 6 0.00 0.01
Error 190,236 8910
conditions as design factors. Table 1 presents the results of the
ANOVA. As the table shows, all of the main and interaction effects
werestatistically significant.This should notbe toosurprising given
the large numberof observations (i.e.,a total of 9000 observations).
Thus,it is crucial toexaminethe effectsizeas well (e.g.,Paxton et al.,
2001). Following accepted practice, we focus on main and interac-tion effects whose sizes were at least medium (i.e.,2 greater than0.06) (Cohen, 1988).
First, approach (2 = 0.84), overdetermination (2 = 0.12), andsample size (2 =0.23) had large main effects. Here, approachwas the most important determinant of the root mean squared
deviation, followed in descending order by sample size and
overdetermination. There are likely meaningful differences in the
root mean squared deviation among the three approaches. It
appears that there was little difference in the root mean squared
deviation between REFA (7.2) and ULSFA (7.3), whereas GEFA
exhibited a much higher level of the root mean squared devia-
tion (29.9). Moreover, it is likely that the levels of the root mean
squared deviation were higher when the number of factors was
small (16.5)than when the number of factors was large (13.1). Thisresult is somewhat counterintuitive and needs some explanation.
In the study, the large number of factors (f= 7) has the larger num-
berof estimatedparameters thanthe small number of factors (f=3):
the former has 140 unknown elements, and the latter has 60. Note
that the number of unknown elements is used as denominator to
calculate the root mean squared deviation.
Second, the ANOVA test reveals two two-way interactions
worthy of examination: that between approach and sample size
(2 =0.58) and that between approach and overdetermination(2 = 0.15). Fig. 1 displays the average values of the root meansquared deviation of the three approaches across sample sizes. On
average, the loading estimates of ULSFA involved a little smaller
values ofg than those under REFA when N 10, whereas REFA
resulted in the smallest value ofg at N=5. GEFA exhibited thelargest values ofgacross all sample sizes. Fig. 1 demonstrates thepoor factor recovery of GEFA particularly for larger sample sizes. In
fact, GEFA had much higher values ofgwith N= 50 than withN= 5.Conversely, REFA and ULSFA performed better in factor recovery
for larger sample sizes. Fig. 2 displays the average values of the
root mean squared deviationof the threeapproachesunder thetwo
levels of overdetermination. When the number of factors is small
(i.e.,f= 3), ULSFA was associated with the smallest level of the root
mean squared deviation (7.3) and REFA was associated with the
second smallest (7.9). Conversely, when the number of factors is
large, REFA involved the smallest level of the root mean squared
deviation (6.6) and ULSFA had the second smallest (7.2). At both
levels of overdetermination, GEFA yielded the largest level of the
root mean squared deviation.
The above ANOVA test suggested that factor recovery of the
three approaches was distinct between the two levels of overde-
termination. To gain a greater understanding of factor recovery
capability of the three approaches under this condition, we further
investigated the overall finite-sample properties of the estimated
loadings of the three approaches across the overdetermination lev-els. Tables 2 and 3 presents the average relative biases, standard
deviations, and mean square errors of factor loading estimates
obtained from thethree approaches under the two levelsof overde-
termination. Among these properties, the mean square error (MSE)
is the average squared difference between a parameter and its esti-
mate, therebyindicatinghow faran estimate is,on average,fromits
parameter value, i.e., the smaller the mean square error, the closer
the estimate is to the parameter. Specifically, the MSE is given by
MSE(j) = E[(j j)2
] = E[(j E(j))2
] + (E(j) j)2. (2)
As shown in Eq. (2), the MSE of an estimate is the sum of its
variance and squared bias. Thus, the MSE accounts for both bias
and variability of the estimate (Mood et al., 1974).
Fig.1. Theaveragevaluesfor indexof rootmeansquareddeviation(g) oftheloading
estimates obtained from the three approaches across different sample sizes.
-
8/10/2019 Jung, 2013 EFA With Small Sample Sizes
4/6
S. Jung / Behavioural Processes97 (2013) 9095 93
Table 2
Overall finite-sample properties of the loading estimates of the three approaches under high overdetermination (f = 3) acrossdifferent sample sizes (RB= relative bias (%),
SD = standard deviation, MSE =mean square error).
GEFA ULSFA REFA
RB SD MSE RB SD MSE RB SD MSE
N= 5 90 0.91 0.91 4 0.46 0.21 8 0.44 0.20
N= 10 195 1.04 1.41 6 0.34 0.11 4 0.34 0.12
N= 20 304 1.12 2.21 9 0.25 0.06 10 0.25 0.06
N= 30 419 1.13 2.95 3 0.20 0.04 2 0.21 0.04
N= 50 608 1.10 4.54 1 0.15 0.02 2 0.17 0.03
Table 3
Overall finite-sample properties of the loading estimates of the three approaches under low overdetermination (f = 7) across different sample sizes (RB= relative bias (%),
SD = standard deviation, MSE =mean square error).
GEFA ULSFA REFA
RB SD MSE RB SD MSE RB SD MSE
N= 5 58 0.62 0.44 20 0.35 0.13 11 0.31 0.09
N=10 217 0.82 0.93 11 0.32 0.11 4 0.27 0.07
N= 20 449 0.97 1.58 25 0.26 0.07 16 0.21 0.04
N= 30 498 1.05 2.12 8 0.24 0.06 7 0.19 0.03
N= 50 486 1.14 3.14 28 0.20 0.04 16 0.15 0.02
In the study,absolutevalues of relative bias greater than 10 per-cent may be singled out as unacceptable (Lei, 2009). As shown in
Table 2, when few factors are retained, both REFA and ULSFA on
average yielded unbiased estimates of loadings across all sample
sizes whereas GEFA yielded tremendously and positively biased
loading estimates regardless of sample sizes. In addition to relative
bias, it is important to evaluatethe stabilityof the three approaches.
The stability of each approach was examined by computing the
standard deviation. REFA produced on average the standard devia-
tions of the estimates almost identical to those of ULSFA. As sample
size increased, the standard deviations of the estimates tended to
decrease across these two approaches. Conversely, GEFA was asso-
ciated with much larger standard deviations, and the degree of
Fig.2. Theaveragevaluesfor indexof rootmeansquareddeviation(g)oftheloading
estimates obtained from the three approaches acrosstwo levels of overdetermina-
tion (3 factors= high overdetermination, 7 factors= lower overdetermination).
standard deviations tended to increase with larger sample sizes.Overall,ULSFA showedthe smallest mean squareerrors of the load-
ingestimates. However, thedifferences in the mean squared errors
of the estimates were negligibly small between ULSFA and REFA.
On the other hand, GEFA clearly exhibits its inconsistency: larger
sample size does not help produce the loading estimates closer to
the true population values.
As Table 3 shows, when a large number of factors are retained,
REFA was theleast biasedof the three approaches.REFAled totoler-
able degreeof bias forestimates ofloadings acrosssamplesizes. The
estimates under REFA were consistently associated with smaller
standard deviations than those under the other approaches. On
average, REFA has the smallest mean squareerrors of factorloading
estimates across all ample sizes. In particular, this tendency of fac-
tor recoverywas more apparentin the two smallest sample sizes. Ingeneral, under low overdetermination, REFA led to more accurate
and stable solutions than the other approaches.
5. Empirical example
The simulation study presented in the previous section com-
pared the performance of the three approaches under various
experimental conditions commonly encountered in behavioral
research. Nonetheless, the range of conditions in this study may
still be limited in scope. Questions are often raised regarding the
validity of results from a Monte Carlo simulation study. In this sec-
tion, we provide concrete empirical evidence supporting results of
the simulation study.An empirical example is presented using the sensory attribute
data collected by quantitative evaluation of fluid milk using a con-
sumer panel (Chapman et al., 2001). The data set consisted of nine
milkproducts describedby eight sensory attributes (e.g., aroma, fla-
vor, texture, etc.).Twelve sensory panelists were asked to rate each
of the products on each attribute, using an intensity scale ranging
from 0 (not present) to 10 (extremely strong). Because the attribute
rating data collected from multiple panelists often reveal a lack of
agreement, the attributeratingsof the panelists are aggregated into
a singlegroup compositevalue. Thearithmeticmeanof theindivid-
ual ratings of the panelists was computed to aggregate the ratings
(see Chapman et al. (2001), pp. 1415). The aggregation of response
data helps minimize individual-level biases and errors, and thus
improves estimation accuracy (Van Bruggen et al., 2002).
-
8/10/2019 Jung, 2013 EFA With Small Sample Sizes
5/6
94 S. Jung / Behavioural Processes97 (2013) 9095
Table 4
Factor loadings and uniquevariancesfor thefour factors from thesensory attribute data (F= factors, = unique variances).
Attributes REFAa ULSFA
Fl F2 F3 F4 Fl F2 F3 F4
Cooked aroma 0.965 0.001 0.027 0.228 0.230 0.979 0.008 0.040 0.209 0.000
Caramel aroma 0.476 0.529 0.615 0.222 0.262 0.524 0.576 0.556 0.292 0.151
Grainy aroma 0.949 0.015 0.251 0.024 0.251 0.975 0.007 0.224 0.021 0.035
Cooked flavor 0.681 0.556 0.090 0.383 0.268 0.727 0.591 0.073 0.341 0.144
Sweet flavor 0.030 0.107 0.865 0.192 0.403 0.046 0.081 0.987 0.147 0.000
Bitter flavor 0.189 0.008 0.242 0.815 0.433 0.187 0.008 0.191 0.965 0.000
Dry texture 0.007 0.888 0.094 0.102 0.371 0.022 0.992 0.094 0.083 0.186
Lingering aftertaste 0.002 0.740 0.332 0.422 0.358 0.023 0.813 0.424 0.398 0.264
a Factornames: F1: Cooked; F2: Drying/lingering; F3: Sweet;F4: Bitter.
Kaisers criterion suggested a four factor solution. To facilitate
interpretation of the results, the factors were then orthogonally
rotated using a varimax rotation. GEFA was not considered for the
study due to its worst performance on factor recovery across all
experimental conditions. In this empirical study, REFA and ULSFA
were applied to the mean attribute ratings. If Heywood cases
(i.e., negative variance estimates) occur in the iteration process,
ULSFA set communalities to one (e.g., Dillon et al., 1987). The
results of these analyses are presented in Table 4. The varimax
rotated factor loadings produced by ULSFA were almost consis-tently larger than the corresponding REFA solutions. This was due
to the existence of zero entries in the estimated unique variances
under ULSFA. Some researchers assume that the Heywood case
variable is explained entirely by the corresponding common factor.
However, this assumption is unrealistic because of the presence of
measurement error in behavioral research. It appears that ULSFA
may overestimate factor loadings and therefore pose a more diffi-
cult interpretation problem. Results from ULSFA indicated that an
attribute of caramel aroma may cross-load (i.e., having large fac-
tor loadings on the second and third factors). Compared to ULSFA,
REFA offered greater conceptual clarity on the extracted factors.
6. Discussion and recommendations
In this article, we undertook investigations of the relative
performance of regularized exploratory factor analysis and gener-
alized exploratory factor analysis with respect to the more familiar
unweighted least squares in exploratory factor analysis using both
simulated and empirical data. Based on our simulation results, we
would provide some recommendations for the applied researcher
in animal behavior.
First, we recommend the adoption of regularized exploratory
factor analysis as a sensible alternative to generalized exploratory
factor analysis, a technique specifically designed to derive fac-
tors when the number of variables is larger than the number
of observations. As we demonstrate, regularized exploratory fac-
tor analysis performed much better than generalized exploratory
factor analysis in terms of factor recovery, under small sample sit-uations. Moreover, the loading estimates produced by generalized
exploratory factor analysis never converge to the true population
values as sample size increases(i.e., the estimates are inconsistent).
Second, if the number of expected factors is small, we rec-
ommend the use of unweighted least squares. On average, this
approachperforms better thanor as wellas regularized exploratory
factor analysis in terms of factor recovery. The relatively good per-
formanceof unweighted leastsquares in situations involving fewer
underlying factors has been previously reported in the literature
(e.g., Preacher and MacCallum, 2002).
Finally, if researchers have little confidence thatthe true num-
ber of factors is small, they should use regularized exploratory
factor analysis because it outperforms unweighted least squares in
factor recovery when there are a relatively large number of factors.
Under the same situation, all three approaches yielded biased esti-
mates of factor loadings. However, regularized exploratory factor
analysis had (acceptably) lower levels of relative bias compared to
the other two approaches. Moreover, regularized exploratory fac-
tor analysis resulted in more accurate estimates of loadings. The
high performance level of regularized exploratory factor analysis
was more prominent in very small samples.
Researchers routinely rely on factor retention criteria such as
parallel analysis (Horn, 1965) in order to determine the number of
factors to retain unless they have an a priori hypothesis about thenumberof factors to extract. Yet, no extantmethod forfactor reten-
tion decisionscan avoiderroneous conclusions.In addition, it is not
straightforward to assess the degree of under- and overdetermina-
tion of the number of factors. Other things being equal, retaining
a small number of factors is deemed preferable because retaining
too many often hinders interpretability. In most cases, however,
retainingtoo fewfactors maytend to reduce communalities, which
in turn has adverse effect on factor recovery in small samples (e.g.,
MacCallum et al., 1999). Unless researchers have tremendous con-
fidence that the correct number of factors is small, we suggest that
theyconsider regularized exploratory factor analysisa complement
or substitute forunweighted least squares under small samplesize.
Our study provides a greater understanding of the three avail-
able approaches to exploratory factor analysis with small samplesizes. We hope that this study leads researchers in animal behavior
to adoptregularized exploratory factor analysis in manysituations,
particularly those in which the researchers should expect to retain
a relative large number of factors. In many research domains, it
is often unavoidable to have data with many measured variables
and small sample size; some specific examples include behavior
genetics and neuroimaging data analysis, among others. In these
domains, use of regularized exploratory factor analysis can also be
valuable.
As doothersimulationstudies, thepresentstudyis notfreefrom
limitation. Althoughthe simulation studytook intoaccount various
experimental conditions that are frequently used in Monte Carlo
simulation studies in the domain of exploratory factor analysis, it
may be necessary to contemplate a wider range of conditions formore careful investigations of the relative performance of the three
approaches.
Appendix A. Supplementary data
Supplementary data associated with this article can be
found, in the online version, at http://dx.doi.org/10.1016/j.beproc.
2012.11.016.
References
Bentler,P.M.,de Leeuw, J.,2011. Factor analysisvia components analysis.Psychome-
trika 76, 461470.
http://dx.doi.org/10.1016/j.beproc.2012.11.016http://dx.doi.org/10.1016/j.beproc.2012.11.016http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0005http://dx.doi.org/10.1016/j.beproc.2012.11.016http://dx.doi.org/10.1016/j.beproc.2012.11.016 -
8/10/2019 Jung, 2013 EFA With Small Sample Sizes
6/6
S. Jung / Behavioural Processes97 (2013) 9095 95
Bollen, K.A.,1996. An alternativetwo stageleast squares (2SLS) estimatorfor latentvariable equations. Psychometrika 61, 109121.
Browne, M.W., 1984. Asymptotically distribution-free methods for the analysis ofcovariancestructures.BritishJournalof Mathematical andStatistical Psychology37, 6283.
Browne, M. W., Cudeck, R., Tateneni, K., Mels, G. (1998) CEFA: ComprehensiveExploratory Factor Analysis. WWW document and computer program. URLhttp://quantrm2.psy.ohio-state.edu/browne/
Budaev, S.V.,2010. Usingprincipal components and factor analysisin animalbehav-ior research: caveats and guidelines. Ethology 116, 472480.
Chapman, K.W., Lawless, H.T., Boor, K.J., 2001. Quantitative descriptive analysis
andprincipalcomponent analysisfor sensorycharacteristics of ultrapasteurizedmilk. J. Dairy Sci. 84, 1220.
Cliff, N., 1966. Orthogonal rotation to congruence. Psychometrika 31, 3342.Cohen, J., 1988. Statistical Power Analysis for the Behavioral Sciences, 2nd ed.
Lawrence Earlbaum Associates, Hillsdale, NJ.Dillon,W.R.,Kumar,A.,Mulani,N.,1987. Offendingestimatesin covariancestructure
analysis: comments on the causes of and solutions to Heywood cases. Psychol.Bull. 101, 126135.
Fabrigar, L.R.,Wegener,D.T., MacCallum, R.C.,Strahan,E.J., 1999. Evaluating the useofexploratory factor analysis in psychological research. Psychol. Methods 4 (3),272299.
Havstad, K.M., Olson-Rutz, K.M., 1991. Sample size determination for studyingselected cattle foraging behaviors. Appl. Anim. Behav. Sci. 30, 1726.
Hogarty, K.Y., Hines, C.V., Kromrey, J.D., Ferron, J.M., Mumford, K.R., 2005. Thequality of factor solutions in exploratory factor analysis: the influence of sam-ple size, communality and overdetermination. Educ. Psychol. Measur. 65, 202226.
Horn, J.L., 1965. A rationale and test for the number of factors in factor analysis.Psychometrika 30, 179185.
Jreskog,K.G., 1977. Factor analysisby leastsquareand maximum-likelihood meth-ods. In: Enslein, K., Ralston, A., Wilf, H.S. (Eds.), Statistical Methods for DigitalComputers. Wiley,New York, pp. 125165, III.
Jung, S., Lee, S., 2011. Exploratory factor analysis for small samples. Behav. Res.Method 43, 701709.
Konecn, M., Weiss, A., Lhota, S., Wallner, B. Personality in Barbary macaques(Macaca sylvanus): temporal stability and social rank. J. Res. Personal.,http://dx.doi.org/10.1016/j.jrp.2012.06.004, in press.
Lei, P.-W., 2009. Evaluating estimationmethods for ordinal data in structuralequa-tion modeling. Qual. Quant. 43 (3), 495507.
Liu, X., Gershenfeld, H.K., 2003. An exploratory factor analysis of the tail suspen-sion test in 12 inbred strains of mice and an F2 intercross. Brain Res. Bull. 60,223231.
Lorenzo-Seva, U., Ferrando, P.J., 2006. FACTOR: a computer program to fit theexploratory factor analysis model. Behav. Res. Methods, Instrum. Comp. 38,8891.
MacCallum, R.C., Widaman, K.F., Zhang, S., Hong, S., 1999. Sample size in factoranalysis. Psychol. Methods 4, 8499.
Mood, A.M., Graybill, F.A., Boes, D.C., 1974. Introduction to theTheory of Statistics.McGraw-Hill, New York.
Muthn, L.K.,Muthn, B.O. (2006). Mplus.Statistical Analysis with Latent Variables.Users Guide, version 4.1. Los Angeles, California.
Paxton,P., Curran, P.J.,Bollen, K.,Kirby,J.B., Chen,F., 2001. Monte Carlo experiments:design and implementation. Struct. Equat. Model.8, 287312.
Preacher, K.J., MacCallum, R.C., 2002. Exploratory factor analysis in behaviorgenetics research: factor recovery with small sample sizes. Behav. Genet. 32,153161.
Trendafilov, N.T., Unkel, S., 2011. Exploratory factor analysis of data matri-ces with more variables than observations. J. Computation. Graph. Stat. 20,874891.
Tucker, L.R., Koopman, R.F., Linn, R.L., 1969. Evaluation of factor analytic researchprocedures by means of simulated correlation matrices. Psychometrika 34,421459.
Van Bruggen, G.H., Lilien, G.L., Kacker, M., 2002. Informants in organizational mar-keting research:why usemultiple informants and howto aggregate responses.
J. Mark. Res. 34 (November), 469L 78.Velicer, W.F., Fava, J.L., 1998. Effects of variable and subject sampling on factor
pattern recovery. Psychol. Methods 3, 231251.Wijsman, R.A.,1959. Applications of a certain representationof theWishart matrix.
Ann. Math. Stat. 30, 597601.
http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://quantrm2.psy.ohio-state.edu/browne/http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://dx.doi.org/10.1016/j.jrp.2012.06.004http://dx.doi.org/10.1016/j.jrp.2012.06.004http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0140http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0135http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0130http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0125http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0120http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0115http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0110http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0100http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0095http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0090http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0085http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0080http://dx.doi.org/10.1016/j.jrp.2012.06.004http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0070http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0065http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0060http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0055http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0050http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0045http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0040http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0035http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0030http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0025http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0020http://quantrm2.psy.ohio-state.edu/browne/http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0015http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010http://refhub.elsevier.com/S0376-6357(12)00251-3/sbref0010
top related