Tackling c yclicity in causal models with cross -sectional data using a partial least square approach. Implication for the sequential model on internet appropriation. Lamberti Giuseppe a Lopez -Sintas Jordi b Pandolfo Giuseppec

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Tackling cyclicity in causal models with cross-sectional data using a partial least square

approach. Implication for the sequential model on internet appropriation.

Lamberti, Giuseppe,a* Lopez-Sintas, Jordi,b Pandolfo, Giuseppec

a,c Department of Economics and Statistics, University of Naples Federico II, Naples, Italy

b Department of Business, Universitat Autònoma de Barcelona, Barcelona, Spain

*Corresponding author: a Giuseppe Lamberti, Department of Economics and Statistics,

Room C1, University of Naples Federico II, Via Cintia, 21, 80126 Naples, Italy. Email:

giuseppe.lamberti@unina.it, ORCID: http://orcid.org/0000-0002-8666-796X

b Jordi Lopez Sintas, Department of Business, School of Economics and Business, B

Building, Room B1/118. Universitat Autònoma de Barcelona. Campus UAB 08193,

Bellaterra (Barcelona) Spain. Email: jordi.lopez@uab.cat ORCID: http://orcid.org/0000-

0001-5441-4039

c Giuseppe Pandolfo, Department of Economics and Statistics, Room C5, University of

Naples Federico II, Via Cintia, 21, 80126 Naples, Italy. Email: giuseppe.pandalfo@unina.it

ORCID: http://orcid.org/0000-0003-3668-0389

Abstract

Working with SEM and cross-sectional data, and depending on the studied phenomenon,

assuming an acyclic model may mean that we obtain only a partial view of the mechanisms

that explain causal relationships between a set of theoretical constructs, given that variables are

treated as antecedents and consequences. Our two-step approach allows researchers to identify

and measure cyclic effects when working with cross-sectional data and a PLS modelling

algorithm. Using the resources and appropriation theory and the sequential model of internet

appropriation, we demonstrate the importance of considering cyclic effects. Our results show

that opportunities for physical access followed by digital skills acquisition enhance internet

usage (acyclic effects), but also that internet usage intensity, in reverse, reinforces both digital

skills and physical access (cyclic effects), supporting Norris’ (2001) social stratification

hypothesis regarding future evolution of the digital divide.

Keywords: Cyclic effects, PLS-SEM, digital divide, internet appropriation, digital skills, RA

theory

1. Introduction

Structural equation modelling (SEM) is a widely used multivariate technique for analysing

complex systems of variables. The two most important prerequisites for SEM are (1) that a

cause-effect relationship is hypothesized between variables, and (2) that most variables are not

directly observable (i.e., they are latent) and so must be measured using a specific set of

indicators.

The literature documents different algorithms that can be used to estimate these models.

The classic approach is the well-known common factor-based (i.e., covariance-based)

technique (Ullman and Bentler 2012), which considers latent variables to be common factors

that explain co-variation between associated indicators (Sarstedt et al. 2016). This approach is

generally based on strict assumptions regarding distributions and sample size. Partial least

squares SEM (PLS-SEM) is an alternative approach (Hair et al. 2016; Wold 1985) that

maximizes variations in the observed variables following a soft procedure that requires no

assumptions regarding distributions and sample size (Hair et al. 2018).

In almost all cases, SEM application is conditioned by a critical hypothesis that Hyttinen

(2012) defines as the “acyclic” hypothesis, which assumes that variables are antecedents or

consequences, and that the causal relationship between variables can be estimated considering

a specific time interval. In other words, the acyclic hypothesis operates in a SEM when a

unidirectional sequential law regulates the relationship between variables. However, there are

several situations in which variables influence each other in a cyclic manner, which means that

we cannot assume acyclicity if we want to measure the complete structure of causal

relationships between variables.

One sociology scenario which merits consideration in terms of acyclic and cyclic effects

is how to explain social inequalities in internet adoption and use. The resources and

appropriation (RA) theory (van Deursen and van Dijk 2015; van Dijk 2005, 2020) endeavours

to explain how social inequalities are produced and reproduced in internet appropriation (the

digital divide). Accordingly, the digital divide results from four constructs, namely, attitudes

(i.e., reasons and motivations to use the internet), access (i.e., physical access to devices and

connections), skills (i.e., mastery of the necessary technology), and usage (i.e., what use is

made of the internet). The RA theory and model of internet appropriation operates on the

assumption that these constructs influence each other sequentially, yet intuitively, it must be

that internet usage also affect attitudes, access, and skills. Moreover, the model does not

consider a time dimension, but reflects a snapshot of a single moment in time.

In proposing a new SEM algorithm that takes into account the time dimension,

Asparouhov, Hamaker, and Muthén (2018) and Drton, Fox, and Wang (2019) resolved the

problem of cyclicity in SEM; however, their proposal is based on longitudinal data, i.e., the

same set of variables measured at different times, and longitudinal data are needed to apply

their method. Since this kind of data is not usually available in SEM studies, analyses are cross-

sectional.

In this article, we propose a two-step approach for measuring cyclic effects when working

with cross-sectional data using a PLS algorithm. It is based on, first, estimating the classical

causal model, and second, using the resulting dependent variables scores to estimate the cyclic

effects.

Our approach applies the same philosophy as used for hierarchical models with higher-

order constructs in PLS-SEM (Becker, Klein, and Wetzels 2012; Crocetta et al. 2021; Sarstedt

et al. 2019). Hierarchical models use multidimensional constructs that exist at a higher level of

abstraction but are quantified using lower-order sub-construct latent scores as proxies.

Summarizing, this article aims offering a methodological contribution in further

developing PLS-SEM to measure a cyclic feedback loop. It also offers a sociological

contribution in extending the sequential model of internet appropriation (van Deursen and van

Dijk 2015; van Dijk 2005, 2020) to account for possible cyclic effects operating on the digital

divide.

The rest of the paper is organized as follows. We first introduce the problem of cyclicity

using an example from the sociology field. We next briefly describe the digital divide concept,

the RA theory (van Dijk 2020), and the sequential model of internet appropriation (van Deursen

and van Dijk 2015; van Dijk 2005, 2020), and also discuss the importance of considering cyclic

effects in order to have a complete view of the social mechanisms that drive internet

appropriation (Section 2). We then describe our two-step approach to estimating cyclic effects

when using PLS-SEM (Section 3), and, using data from a Eurostat information and

communication technology (ICT) usage survey, we illustrate how to estimate the cyclic

effect in the model of internet appropriation (Section 4). Finally, we discuss the results and the

methodological and substantive contributions of our research (Sections 5 and 6).

2. Conceptual background

2.1.1. RA theory and the digital divide

The digital divide is not just a metaphor, but points to a social problem: unequal access to and

use of ICTs. Nor is the digital divide a theory, as underlined by van Dijk (2002), as it has

successfully directed attention towards social, political, and academic debates (Attewell 2001).

While the digital divide initially referred to unequal access to the ICTs, the evidence is that the

concept is more complex than mere access (Norris 2001). Unequal access to ICTs nowadays is

understood to be just a starting point for unequal endowment in devices, which also

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Tacklingcyclicityincausalmodelswithcross-sectionaldatausingapartialleastsquareapproach.Implicationforthesequentialmodeloninternetappropriation.Lamberti,Giuseppe,a*Lopez-Sintas,Jordi,bPandolfo,Giuseppeca,cDepartmentofEconomicsandStatistics,UniversityofNaplesFedericoII,Naples,ItalybDepartmentofBusines...

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Tackling c yclicity in causal models with cross -sectional data using a partial least square approach. Implication for the sequential model on internet appropriation. Lamberti Giuseppe a Lopez -Sintas Jordi b Pandolfo Giuseppec

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