**Modelling for understanding AND for
prediction/classification - the
power of neural networks in research**

**Eduardo Cascallar ^{ab},
Mariel Musso^{acd}, Eva Kyndt^{a} and Filip
Dochy^{a} ^{}**

^{a}University of
Leuven, Belgium

^{b}Assessment Group
International, USA / Belgium

^{c}National Research
Council (CONICET)/CIIPME, Argentina

^{
}^{d}Universidad
Argentina de La Empresa, Argentina^{ }

*Article received 28 November 2014 /
revised 18 January 2015 /
accepted 18 January 2015 / available online 30 January
2015*

**Abstract**

Two articles,
Edelsbrunner and, Schneider (2013), and Nokelainen and
Silander (2014) comment
on Musso, Kyndt, Cascallar, and Dochy (2013). Several relevant
issues are
raised and some important clarifications are made in response
to both
commentaries. Predictive systems based on artificial neural
networks continue
to be the focus of current research and several advances have
improved the model
building and the interpretation of the resulting neural
network models. What is
needed is the courage and open-mindedness to actually explore
new paths and
rigorously apply new methodologies which can perhaps,
sometimes unexpectedly, provide
new conceptualisations and tools for theoretical advancement
and practical
applied research. This is particularly true in the fields of
educational
science and social sciences, where the complexity of the
problems to be solved
requires the exploration of proven methods and new methods,
the latter usually
not among the common arsenal of tools of neither practitioners
nor researchers
in these fields. This response will enrich the understanding
of the predictive
systems methodology proposed by the authors and clarify the
application of the
procedure, as well as give a perspective on its place among
other predictive
approaches.

Keywords: Artificial
neural networks;
Response to Commentaries; Methodology; Data Modelling

*Research is the process of
going
up alleys to see if they are blind*.

Marston Bates

Two articles, Edelsbrunner
and, Schneider (2013),
and Nokelainen and Silander (2014) comment on Musso, Kyndt,
Cascallar, and
Dochy (2013). Several relevant issues are raised and some
important
clarifications need to be made in response to both
commentaries. This response
will enrich the understanding of the predictive system
methodology proposed by
the authors and clarify the application of the procedure, as
well as give a
perspective on its place among other predictive approaches.

Edelsbrunner and Schneider
(2013) in their
commentary on Musso, Kyndt, Cascallar and Dochy (2013) argue
that artificial
neural networks (ANNs) should only be used as exploratory
modelling techniques,
in spite of being powerful statistical modelling tools with
demonstrated
ability to improve outcomes of classifications and predictions
over traditional
statistical methods (Marquez, Hill, Worthley, & Remus,
1991). Garson (1998,
pp. 11-14) cites more than thirty-five articles which have
shown the ability of
ANNs to outperform traditional techniques in specific
circumstances. In
addition, Haykin (1994, pp. 4-5) summarizes some of the main
favourable
properties of ANNs which explain their advantages over
traditional methods. The
reasons Edelsbrunner and Schneider (2013) argue for their
rather strong
position are centred on two main arguments: (a) that the
output from ANNs
cannot be fully translated into a meaningful set of rules
because of a lack of
accessibility to the input-output relationships, and (b) that
there is a lack
of equivalent statistical parameters in ANNs when compared to
more traditional
statistical techniques. These are the two fundamental
misconceptions that will
be addressed.

One of the essential
requirements for development
and advancement in science is the willingness and vision to
explore new
conceptualizations and methods. In particular, as is the case
in the study by
Musso et al. (2013), the ability to bring together data from
interdisciplinary
domains (e.g., Decuyper, Dochy, & Van den Bossche, 2010),
and to use new
methodologies for analyses that are commonly applied in other
disciplines such
as business, finance, and the social sciences (Al-Deek, 2001;
Detienne,
Detienne, & Joshi, 2003; Laguna & Marti, 2002; Neal
& Wurst, 2001;
Nguyen & Cripps, 2001; White & Racine, 2001, and
others as stated in
Musso et al., 2003).

The literature still shows
relatively few studies
applying neural networks in education and in educational
assessment in
particular (Everson, Chance, & Lykins, 1994; Wilson &
Hardgrave, 1995),
although ANNs have been shown to improve the validity and the
accuracy of the
predictions and/or classifications, and also improve the
predictive validity of
test scores (Everson et al., 1994; Perkins, Gupta, &
Tamanna, 1995; Weiss
& Kulikowski, 1991). More recently, several studies have
shown the
applicability and use of this methodology in education (e.g.,
Cascallar,
Boekaerts, & Costigan, 2006; Kyndt, Musso, Cascallar,
& Dochy, 2011; Kyndt,
Musso, Cascallar, & Dochy, 2015; Musso & Cascallar,
2009a; Musso &
Cascallar, 2009b; Musso, Kyndt, Cascallar & Dochy, 2012;
Musso et al.,
2013; Pinninghoff Junemann, Salcedo Lagos, & Contreras
Arriagada, 2007;
Ramaswami & Bhaskaran, 2010; Zambrano Matamala, Rojas
Díaz, Carvajal
Cuello, & Acuña Leiva, 2011). These recent studies have
used ANNs both for
prediction/classification as well as for the understanding of
the underlying
variables involved in the educational outcomes studied. Now it
is important to
show that recent advances in ANN analysis have addressed the
main concerns
expressed in Edelsbrunner & Schneider (2013).

First, the concerns regarding
the presumed “opacity”
of ANN in terms of their input-output relationships will be
addressed. The
authors undermine their own estimate of the value of ANNs as a
“promising
technique” by essentially arguing that it is contrary to good
scientific
practice for theory-building given the presumed “opaque”
nature of their
internal structure which makes interpretation difficult if not
impossible. The
often and now quite outdated argument of ANNs as “black boxes”
(cf. Benitez,
Castro & Requena, 1997) is therefore raised once again.
However, these
arguments are raised ignoring the vast amount of research that
has been going
on in this field to overcome this initial drawback of
predictive systems
analyses (e.g., Frey & Rusch, 2013; Intrator &
Intrator, 2001; Lee,
Rey, Mentele, & Garver, 2005; Tzeng & Ma, 2005; Yeh
& Cheng 2010).

Considering the nature and
centrality of modelling
in science, as was clearly presented by Frigg and Hartmann
(2006), models can
perform two different representational functions, which are
not mutually
exclusive as scientific models. First, they can be a
representation of an
aspect or selected part of the world, what they call the
“target system”. In
this case, what can be modelled are either phenomena or data.
The second notion
of modelling is the representation of a theory in that it
represents its rules,
laws and axioms.

Clearly, ANNs contribute to
the construction of
better representational models consisting of “models of data”
(Suppes, 1962).
In particular, this contribution is based on ample research
that has been
crucial in making the link between ANNs representations and
their relationship
to the obtained outputs. As an anecdote, it is interesting and
revealing that
Edelsbrunner and Schneider (2013) cite the paper of Benitez,
et al. (1997)
which presents an addition to the usual ANN techniques which
according to
Benitez et al. (1997) provide “such an interpretation of
neural networks so
that they will no longer be seen as black boxes” (p. 1156),
which clearly
contradicts the use of the article of Benitez et al. (1997) as
supporting the
“black box” unique perception of ANNs. The proposed approach,
in this case is
based on the determination of the equality between
multilayered perceptron
ANNs, precisely the one used by Musso et al. (2013), and fuzzy
rule-based
systems. The operator derived from this equivalency concept
results in the
transformation of fuzzy rules into a format which can be
easily understood. Thus,
the knowledge generated by the ANN after the learning process
is finished can
be more easily and clearly explained, “so that they can no
longer be considered
as black boxes” (Benitez et al., 1997, p. 1156), while
retaining all the
advantages and power of the ANNs as very efficient computing
representations as
automated knowledge acquisition procedure models, and as
universal approximators
(Ripley, 1996). In fact, West, Brockett, and Golden (1997)
state that neural
networks “are a well-defined adaptive gradient search
procedure for parameter
fitting in a complex nonlinear model, and not a ‘black box’ at
all” (p. 389).

In addition, the efforts to
develop better and more
comprehensive visualisation techniques for the complex
interactions in an ANN,
such as those suggested by Tzeng and Ma (2005) have
contributed to open the
“black box” and help the researcher in determining underlying
dependencies
between inputs and outputs of a neural network. As a
consequence, they do not
only facilitate the design of efficient ANNs, but also enable
the use of ANNs
for problem solving. It is true that visualisation is not
explanation, but they
are powerful tools to guide the refinement of neural network
structures for
problem solving (e.g., classification tasks) using ANNs or
other machine
learning models. Another significant addition to the
literature which “opens
the box” in ANN analyses is the concept of structured neural
network (SNN)
techniques used for modelling (Lee, Rey, Mentele, &
Garver, 2005). In this
approach, the actual construction of the network is based on
existing
contextual and theoretical knowledge to assist in the design
of the ANN
structure of inputs. In fact, a similar approach was followed
by Musso et al.
(2013), by populating the inputs based solely on solid
theoretical constructs
derived from previous cognitive, motivational, and
sociodemographic research
and models, avoiding blind data mining techniques (Hand,
Mannila & Smyth,
2001), and based on the factor analysis and structural
equation modelling (SEM)
of several variables to determine their potential weight in
the problem.

Cause-and-effect
relationships have been
traditionally modelled, among others, by SEM and Partial Least
Squares (PLS)
approaches. But these procedures have their own shortcomings.
In PLS, there is
no theoretical rationale for all indicators to have the same
weighting
(Haenlein & Kaplan, 2004), and the PLS procedure does not
take into account
the fact that some indicators may be more reliable than others
and should,
therefore, receive higher weights (Chin, Marcolin, &
Newsted (2003). In
addition, there is the difficulty of interpreting the loadings
of the
independent latent variables in PLS (which are based on
cross-product relations
with the response variables). Regarding SEM several authors
also point out some
issues that require attention from the researcher or that are
still awaiting
further research (Lei & Qiong
Wu, 2007; Schermelleh-Engel,
Kerwer, & Klein, 2014; Weston
& Gore, 2006). Among the issues noted with SEM are
possible data problems,
such as missing data, non-normality of observed variables, or
multicollinearity; estimation problems that could be due to
data problems or
identification problems in model specification; or
interpretation problems due
to unreasonable estimates. These potential problems have led
to suggestions
involving the development of “mixture PLS” models (Hahn,
Johnson, Herrmann,
& Huber, 2002), hierarchical Bayesian methods in SEM
models (Ansari,
Jedidi, & Jagpal, 2000) and new ways of evaluating fit in
non-linear
multilevel structural equation models (Schermelleh-Engel et
al., 2014). Even if
nonlinear SEM and PLS models could handle asymmetric
relationships, they still
do not solve the problems associated with large data and
complex interactions.
The SNN approach takes into account these complexities and
non-linearity in
data sets, while maintaining the advantages of the ANN general
model.

Another significant addition
to the battery of
approaches that researchers have explored to eliminate the
“black box” risk of
ANNs is the inclusion of sensitivity analysis for each of the
variables in the
model (Kim & Ahn, 2009) in order to extract the necessary
information for
model validation and process optimisation, from the
relationships between
inputs and outputs in the ANN. This method, based on the
relative importance
(RI) parameter estimate improves on Garson’s (1991) use of
relative importance
weights, and uses sensitivity analysis to determine the causal
importance of
the input variables on the outputs. The sensitivity is a
measure of the increase
in the error of the predicted value as each variable is
excluded from the
model, and demonstrates systematically the degree of influence
on the network
weights of each participating variable. The RI methods used in
both
classification and prediction models are another evidence of
the fallacy of the
view of neural networks as black-boxes beyond human
understanding.
Incidentally, Kim and Ahn (2009) also compared the results
from the ANN
analysis with logistic regression and classification and
regression trees
(CART) analyses, with ANN models obtaining better results in
both training and
testing sets of data. Other authors (e.g., Blackard &
Dean, 1999) have
compared ANNs absolute accuracy and relative accuracy compared
to predictions
based on discriminant analysis (DA) models, with a consistent
finding that ANN
models outperformed the DA models.

A very interesting comparison
of methods to
accurately assess the contribution of variables in ANN
architectures has been
reported by Olden, Joy, and Death (2004). The authors compare
nine different
methods for quantifying variable importance in ANNs using
simulated data with
known properties. The use of simulated data, when the true
importance of the
variables is known, provides a solid base for future
developments in this
field, which are not possible with natural data as is the case
with Gevrey,
Dimopoulos, and Lek (2003). The nine methodologies studied by
Olden et al.
(2004) included: connection weights, Garson’s algorithm,
partial derivatives, input
perturbation, sensitivity analysis, forward stepwise addition,
backward
stepwise elimination, improved stepwise selection 1, and
improved stepwise
selection 2 (see Olden et al., 2004 for details on these
methods). The results
indicated that the connection weights approach showed the best
overall
performance both in terms of accuracy (degree of similarity
between true and
estimated variable ranks) and precision (degree of variation
in accuracy), when
estimating the true importance of all the variables in the
ANN. Partial
derivatives, input perturbation, sensitivity analysis and both
versions of the
improved stepwise selection methods showed moderate
performance in the
simulations. When estimating the actual ranks, the connection
weights approach
once again was the method which exhibited the best
performance. In addition,
Olden and Jackson (2002) reviewed a randomisation approach to
better evaluate
and understand the contribution of predictors in ANN analysis.
They conclude by
stating: *“Thus, by
coupling this new
explanatory power of neural networks with its strong
predictive abilities, ANNs
promise to be a valuable quantitative tool to evaluate,
understand, and predict
ecological phenomena” (Olden & Jackson, 2002, p. 135).*

All of these examples
demonstrate that using the
appropriate techniques, the complexity of an ANN does not need
to translate
into “opacity”, and researchers are not limited in their
ability to gain
insight into the explanatory factors of the prediction and
classification
processes performed efficiently by ANNs. Studies such as Olden
et al. (2004),
Gevrey et al. (2003), and Lek, Belaud, Baran, Dimopoulos, and
Delacoste (1996),
are but the beginnings of a vast number of applications that
have “opened the
box” in ANN analysis. In addition, regularisation approaches
have been used to
enhance the interpretation of ANN results (Intrator &
Intrator, 2001), and
the estimation of interaction effects in ANNs was used and
demonstrated by
Donaldson and Kamstra (1999). Therefore, contrary to what has
been pointed out
by Edelsbrunner and Schneider (2013) and quoted by Golino and
Gomes (2014), the
ANN approach offers the potential to examine the complex
relationships amongst
its components.

An additional important
advantage of ANN analysis
refers to the need to capture the complexity of the
interaction of various
factors in the understanding of also complex phenomena
(Agrawal, 2001). It is
difficult to find large-N studies with a large set of
variables, particularly
in the social and educational sciences. So, most studies
attempt to develop
causal models based on a very limited set of variables,
without the capacity to
encompass a large number of predictors, and therefore not
providing the possibility
to observe their complex interactions (Boekaerts &
Cascallar, 2006;
Cascallar et al., 2006). A resulting problem is that
meta-analyses trying to
find general statistical correlations face very serious
problems as
interactions between the factors analysed are not known, which
in turn leads to
wrong estimations of relevance. Related to this problem is the
fact that in all
studies that knowingly or unknowingly exclude a relevant
factor, the importance
of all other variables shifts dramatically. This effect has
been noted in very
diverse fields ranging from natural resource estimation to
self-regulated
learning (Agrawal & Chhatre, 2006; Boekaerts &
Cascallar, 2006).
Studies which only take into account a few variables, in
rather simple designs,
and do not consider very important but complex interactions
with a larger
number of participating factors can and do often show
contradictory results.
This should not be considered a trivial problem for the
conceptualisation of
various effects and phenomena in every scientific field
(Boekaerts &
Cascallar, 2006). Frey and Rusch (2013) present an interesting
study in the
area of social-ecological systems which uses ANNs with an
analytic approach
that produces an open architecture in which it is possible to
establish the
input-output relationships which Edelsbrunner and Schneider
(2013) seem to
perceive are unachievable for ANNs. These analyses suggested
by various authors
(Thrush, Coco & Hewitt, 2008; Yeh & Cheng 2010) make
the relationships
among the various input-output variables explicit.

The second main argument
regarding problems
associated with the ANN methodology, as claimed by
Edelsbrunner and Schneider
(2013), has to do with the lack of some statistical parameters
in ANNs. This
ignores the evidence that there has also been an abundance of
research to
provide the ANN model with equivalent information. There have
been increasing
efforts for some time, to embed ANNs in general statistical
frameworks (Cheng
& Titterington, 1994), with Bridle (1992) comparing and
blending ANNs with
Markov-chain models, and applying Bayesian approaches and
methods in the
modelling of neural networks (MacKay, 1992). More recently, He
and Li (2011)
provide an interesting example of such work. They used the
standard
backpropagation algorithm derived in vector form, and they
were successful in
determining the confidence interval and prediction intervals
for the ANN, while
also exploring which neural network structural characteristics
had more of an
impact on such parameters. In particular, when the
Levenberg-Marquardt
backpropagation algorithm is used to train a neural network,
since the Jacobian
matrix has been calculated to update the weights and biases of
the neural
network, the confidence interval with the corresponding
confidence level can be
computed to evaluate the predictive capability of the ANN. In
addition, on
similar topics, Zapranis and Livanis (2005) state that given
that ANNs are a
good example of consistent non-parametric estimators with
powerful universal
approximation properties, they require that the development
and implementation
of neural network applications has to be based on established
procedures for
estimating confidence and especially prediction intervals.
They go on to review
the main state-of-the-art approaches for the construction of
confidence and
prediction intervals, and evaluate their strengths and
weaknesses. After
comparing them in a controlled simulation, the authors suggest
that a
combination of bootstrap and maximum likelihood approaches are
superior to
analytic approaches when constructing the prediction intervals
(Zapranis &
Livanis, 2005). On the other hand, other authors propose the
construction of
confidence intervals for neural networks based on least
squares estimations and
using the linear Taylor expansion of the nonlinear model
output, which also
detects ill-conditioning of ANN candidates and can estimate
their performance
(Rivals and Personnaz, 2000).

In
terms of the comparison between ANNs and logistic
regression, in neural network analysis the purpose of the
hidden layer is to
map a set of patterns, which are linearly non-separable in
the input space,
into the so-called image-space in the hidden layer, where
these patterns may
become linearly separable. As in logistic regression,
decision surfaces in the
neural networks are hyperplanes in the input space. The
key difference, though,
between neural networks and logistic regression is that
each hidden neuron
(other than the bias neuron) produces an output that
corresponds to a distinct,
discriminating hyperplane in the input space. When these
are weighted, summed,
and transformed at an output neuron, the resulting output
corresponds very
closely to a multidimensional step function. It is found
that the boundaries of
regions of similar probability are defined by the
discriminating hyperplanes,
which crisscross the input space
(Dreiseitl & Ohno-Machado, 2002).

Given the vast number of
practical applications
already mentioned in the original article by Musso et al.
(2013), it is
unfortunate that Edelsbrunner and Schneider (2013) choose to
exemplify an
unrealistic example of application of ANNs in a contrived
situation in which a
student is eliminated from a programme based on a neural
network
classification. ANNs, like any other methodology provides the
researcher or
applied scientist with information. As we have already shown
from the
literature cited, in the case of ANNs there are a number of
methods to
establish the necessary input-output relationships and to
determine the
confidence and prediction intervals provided by an ANN.
Therefore, the contrived
diagnostic example provided by Edelsbrunner and Schneider
(2013, pp. 100) shows
an underestimation/misinterpretation of the potential of ANNs.
Furthermore,
poor advice is always a problem, as would be the case in this
example, with the
unfortunately frequent decision-making of students’ career
paths determined by
a single-point examination. On the other hand, a trusted
result from a properly
constructed and tested ANN could provide valuable diagnostic,
educational, and
public policy information. In fact, the research carried out
by some of these
authors (Cascallar et al., 2006; Kyndt et al., 2011, 2015;
Luft, Gomes, Priori
& Takase, 2013; Musso & Cascallar, 2009a; Musso et
al., 2012, 2013) provides
examples of useful diagnostic models in the educational field.
It is a false
dichotomy to present modelling for understanding versus
modelling for
prediction. In reality, both are achievable and in fact they
should be
integrated for the advancement of the field and the success of
each
application. Much insight has been gained by integrating
understanding with
predictive and classification models. As is good practice in
various fields,
especially in applied statistics and mathematical modelling,
the various approaches
constitute a toolbox that the professional has available in
order to apply the
best method for the problem at hand. The fact that our article
(Musso et al.,
2013) demonstrated the use of ANNs in a given academic
application is not meant
to be exclusionary. On the contrary, the field requires the
integration of
mathematical modelling and statistical techniques.

Regarding the comments in
Nokelainen and Silander
(2014) on the article by Musso et al. (2013), they can be
summarized in two
main points. The first point questions whether the methodology
used was
rigorous in its procedures, and the second suggests comparing
the neural
network results with those obtained from another
discriminative classifier in
addition to the comparison to a generative classifier such as
discriminant
analysis.

It is very important to
clarify that the data
reported in Musso et al. (2013) rigorously followed the
standards established
by the Message Understanding Conferences (MUC) (Grishman &
Sundheim (1996).
As is clearly stated in the Musso et al. (2013) article, “the
training and
testing samples were selected at random from the existing data
and the
proportions were adjusted in order to maximize the training
sample while
preserving the appearance of all detected patterns in the
testing sample, so as
to be able to appropriately test the model” (p. 60). The two
samples were
chosen at random, precisely to avoid what Nokelainen and
Silander (2014) put
forward. These authors seem to have misinterpreted the
sections on analyses
procedures and architecture of the neural network (Musso et
al., 2013, pp.
52-54) in which the process is described in detail, and they
completely
misjudge when they state that “The paper by Musso and her
colleagues (2013)
practically acknowledges that such a discipline was not
rigorously followed.”
(Nokelainen & Silander, 2014, p. 79). It is clearly stated
in the above
mentioned sections the way in which the sample was divided,
the complete independence
of the randomly selected training and testing subsets, and the
criteria
followed to determine the proportions of cases in each of the
two subsets.
Ironically, the procedures followed coincide with those
suggested by
(Nokelainen & Silander, 2014, p. 79). Let us state
unequivocally that both
subsets of cases in the training and testing samples were
analyzed separately.
In addition, all training of the neural network model was
carried out on the
training sample, as well as all parameter adjustments, until
the desired level
of precision was attained. Then, the model was independently
tested on the
testing sample, capturing the generalization of the network
structure and the
learning parameters. None of the model building took place on
the testing
sample as Nokelainen and Silander (2014) incorrectly assume.
Thus, the performance
of the model with the testing subset actually provides an
indication of the
generalization of the model, not just “fit” as Nokelainen and
Silander (2014,
pp. 79) also incorrectly state.

A related comment regarding
the “ethical standards”
of the Musso et al. (2013) paper is truly surprising. Do
Nokelainen and
Silander (2014) truly believe or imply that the authors could
not “refrain from
cheating (using the test data)” (Nokelainen & Silander
(2014, p. 79) in
developing the model? If so, it is alarming, because they are
making a serious
assumption regarding the authors or at best an implication of
ignorance of
basic rules of science and of this methodology in particular.
Their fear of
“cheating” and their implication that the testing sample
analysis should be
carried out by different researchers because of this assumed
temptation to
cheat could be extended to all research in all areas and all
statistical
methods. It is precisely part of the scientific method to
follow any scientific
finding with careful replications, not simply to avoid
cheating, but to truly
evaluate the generalizability of scientific results. It does
not mean that we
cannot trust researchers, at least a priori, with carrying out
an ethically
sound analysis. If not, all findings, including theirs, would
be in question.
Certainly, the Musso et al. (2013) article followed careful
and rigorous
methodological procedures. If their question has to do with
the perfect
classification obtained, it is the product both of the
appropriate modelling
process carried out, and of the granularity of the expected
results given the
available data; it should be noted that the correlation
between the individual
GPA scores of the students in the whole testing sample and
their predicted
score (with data from one year in advance), was .86 (Musso et
al., 2013, p.
64).

Regarding the suggestion to
use other discriminative
classifiers, such as logistic regression, to compare with the
results obtained
with the neural network model, it is a good suggestion which
has already been
carried out in the literature (Kim & Ahn, 2009), and it
has been found that
neural networks obtained better classification results. In
fact, some of the
authors in Musso et al. (2013) already have carried out such
analyses in
research currently underway, with the same results favourable
to neural
networks (Musso, Boekaerts, Segers, & Cascallar, in
preparation).

The field of machine learning
research and the
related predictive systems is in constant development and new
advances are
introduced at a rapid pace (Monteith, Carroll, Seppi, &
Martinez, 2011).
Several methods have been suggested to improve the performance
of machine
learning algorithms and of neural network methods in
particular, some of them
using Bayesian approaches which have shown excellent potential
(Aires, Prigent,
& Rossow, 2004; Orre, Lansner, Bate, & Lindquist,
2000). We share the
view expressed by Nokelainen and Silander (2014) that
continued research in
this field should be pursued, and ensemble methods (Rokach,
2010), such as
those involving bootstrap aggregating (Sahu, Runger, &
Apley, 2011), and
Bayesian model combination (Monteith et al., 2011), together
with multiple
classifier systems (Roli, Giacinto, & Vernazza, 2001) are
among those that
should continue to be considered in certain applications.

In conclusion, we can state
that as was very
accurately stated by Anders and Korn (1996) in their work on
model selection in
neural networks, the process of model selection in ANN can be
informed by
statistical procedures and methods. Statistical methods can
improve the model
building and the interpretation of ANNs. What is needed is the
courage and
open-mindedness to actually explore new paths and new
methodologies which can
perhaps sometimes unexpectedly provide new conceptualisations
and tools for
theoretical advancement and practical applied research. This
is particularly
true in the fields of educational science and social sciences,
where the
complexity of the problems to be solved requires the
exploration of proven
methods and new methods, the latter usually not among the
common arsenal of
tools of neither practitioners nor researchers in these
fields.

Keypoints

- Artificial Neural
Networks are powerful mathematical
modelling tools for classification and prediction.

- Advances in
Artificial Neural Network methodologies
have made them more transparent and useful, avoiding the
original “black box”
characteristics in their early development.

- There is a long
history with significant recent
advances which has achieved strong ties between traditional
statistical
constructs with their equivalent in Artificial Neural
Networks.

- Artificial Neural
Networks are a useful methodology
that can advance our understanding of phenomena when
modelling for
understanding and modelling for classification/predictions
are combined.

- Artificial Neural
Networks are an additional
important tool in the researcher’s toolbox which can be
particularly useful to
tackle highly complex and large data sets with interactions
among the variables
which are not fully understood.

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