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The International Journal of Human Resource
Management
ISSN: 0958-5192 (Print) 1466-4399 (Online) Journal homepage: http://www.tandfonline.com/loi/rijh20
Supervisor support, control over work methods
and employee well-being: new insights into
nonlinearity from artificial neural networks
Mark John Somers, Dee Birnbaum & Jose Casal
To cite this article: Mark John Somers, Dee Birnbaum & Jose Casal (2018): Supervisor support,
control over work methods and employee well-being: new insights into nonlinearity from artificial
neural networks, The International Journal of Human Resource Management
To link to this article: https://doi.org/10.1080/09585192.2018.1540442
Published online: 19 Nov 2018.
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Supervisor support, control over work methods and
employee well-being: new insights into nonlinearity
from artificial neural networks
Mark John Somers
a
, Dee Birnbaum
b
and Jose Casal
a
a
Martin Tuchman School of Management, New Jersey Institute of Technology, Newark, NJ,
USA;
b
Commerce & Business, Rhodes College, Memphis, TN, USA
ABSTRACT
The purpose of this study was to test a nonlinear model of
psychological well-being at work. Specifically, artificial
neural networks (ANNs) were used to identify and map
nonlinearities among supervisor support, control over work
methods and employee well-being. Our findings confirmed
results from prior studies in that ANNs explained signifi-
cantly more variance in well-being than did OLS regression.
Visualization of nonlinear relationships extended prior
research, demonstrating strong patterns of nonlinearity
between two dimensions of supervisor support, direct sup-
port and trust, and well-being. Discussion was focused on
the implications of observed nonlinearities for theory devel-
opment and on the value of ANNs in building more accur-
ate predictive models of employee well-being.
ARTICLE HISTORY
Received 23 June 2017
Accepted 16 October 2018
KEYWORDS
Artificial neural networks;
nonlinear models; employee
well-being; support
and control
Stress and psychological well-being at work have important implications
for individuals and organizations. Well-being influences a range of out-
comes directly relevant to human resources management including job
performance, absenteeism, and turnover (Hausser, Mojzisch, Niesel, &
Schulz-Hardt, 2010). Reinforcing this point, recent work quantifying the
health consequences of work-related stress found that it is responsible
for 5–8% of healthcare costs in the United States, and 120,000 deaths per
year (Goh, Pfeffer, & Zenios, 2015).
The importance of psychological well-being at work is also evident in
recent calls for scholars and work organizations to pay more attention to
this issue by increasing their focus on HRM policies and practices that
foster employee well-being (Goh et al., 2015; Guest, 2017). These con-
cerns are heightened by the current state of research in this area. Indeed,
the need for more efficacious theories, models and methods that translate
CONTACT Mark John Somers mark.somers@njit.edu
ß2018 Informa UK Limited, trading as Taylor & Francis Group
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT
https://doi.org/10.1080/09585192.2018.1540442
into better stress management in the workplace has been recognized
(Spector & Pindek, 2015). Specifically, meta-analyses found that relation-
ships between its hypothesized antecedents and well-being were spotty, with
levels of explained variance indicating that modifications to current theory
are needed (Hausser et al., 2010; Viswesvaran, Sanchez, & Fisher, 1999).
Although different models and frameworks are evident in the well-
being literature, several commonalties are present. To begin with, well-
being is defined in terms of intra-psychic processes through which
individuals adapt to external forces and demands (Hobfoll, 1989; Karasek
& Theorell, 1990). Further, these demands are hypothesized to be miti-
gated by available resources which act to buffer them (Karasek, 1979)by
providing a source of stability that limits stress and perceived vulnerabil-
ity (Hobfoll, 1989). Finally, within the broad range of potential resources,
control of work methods and social support have emerged as the most
efficacious and most studied work-related resources (cf., Hausser et al.,
2010; Viswesvaran et al., 1999).
Critics of current theory have taken issue with the implicit assumption
of linearity that has guided research on this topic (Ferris, Bowen,
Treadway, Hochwarter, Hall, & Perrewe, 2006), and its implications for
mitigating stress at work. Thus, the notion that work characteristics such
as support and control act independently and additively on stress and
well-being has been questioned. Rather, the work environment was rede-
fined such that relationships between work characteristics and work
stress were hypothesized to be more contextually driven, and more com-
plex (Michaelides & Karanika-Murray, 2008).
Introducing nonlinearity into research on stress and well-being opens
up new lines of inquiry. With respect to theory development, a nascent
nonlinear model of well-being calls for rethinking how the work envir-
onment is experienced, and how the psychological adaptation process is
changed (Karanika-Murray & Cox, 2010; Michaelides & Karanika-
Murray, 2008). With respect to HR practice, the emphasis on context-
ual influences in the nonlinear model addresses the need for new ideas
and new programs to promote well-being (cf., Goh et al., 2015)by
shifting the focus from immediate work activities to the broader work
environment.
Initial work has established the predictive efficacy of nonlinear models
of work stress and well-being by leveraging advances in neural comput-
ing. Results were encouraging in that artificial neural networks (ANNs)
significantly outperformed OLS regression (Karanika-Murray & Cox,
2010; Ladstatter, Garrosa, & Dai, 2014) indicating the presence of nonli-
nearity (cf., Scarborough & Somers, 2006). However, while these studies
were encouraging in that they established the plausibility of the nonlinear
2 M. J. SOMERS ET AL.
model, few clues were offered about where nonlinear relationships pre-
sent and what they meant for theory and HR practice.
This study extends prior work on nonlinearity in stress and well-being
research in several ways. To begin with, based on prior work focused on
the conceptual development of a nonlinear model of well-being
(Karanika-Murray & Cox, 2010; Michaelides & Karanika-Murray, 2008),
complexity, context and salience were used to identify processes where
nonlinearity was most likely to be present, to select variables and rele-
vant theory associated with those processes, and to assess the meaning
and implications of nonlinearity with respect to understanding and man-
aging well-being at work.
In addition, nonlinear relationships among variables were mapped using
the visualization capabilities of ANNs. In prior studies, model fit statistics
from ANNs have been used to establish the case for nonlinearity by com-
paring them with those from linear statistics (cf., Karanika-Murray & Cox,
2010). In extending this work, we used the data visualization properties of
ANNs in this study to map patterns of nonlinearity to better understand
underlying nonlinear processes and their implications for theory and prac-
tice. Further, by identifying where nonlinearity was present, we moved
research from an exploratory phase to the confirmatory phase necessary
fortheorydevelopment(cf.,Scarborough&Somers,2006).
Background
Unlike most areas in organizational behavior and HRM, in which theory
is based on the (often implicit) assumption of linearity, a nonlinear alter-
native is evident in well-being research. To understand the tenets and
processes associated with the nonlinear model, it is helpful to contrast
them to linear models of stress and well-being.
The demand/support/control model
The demand/support/control (D/C/S) Model is based on the premise
that psychological adaptation to the work environment is influenced by
two work-related resources, control over work methods and social sup-
port in the workplace, which act to mitigate work stress, and increase
well-being. The model’s influence is highlighted by a recent meta-analysis
which found that social support and autonomy at work were among the
most studied work-related resources with respect to well-being (Nielsen
et al., 2017).
Initial formulations of the D/C/S Model were parsimonious and ele-
gant. Support and control were hypothesized to exhibit direct, additive
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 3
influences on stress and well-being (Karasek, 1979; Karasek & Theorell,
1990); that is, a simple ‘more is better’mechanism was hypothesized to
drive well-being at work. As such, the D/C/S Model was able to offer
more precise specification of process than did other models of well-being
such as conservation-of-resources theory (Thomas & Lankau, 2009), with
better empirical results (cf., Nielsen et al., 2017).
Nonetheless, the D/C/S Model underperformed expectations.
Specifically, Hausser et al. (2010) reported support for additive effects in
approximately 50% of studies conducted from 1979 to 2007, and with
only 28% fully supporting the D/C/S. Model. Modifications to improve
model performance focused on increasing the complexity of underlying
processes, while retaining the assumption of linearity. Complexity was
introduced by hypothesizing conditional relationships in the form of
interaction effects between support, control and well-being (Johnson &
Hall, 1988).
Empirical tests of these modifications were disappointing. Hausser
et al. (2010) reported that tests of interaction effects (e.g. the multiplica-
tive model) were supported in only 40% of studies conducted between
1979 and 1997 and in only 21% for those conducted from 1998 to 2007.
Similarly, Viswesvaran et al. (1999) meta-analysis found limited support
for the multiplicative model, and a corrected correlation of .21 for the
additive model.
The notion of conditional relationships was extended further with the
triple match hypothesis (cf., Hausser et al., 2010). In this case, sources of
demands, support, control and well-being were matched to further align
work characteristics with well-being. Increments in explained variance
were low (cf., Chrisopoulos, Dollard, Winefield, & Dormann, 2010)so
that the expected improvements in predictive efficacy were not realized.
A nonlinear model of well-being
Interest in nonlinearity with respect to well-being came from a variety of
sources. Interest in exploring alternatives to the D/C/S Model was one
factor (cf., Karanika-Murray, Antoniou, Michaelides, & Cox, 2009), but
the development of a nonlinear model of well-being stemmed from other
factors as well. The earliest work in this area focused on curvilinear rela-
tionships between work characteristics and well-being. In particular, the
Vitamin Model (Warr, 1987) is based on the hypothesis that increases in
work characteristics do not lead to proportional increases in well-being
across the entire range of both variables. Rather, using a vitamin analogy,
in which increases in dosages of vitamins are beneficial up to threshold
levels, Warr (1987) theorized that work characteristics have a positive
4 M. J. SOMERS ET AL.
influence on well-being up to a point, after which their beneficial effect
levels off or becomes harmful. That is, relationships are hypothesized to
be curvilinear, characterized by clear threshold levels that act as tip-
ping points.
Tests of the curvilinear hypothesis have produced mixed results. Some
studies have reported evidence of curvilinear relationships between work
characteristics and well-being (cf., Warr, 1990; de Jonge & Schaufeli,
1998) while others found little or no evidence of curvilinearity (cf.,
Fletcher & Jones, 1993; Rydstedt, Ferrie, & Head, 2006). Increments in
explained variance were also comparatively small in studies where the
curvilinear hypothesis was supported. Nonetheless, the Vitamin model
raised the possibility that relationships between work characteristics and
well-being might not be linear. It was augmented by Person-environment
fit models (Edwards, Caplan, & Harrison, 1988), theory from the com-
plexity sciences (Michaelides & Karanika-Murray, 2008) and application
of the general adaptation syndrome (Selye, 1974) in which psychological
adaptation was thought to follow a similar, nonlinear pattern than does
physiological adaptation (Karanika-Murray & Cox, 2010).
These viewpoints coalesced into a nonlinear model of employee well-
being that was grounded in the notion that work environments are
complex, with certain characteristics gaining salience and influencing
psychological responses to well-being at work (Ferris et al., 2006;
Karanika-Murray & Cox, 2010; Michaelides & Karanika-Murray, 2008).
Complexity operates such that the work environment is experienced dif-
ferentially based on threshold values of (salient) antecedents of well-
being. That is, conceptual models of well-being, based on the assumption
of linearity (such as the D/C/S Model), are grounded in the notion that
changes in the values of antecedent variables result in a concomitant
change in the amplitude of well-being (based on the direction of the
change). In contrast, the nonlinear model is based on the position that
there are threshold values of antecedent variables, which when crossed,
alter the nature of underlying processes so that a change in state (rather
than amplitude) results (Michaelides & Karanika-Murray, 2008).
This conceptualization represents a significant break from prior theory
on employee well-being. To begin with, the nonlinear model focuses
attention on interconnections among work characteristics so that they
act conjointly to form a work environment. Further, the psychological
processes associated with well-being are seen as discontinuous.
Consequently, the influence of changes in levels of antecedent variables
on well-being is dependent on their relative levels. That is, because proc-
esses operate differently on either side of a threshold level or tipping
point, large changes in the levels of support and/or control might have
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 5
little influence on well-being above threshold levels, but small changes in
support and/or control might have a large influence on well-being below
threshold levels for these variables (cf., Michaelides & Karanika-Murray,
2008; Scarborough & Somers, 2006).
Empirical testing using ANNs has provided support for the propos-
ition that relationships between work characteristics and well-being are
nonlinear. In particular, Karanika-Murray and Cox (2010) found that
ANNs explained significantly more variance than did OLS regression in
wear-out (R
2
¼.26 vs. .17) and job satisfaction (R
2
¼.37 vs. .27).
Similarly, Ladstatter et al. (2014) used data visualization from ANNs to
demonstrate that relationships between burnout, work overload, and
contact with pain and death were nonlinear for hospital nurses.
However, the scope and form of nonlinear relationships between its ante-
cedents and well-being remain unclear. Thus, while it is likely that nonli-
nearity is present, its implications have not been fully examined.
The study
This study is built around variables that are salient in the workplace,
which are likely to be embedded in complex, nonlinear processes, and
which are prominent in the well-being literature. We identified the
supervisor-subordinate relationship as a salient contextual variable that
was likely to generate the discontinuities that define nonlinear processes.
The centrality of the supervisor is well-established. Supervisors operate as
the faces of their organizations, and thus exert considerable influence
over how subordinates interpret their work environments (Eisenberger
et al., 2010).
Regarding complexity and discontinuity, the supervisor-subordinate
relationship is governed by complex social exchange processes that affect
how the work environment is experienced. In particular, LMX theory
suggests that the quality of leader-member relations and consequent in-
group and out-group status (Graen & Uhl-Bien, 1995) results in qualita-
tive differences in how subordinates experience their day-to-day work
environments, and those differences have been linked to employee well-
being (Lyons & Schneider, 2009).
As the nexus for subordinates to the organization, the supervisor also
influences two key drivers of well-being at work, support and control.
Thus, the supervisor-subordinate relationship is tied to support and con-
trol to form a complex set of relationships that are potentially discon-
tinuous (i.e. nonlinear). Specifically, supervisor support is a direct
influence of employee well-being (Rhoades & Eisenberger, 2002).
Further, supervisors influence control over work methods by deciding
6 M. J. SOMERS ET AL.
how much autonomy and job-related information subordinates are given
(Lee & Ashforth, 1993), both of which are affected by in-group and out-
group status (Graen & Uhl-Bien, 1995).
Supervisor support
Perceived supervisor support concerns the degree to which employees
feel that their supervisors value their contributions and are concerned
about their well-being (Kottke & Sharafinski, 1988). Supervisor support
has been viewed as a dimension of perceived organizational support,
and, as is the case with other components of organizational support, it is
posited to mitigate work stress (Rhoades & Eisenberger, 2002).
Supervisor support has been studied as an influence of employee well-
being, but the complexity of this variable has not been fully explored.
Specifically, in most well-being research, social support is either aggre-
gated into an omnibus indicator that includes multiple sources or super-
visor/managerial support has been studied as a unidimensional construct
(cf., Hausser et al., 2010). However, perceived supervisor support
includes a fairness/justice component (Rhoades & Eisenberger, 2002)
which can influence subordinate self-esteem (De Cremer, van
Knippenberg, van Knippenberg, Mullenders, & Stinghamber, 2005), and
a trust element tied to the quality of the supervisor-subordinate relation-
ship (Brower, Schoorman, & Tan, 2000).
The conditions for nonlinear processes with respect to well-being
include salience, complexity, and discontinuity (Michaelides & Karanika-
Murray, 2008).
Nonlinear relationships between supervisor support and well-being are
justified by the salience of the supervisor in the workplace, qualitative
differences in how the work environment is experienced based on the
quality of the supervisor-subordinate relationship, and the complexity of
the supervisor support variable. We, therefore, postulate that relation-
ships among supervisor support, perceived fairness and perceived trust,
and well-being are nonlinear.
Control over work methods
Control over work methods refers to degree of autonomy over aspects of
the work environment that include decision latitude, scheduling, control
over job related information, and input into setting objectives (cf., Lee &
Ashforth, 1993). In examining the relationship between control over
work methods and work stress, Karasek and Theorell (1990) argued that
high job demands can be mitigated by high levels of control which
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 7
fosters learning thereby lowering levels of psychological stress. Morrison,
Cordery, Girardi, and Payne (2005) extended this hypothesis by positing
that control over work builds self-esteem and self-efficacy, which act to
enhance psychological well-being at work.
Hypothesized relationships between control and well-being vary from
a simple, direct influence to conditional relationships in which social
support acts as a moderator variable. Although empirical studies consist-
ently support the direct, additive model (Hausser et al., 2010), linking
support and control with respect to well-being is a first step in testing
the proposition that the work environment cannot be parsed into distinct
components which act independently on well-being.
This proposition is based on the view that control over work methods
is not entirely a psychological phenomenon, but that it has been concep-
tualized and studied in this manner. Specifically, in linking control to
learning and self-esteem, the focus is mostly on the individual. However,
control over work methods is also a social phenomenon in that task
assignment and task autonomy are governed partly by one’s relationship
with one’s supervisor.
Control over work methods, therefore, is negotiated to some degree,
and the nature of those negotiations are influenced by the quality of the
supervisor-subordinate relationship. In-group subordinates benefit from
better job information and more autonomy over work in relation to out-
group subordinates (Mayo, Sanchez, Pastor, & Rodriguez, 2012) so that
the degree of control over work methods is likely to differ between these
two groups. As such, control over work methods are likely to be experi-
enced differentially (which is consistent with nonlinear relationships with
well-being) rather than uniformly.
As is the case with support, control over work methods with respect
to well-being is typically studied as a unidimensional variable (cf.,
Hausser et al., 2010). However, like supervisor support, control is a
multidimensional variable that includes horizontal and vertical rela-
tionships (cf., Alexander & Randolph, 1985). Thus, studying well-being
with a truncated conceptualization of control and a restricted defin-
ition of support reduces the complexity of the work environment,
thereby limiting the ability to detect nonlinear relationships among
these variables.
This complexity of control of work methods in conjunction with dif-
ferences in how control is experienced, based on the quality of super-
visor-subordinate relationships, are hypothesized to result in
discontinuities that define nonlinear processes. We, therefore, postulate
that relationships between control over work methods, supervisor sup-
port, and well-being are nonlinear.
8 M. J. SOMERS ET AL.
Artificial neural networks
Artificial neural networks are advanced algorithms that use statistical func-
tions to identify patterns in data. Swingler’s(1996) definition of ANNs is
among the most accessible. ANNs are defined as computational systems
designed to capture salient features from a set of input variables and then
map them to a set of output variables in a way that makes sense to end
users. Although ANNs are characterized as ‘learning’patterns in data, it
should be made clear that learning is accomplished with statistical functions
and is not equivalent to human learning (Scarborough & Somers, 2006).
There are several neural computing paradigms (e.g. ANNs), each with
different topologies or architectures and applications. Feedforward neural
networks that use backpropogation of error are best suited to problems
that involve prediction (Gurney, 2003). A schematic diagram of a feed-
forward ANN with backpropogation of error is presented in Figure 1.
This diagram depicts the topology of the ANN, which is comprised of
input, hidden and output layers. Specifically, the ANN depicted in Figure 1
has three neurons in the input layer, three in the hidden layer, and one
in the output layer. The input layer represents predictor variables or
input variables and the output layer represents the criterion variable. The
hidden layer is comprised of neurons which contain statistical functions
that act on input data by summing it and applying weights to reduce
observed error. In a feedforward neural network, data and information
Figure 1. Schematic of an artificial neural network.
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 9
move from the input layer to the hidden layer and then to the output
layer. A prediction is generated for each observation using the statistical
functions embedded in the neurons in the hidden layer of the ANN. At
that point, error, as defined by the difference between predicted and
observed values, is calculated. Error is then fed back to the hidden layer
of the ANN, data are passed through the ANN again, and weights are
adjusted to slightly reduce observed error. That process is termed back-
propogation of error (Bishop, 1995). (See Figure 1)
Given that error is reduced gradually with each pass of data through the
ANN architecture, it can take thousands of iterations before an acceptable
reduction in error is achieved. That is, there are many cycles in which
data move forward through the ANN, and error is propagated backward,
and gradually reduced. This process is termed training, and it defines how
a feedforward ANN learns patterns in data. As training progresses, pat-
terns in the data are learned by increasing weights for some connections
among the neurons in the input, hidden and output layers of the ANN,
while weights for other connections are decreased. Importantly, the neu-
rons in the hidden layer act in concert to identify and map complex, non-
linear relationships among the input variables and the variables in the
output layer, if such relationships are present in the data (Bishop, 1995;
Ripley, 1996).
A feedforward neural network with backpropogation of error was used
in this study examine relationships between hypothesized antecedents
(i.e. supervisor support and control) and well-being. Although well-being
research using ANNs is sparse, ANNs have been applied to other areas
in organizational research with good results when compared to linear
methods. Specifically, ANNs have provided new insights into leadership
(de Oliveira, Possamai, Dalla Valentina, & Flesch, 2013), turnover
(Somers, 1999) and job performance (Somers, 2001; Somers & Casal,
2009). More generally, it has been argued that ANNs should be more
widely used in organizational research because they have the potential to
open new lines of inquiry to spur theory development, and to address
long standing problem areas by exploring the possibility that disappoint-
ing results might be a consequence of studying nonlinear processes with
linear methods (Aiken & Hanges, 2015; Oswald & Putka, 2016;
Scarborough & Somers, 2006: Tonidandel, King, & Cortina, 2018).
Method
Study participants and procedures
The sample was comprised of 235 registered nurses in a large hospital
located in the United States. All participants were full-time employees.
10 M. J. SOMERS ET AL.
The study was sponsored by management, and data were collected on-
site during normal working hours. Participation was voluntary and 100%
of those nurses asked to complete the survey agreed to do so. In order
to obviate problems with common method variance, questionnaires were
administered at two different times. The first administration assessed
hypothesized antecedents of well-being (support and control), and the
second several weeks later, assessed well-being. The sample was 92%
female with a mean age 38.51 years, and an average tenure of 10.49 years.
All of the respondents held bachelor’s degrees in nursing.
In an ANN analysis, data are partitioned into training and test sam-
ples. Test data (e.g. a holdout sample) are cases that were not used by
the ANN to learn patterns in data, and thus, provide a good indicator of
the generalizability of results (Bishop, 1995). In this study, 25% of the
sample was used for test data so that the training sample was 178 and
the test sample was 57. Test data were also used in regression analyses
by applying unstandardized weights to test data and then calculating the
correlation between actual and predicted values. Test data provide the
fairest and most accurate assessment of predictive accuracy across OLS
regression and ANNs (Somers & Casal, 2009).
Measures
Supervisor support
Perceived support from one’s supervisor was measured with the support,
fairness and trust scales from a measure developed and validated by
Koys and DeCotiis (1991). Responses were along a five-point Likert type
scale ranging from strongly disagree to strongly agree. Higher scores,
thus, were indicative of greater levels of support. Trust in one’s super-
visor was assessed with a five item scale, and Cronbach’s alpha was .89.
A sample item is ‘My boss is the kind of person I can level with’.
Perceived fairness was measured with a four-item scale, and Cronbach’s
alpha was .81. A sample item is ‘I can count on a fair shake from my
boss’. Support from one’s supervisor was measured with a five item scale,
and Cronbach’s alpha was .92. A sample item is ‘I can count on my boss
to help me when I need it’.
Control over work methods
Control over work methods was measured with scales developed by
Alexander and Randolph (1985) that were tailored to nursing work. Two
dimensions of control over work methods were assessed: horizontal par-
ticipation and vertical participation. Horizontal participation is defined
as the degree to which nurses were involved with peers in decision-
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 11
making and defining tasks. Vertical participation refers to the degree to
which supervisors and subordinates consult with each other with respect
to job-related tasks and decision-making.
Both horizontal and vertical participation were measured with five-
point Likert-type scales with the following response categories: ‘never’,
‘seldom’,‘sometimes’,‘often’and ‘very often’, The horizontal participa-
tion measure was comprised of five items and Cronbach’s alpha was .65.
A sample item is ‘I do not play an active role in making decisions in my
work group’. The vertical participation was also comprised of five items
and Cronbach’s alpha was .79. A sample item is ‘I have to check with
my supervisor before I do almost anything’.
Stress and well-being at work
Well-being was measured with Warr’s(1990) scale. The item stem for
this measure is ‘Think of the past few weeks, how often did your job
make you feel each of the following’, and the response scale varied along
six points ranging from ‘never’to ‘most of the time’. Twelve psycho-
logical states that measure stress and psychological well-being at work
followed the item stem. A sample of them includes ‘tense’,‘worried’,
‘gloomy’,‘optimistic’and ‘calm’. Chronbach’s alpha was .86.
Control variables
Based on previous research suggesting that job tenure is related to the
quality of supervisor–subordinate relationships (Harris, Kacmar, &
Carlson, 2006), it was entered as a control variable in all analyses.
Further, age influences well-being and it was also treated as a control
variable in all analyses (cf., Hausser et al., 2010).
Data analysis
Analytical methods
Data were analyzed with OLS regression and ANNs. OLS regression was
used to estimate linear relationships between support, control and well-
being. ANNs were used to test for nonlinear relationships among these
variables. Age and job tenure were included in all analyses as con-
trol variables.
OLS regression was conducted with SPSS. Neural networks were built
and trained using the neural networks module in the STATISTICA soft-
ware package. Following procedures recommended by Somers and Casal
(2009) results from two neural computing paradigms, radial basis func-
tions (RBF) and multilayer perceptrons (MLP), were compared. Both
12 M. J. SOMERS ET AL.
RBFs and MLPs are feedforward neural networks that use backpropoga-
tion of error. Thus, they have the same architectures (i.e. input, hidden
and output layers), but use different statistical functions to identify pat-
terns in data. MLPs typically use sigmoid (e.g. hyperbolic tangent) func-
tions in their hidden layers while RBF networks use Gaussian functions
(Bishop, 1995).
The number of neurons in the hidden layers of the MLP and RBF net-
works was varied systematically, and results were compared. RBF net-
works consistently outperformed MLP networks. The RBF network that
generated the most accurate predictions had eight neurons in the hidden
layer. Thus, its network architecture or topology was comprised of seven
neurons in the input layer representing our antecedent variables, eight in
the hidden layer, and one in the output layer representing employee
well-being.
Assessment of model fit
Predictive accuracy across models was assessed with the squared correl-
ation of predicted and actual values for the criterion variable (R
2
).
This metric has been used extensively to compare the model fit of ANNs
in relation to conventional statistical methods (Scarborough &
Somers, 2006).
Importance of predictor variables
Neural computing has not advanced to the point where the equivalent of
a standardized regression coefficient has emerged, but there has been
progress in estimating the relative importance of predictor variables. The
neural network module in STATISTICA uses a technique developed by
Hunter, Kennedy, Henry, and Ferguson (2000) in which each predictor
variable is made unavailable to the network by using mean substitution.
Decrement in network performance is then calculated and sensitivities
for each predictor variable are expressed as the ratio of network error
when the variable is removed from and included in the model. Higher
values are indicative of greater variable importance.
Results
Descriptive statistics are presented in Table 1.
OLS regression and ANN analyses
Regression and ANN analyses are summarized in Table 2. Results
diverged considerably in that the strongest predictor variables in the OLS
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 13
regression were among the weakest in the ANN analysis. Specifically,
age and vertical participation were the strongest predictor variables of
stress and well-being in the linear model (b¼.23, t¼3.055, p<
.01 and b¼.27, t¼2.056, p<.05), but were among the weakest
predictors in the RBF neural network analysis as indicated by a ranking
of sensitivity coefficients. Conversely, supervisor support and trust
emerged as the strongest predictors in the neural network analysis sug-
gesting that relationships between control and stress and well-being
might be linear while relationships between support and stress might
be nonlinear.
With respect to model fit, ANNs outperformed OLS regression.
Specifically, with test data, ANNs explained three times more variance in
stress and well-being (or a 300% improvement) than did OLS regression.
Given that the R square statistic was not statistically significant for OLS
regression, but was for the ANN analysis, it was not necessary to con-
duct statistical tests to establish that these observed increments in model
fit were statistically meaningful.
Patterns of nonlinearity
To explore patterns and pervasiveness of nonlinearity, a visualization
derived from the ANN analysis is presented in Figure 2. It is indicative
Table 1. Descriptive statistics.
Variable Mean SD 1 2 3 4 5 6 7 8
1. Age 38.51 10.49 –
2. Job tenure 7.04 7.11 .49 –
3. Fairness 3.59 .79 .01 .09 –
4. Support 3.57 .92 .02 .13 .71 –
5. Trust 3.64 .86 .02 .15 .73 .71 –
6 .Horizontal participation 3.15 .71 .03 .17 .35 .35 .33 –
7. Vertical participation 3.08 .81 .08 .20 .53 .48 .41 .76 –
8. Work stress 3.19 .81 .20 .04 .44 .42 .41 .25 .33 –
Notes. Correlations in boldface p<.01.
Table 2. Comparison of OLS regression and RBF neural network for work stress.
Predictor OLS regression RBF neural network
bSensitivity coefficient and rank
Age .23 .9980 (7)
Job tenure .04 1.0002 (6)
Fairness .09 1.002 (3)
Support .04 1.006 (2)
Trust .12 1.013 (1)
Horizontal participation .04 1.0007 (4)
Vertical participation .271.0003 (5)
Model fit:
R
2
training .27 .41
R
2
test .08 .24
Notes. p<.05; p<.01.
14 M. J. SOMERS ET AL.
of pervasive patterns of nonlinearity with respect to support and trust. In
particular, a floor in which low levels of sensitivity is evident; that is,
comparatively large changes in the levels of support and trust have a
comparatively small influence on levels of stress and well-being.
However, as both supervisory support and supervisory trust fell below
the threshold value of 2.5, an area of high sensitivity is evident, in which
steep spikes in work stress result from comparatively small changes in
the levels of support and trust. These disproportionalities and disconti-
nuities are characteristic of nonlinear relationships (Scarborough &
Somers, 2006).
Discussion
HR theory and practice has been focused primarily on outcomes of inter-
est to organizations such as productivity (Guest, 2017). As evidence
Figure 2. Nonlinear relationships between trust, support and work stress.
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 15
accumulates that promoting and managing employee well-being is
increasingly important to people and organizations, calls to direct more
attention to this issue are evident in the literature (Goh et al., 2015)asis
recognition of the need for new theories, analytical models and methods
(Spector & Pindekk, 2015).
Poor empirical results using linear methods coupled with emerging
theory raise possibility that underlying processes related to well-being
might not be linear (Ferris et al., 2006; Michaelides & Karanika-Murray,
2008). Our findings affirmed results from prior studies and extended
them by identifying where discontinuities typical of nonlinear relation-
ships were present.
Implications for theory development
A nonlinear model requires rethinking how the work context affects
well-being. The model is based on the general proposition that nonlinear
processes are embedded in constellations of antecedent variables that
combine to form complex nonlinear relationships with respect to well-
being (Michaelides & Karanika-Murray, 2008). Thus, work environments
should be defined more broadly than is the case in prior studies, and
with less emphasis on trying the distill the work context into a small set
of key predictor variables.
Our findings supported the first part of this proposition, but not the
second. Specifically, well-being was influenced most by a small number
of salient variables related to supervisor support, but those relationships
were characterized by pervasive patterns of nonlinearity. This point is
reinforced in that the ANN in this study explained slightly more variance
in test data in well-being (24% vs. 21%) than did the ANN in Karanika-
Murray and Cox (2010), but with 11 fewer predictor variables.
The pervasiveness of nonlinearity with just a few predictors is demon-
strated by data visualization from our ANN analysis. As indicated in
Figure 1, the work environment appears to be bifurcated based on the
levels of supervisor support and trust. Thresholds for both of these varia-
bles are approximately 2.5. Below that level (i.e. out-group), the work
environment appears to be so threatening that even small decreases in
perceived support and trust are associated with very steep spikes in work
stress. That is, even small changes in the level of either or both variables
are associated with disproportionate spikes in work stress. In contrast,
subordinates who experience moderate to high levels of trust and sup-
port (i.e. in-group) seem to operate in a work environment characterized
by psychological safety, until a second threshold is reached so that very
high levels of support and trust are again associated with spikes in stress.
16 M. J. SOMERS ET AL.
The same processes that diminish well-being when support is low
might also reduce well-being when support is very high. That is, even
though supervisor support is beneficial with respect to stress and well-
being (Thomas & Lankau, 2009), this relationship might change based
on changes in social identity when levels of supervisory support are very
high. Specifically, very high levels of support might change one’s social
identity and standing in the work group resulting in resentment from
coworkers and/or felt pressure to meet increased expectations of one’s
supervisor. Thus, boomerang effects might increase stress and diminish
well-being (cf., Harris & Kacmar, 2003).
These results direct theory development toward two areas. First, they
point out the importance of gaining a better understanding of the social
context in which work is conducted. Some interest has been expressed in
the relationship between work context, self-esteem and well-being
(Morrison et al., 2005), but it has not been extended to include self and
social identity. In this regard, the discontinuities in relationships between
support, trust and well-being observed in this study direct theory devel-
opment toward explaining why such profound differences were present.
With its focus on self and social identity and social context, faultline the-
ory (Bezrukova, Spell, Caldwell, & Burger, 2016) seems to an excellent
addition to theory on employee well-being.
The second area for theory development concerns establishing where
discontinuities are present rather than explaining the processes associated
with being on either side of threshold levels. This study suggests that
salience in the workplace is likely the most important criterion in identi-
fying antecedents where nonlinear relationships with well-being are likely
to be present. The complexity that drives nonlinear processes, therefore,
seems to stem from those aspects of the work environment have the
most influence on one’s day-to-day work life. As such, models of well-
being might be expanded to include variables that are central to one’s
work life and where discontinuities are likely to be present, but not
necessarily associated with immediate work activities such as person-
organization value congruence and perceived organizational justice.
Implications for practice
Incorporating nonlinearity into developing HR practices to raise the
importance of well-being in organizations and to promote well-being in
the workplace directs attention toward complexity and context. Given
that these are significant changes in relation to past practices, this study
argues against developing ‘quick fixes’as a response to recent, urgent
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 17
calls for organizations to address well-being at work (Goh et al., 2015;
Guest, 2017).
A framework is helpful in identifying the areas where nonlinear proc-
esses are likely to affect well-being. Guest (2017) identifies five HR prac-
tice areas that promote well-being at work: investing in employees,
providing engaging work, a positive social and physical environment,
voice, and organizational support. HR theory and practice with respect
to well-being has focused primarily on engaging work, but our results
point a positive social environment mediated by perceived supervisor
support as important influences of well-being. That is, consistent with
the nonlinear model of well-being in general and with our findings in
particular, well-being appears to be strongly influenced by how the work
environment affects social and self-identity, which then operate as an
interpretative framework with respect day-to-day work activities.
Our findings regarding supervisory support demonstrate this point.
The discontinuities observed when support was at low and high levels
resulted in a bifurcated work environment where the same event is likely
to be interpreted very differently based on the level of support one
receives. As such, it is not a matter of increasing supervisory support to
increase well-being as present theory and research suggest (cf.,
Viswesvaran et al., 1999), bur rather developing a better understanding
of how support influences how subordinates interpret work activities and
work relationships.
HR interventions such as managerial training programs that emphasize
the importance of direct support and trust in promoting and maintaining
subordinate well-being are a good first step in defining well-being as an
important work outcome. Indeed, it is doubtful that most managers/
supervisors are aware of the deleterious consequences of labeling and
treating subordinates as out-group.
Follow through, however, requires more extensive organizational
change programs that foster positive work environments and increased
levels of organizational support. In this regard, the discontinuities associ-
ated with the nonlinear relationships observed in this study are helpful
in implementing and assessing programs to promote employee well-
being. Specifically, when processes are nonlinear, increases in the per-
ceived quality of the work environment or levels of organizational sup-
port will have very little influence on well-being until threshold levels are
crossed. This pattern indicates that HR programs that do not achieve ini-
tial success are not necessarily ineffective so that persistence rather than
modification or discontinuation might well be the best path forward.
Our study also has implications for building more accurate analytical
models of workplace risk. There has been ongoing interest in this area
18 M. J. SOMERS ET AL.
(Karanika-Murray et al., 2009), and it is likely to increase as human cap-
ital analytics and data science methodologies are integrated into HR
practice (cf., Tonidandel et al., 2018). Increased model accuracy gener-
ated by ANNs has direct implications for assessing stress levels in organ-
izations, identifying trends and patterns, and in early interventions (cf.,
Karanika-Murray & Cox, 2010). Results from these analyses can be used
to develop more effective policies to promote and maintain well-being
and to lower organization’s health care costs.
Limitations and directions for future research
In interpreting our findings, it is important to keep in mind that data
were cross-sectional so that measures of well-being were taken only
once. Longitudinal studies, while less common, offer a better perspective
on employee well-being at work. In addition, our sample was vocation-
ally restricted and might not generalize to other occupational groups.
With respect to future research, consistent with calls for new models
and methods for research in this area (Spector & Pindek, 2015), this
study provides additional support for exploring nonlinear processes
related to employee well-being. The advantages of doing so go beyond
increments in model fit (e.g. explained variance) to include new insights
into underlying processes which open up new avenues for theory
development.
Several criteria for future studies incorporating nonlinearity into well-
being research are apparent. They include: (a) salience in the workplace;
(b) a theoretical justification for bifurcated processes and discontinuous
relationships; and (c) relevance to well-being. In this study, discontinu-
ities were tied to the quality of supervisor–subordinate relationships and
grounded in LMX theory. LMX theory has received some attention with
respect to employee stress and well-being (cf., Brunetto, Shacklock, Teo,
& Farr-Wharton, 2014), and our results suggest this supervisor-subordin-
ate relationships and well-being should be explored further. In particular,
supervisor support is an obvious area for future research on nonlinearity
and employee well-being future studies can explore relationships among
the three dimensions of supervisor support (direct support, trust and
fairness) and other dimensions of well-being such as burn-out and carry-
over work stress (cf., Warr, 1987) to assess the pervasiveness of nonli-
nearity across multiple indicators of well-being. More generally, variables
such as person-organization value congruence and organizational justice
seem to fit the criteria of salience, relationship to well-being, and discon-
tinuous processes. As such, they are excellent candidates for extending
research in the area of nonlinearity and well-being.
THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT 19
Conclusion
Linear models and linear thinking are prevalent in organizational
research (Scarborough & Somers, 2006; Starbuck & Mezias, 1996).
Theory and research on employee well-being is somewhat outside of this
norm because a nonlinear model has been proposed, and while tested
sparsely, it has been consistently supported. As pressure for work organi-
zations to better manage employee well-being mounts (cf., Goh et al.,
2015), HRM scholars and practitioners will be called upon to generate
new knowledge, new analytical methods, and new programs to promote
psychological well-being at work. From a theory development perspec-
tive, the nonlinear model has the potential to lead to deeper understand-
ing of the processes that underpin well-being at work. With respect to
practice, analytical models of well-being based on ANNs have the poten-
tial to generate more accurate predictions of at-risk employees to better
guide intervention strategies.
Disclosure statement
No potential conflict of interest was reported by the author(s).
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