Visual mapping sentence_a_methodological (1)

ACADEMIA Letters
Visual Mapping Sentence: A Methodological Approach to
Multifaceted Research Design and Analyses
Jacob Hornik
Introduction
Research is a process of intellectual discovery, which has the potential to transform knowl-
edge and understanding of the world around us. Most research in human behavior relies on
domain constructs and population sample. Whereas we know how to cover a population in
such a way that the surveyed sample represents the referenced population (p represent P). And
capable of estimating the degree of error in the sampling. We don’t always realize that there is
another kind of “population”, which is generally less systematically analyzed: the universe or
domains of contents. How can we know - as we can do it in the subjects’ population - that the
research will represent the domain/content population? What kind of tool could help us in this
aim? No methodologies are available to “sample” domain and variables in order to define the
scope of research content. The only tool to assist in content definition, domain sampling, and
systematic knowledge transforming is the Mapping Sentence MS within “Facet Metatheory”.
The objective of this paper is to introduce the MS methodology to the social research com-
munity. What prompted us to draft this paper is the much renewed interest in Facet Theory
(FT) and recent methodological advances in MS (e.g. Hackett & Fisher 2019; Heckett, 2021;
Hornik, 2009). Also, our empirical observation of the ignorance of the academic community
to the two related significant methodologies. This paper offers our reflections on the use of
an advanced method for analyzing visual text as data, utilized during our experience in theory
construction and applied research. The methodologies have been successfully applied by us
and some of our colleagues in different research topics. Some in the construction of theories.
Academia Letters, June 2021
Corresponding Author: Jacob Hornik, hornik@tauex.tau.ac.il
Citation: Hornik, J. (2021). Visual Mapping Sentence: A Methodological Approach to Multifaceted Research
Design and Analyses. Academia Letters, Article 1175. https://doi.org/10.20935/AL1175.
1
©2021 by the author — Open Access — Distributed under CC BY 4.0

For example, a novel theory of the “consumption of time (Hornik @ Feldman, 1981). Also,
in more applied research domains in business research like, surveys constructions (Hornik,
1982). Recently we also used this method in tandem with qualitative content analysis (Hornik
et al. 2019), as it provided additional detailed that the coding of categories alone could not
cover.
Facet Theory
Technically, FT draws on the principles of set theory to define the domain of study presented
by a finite collection of variables. A facet is ‘Any set playing the role of a component set of
Cartesian space, this set being called a facet of that space’ (Borg et al. 2019; Hornik et al.
2009). Put in everyday language, to be effective, the elements of each facet must be mutually
exclusive, and different facets must be conceptually distinct from each other. FT is a formal
approach to theory construction and systematic research. Most social sciences concepts are
multivariate, and therefore their study requires a systematic design for defining observations.
As a metatheory, the facet approach is unconstrained by particular contexts, methods or vari-
ables, offering a lens and disciplined formal processes for the scholarly community. The facet
definitional design aids researchers’ identification of systematic relationships within the em-
pirical data sets. It leads to cumulative results and facilitates the discovery of lawfulness in
complex systems and structures in qualitative data. The theory utilizes the three major con-
stituents of scientific activity: (1) a definitional framework for the universe of observations;
(2) an empirical structure for the collection of observations; and (3) a hypothesis about the
correspondence between the definitional system and the empirical structure. The hypotheti-
cal relations among the variables are specified in the definitional domain, and these relations
must correspond to the observed empirical relations among the variables. The elements of
the facets define profiles in that space, and these profiles correspond to the variables usually
studied. FT can handle input variables of all sorts, including ordinal and nominal variables.
Visual Research Construct
The MS is at the heart of FT to exploratory and confirmatory research. The MS is a visual
spatial representation that contains a variety of facets using common words. Each facet is one
way of classifying the research variables. A properly defined set of m facets provides an m-way
simultaneous classification of variables, namely, a MS. Each facet in the mapping sentence is
specified as having a certain formal role. According to the general hypothesis of FT the roles
of the facets in a mapping sentence provide a rationale for a hypothesis of a correspondence
2

between the definitions of the mapping sentence and an aspect of the observed distribution of
the data. The MS was developed in order that quantitative data may be gathered that reflect
the combined interactions and effects of multiple variables (facets) in structuring experience
within a specified content domain.
The name of the method includes “mapping” and “visual” to demarcate the context of
visual text similar to van Dijck’s term “connective media” (2013). The inclusion of “map-
ping” highlights the processes of this method, which aim to provide both broad and specific
contextual details during the generating research hypotheses and data collection and analysis.
What also guided us in the visual construction is Rose (2011) visual methodologies. The MS
links together the pertinent components of a research domain in such a way that the variables
(facets) and sub-components of the variables (elements) are combined using every day prose
so as to suggest the inter-relationship between facets and elements in the context of a spe-
cific research undertaking. The MS design not only maps all relevant variable but, equally
important it provides information of variables that are left out, or a design for future research.
The concept of a mapping sentence generalizes R.A. Fisher’s design of experiments to
the design of observations, with the added feature that informal verbal connectives are used
to enable the empirical data collection. All the crucial components of a research design are
detailed by the mapping sentence: the subjects or respondents through the population facet
(P); the variable represented by those structuples generated by the Cartesian product (S) of
the substantive facets; and the set of measured responses designated by the range facet (R).
Presented formally:
a : PxSR(PopulationxContent/Stimulifacets)(Response)
The entire domain could be mathematically reconstructed as a Cartesian product of the
form
S = ABC…F…
so that r = α(p,s). For each p�P and s�S corresponds an r�R. By drawing one element from
each of the facets in a domain, one creates a profile commonly referred to as a structuple. The
term structuples refers to their role in structuring the domain of investigation. Formally, each
facet is put into a form of a vertical multi‐tuple
where N (F) = number of elements (f ’s) in F (facet). Assuming that a particular content
domain has been partitioned into n different facets, A, B, C,…, then, Hornik et al.(2009) would
assert that the entire domain could be mathematically reconstructed as a Cartesian product of
the form S = ABC…F…where
3

Consequently, s�S is an n‐tuple s = (ai ,bj ,ck …,fl ,…) where ai �A, bj �B…fl �F.
The following is simple illustrated in the mapping sentence shown in Figure 1
The research domain: Research on evaluation of salespeople
The corresponding facets are: Facet A: Who is the RATER, Facet B: What TRITS are
evaluated,
Facet C: The overall or specific ASPECTS of evaluation.
R = The measuring scale.
An illustration of a possible hypothesis: a1b1c1 > a1b1c2
Such a form of mapping: (1) represents a succinct statement of the research design that
4

Figure 1: A Mapping Sentence for Salespeople Evaluations.
is readily communicable; (2) acts as a template from which questionnaire and other observa-
tional items may be constructed; and (3) facilitates the extension and reduction of the content
of the domain by adding more or collapsing facets. Thus, a mapping sentence is not a prod-
uct, but a process – a process of revising one’s thoughts over the course of research to be
progressively more differentiated and better fitted to data. A general mapping sentence is
never complete, but is always in a temporary state of equilibrium ready to accommodate the
most recent empirical findings.
The visual display of MS guides in the construction of concrete test items. The data can
be coded on the range like, “very wrong … very right” or ‘strongly agree’, ‘agree’, ‘disagree’,
‘strongly disagree’, and to numerically valued continuous variables. Once items are expli-
cated and organized in a mapping sentence, it helps in systematically picking certain subsets
of item types from this universe of content and in formulating concrete hypotheses. The map-
ping sentence constitutes a guide for researchers to design consistent flexible research tools
to address complicated human research. Most important, MS and FT emphasizes crucial as-
pects that have been neglected in other research methods. For example, several researchers
show that in factor analysis, which is commonly used, there is a large investment in statistical
analyses of the data and less in an explication of the involved concepts, their definition, and
5

the rational for the particular structure of a content area (Borg et al 2020; Leue and Beauducel
2021). Compared to our two methodologies factor analysis fares poorly in the interpretability
of the findings because the structure of the content area is determined by loading rather than
by a prior conceptual analysis. Theoretical statements, therefore, can only be post hoc. Fur-
thermore, factor-analytic methods assume that variables are linearly ordered and are measured
at least at the interval level. Yet this cannot be assumed to exist in human behavior. MS and
FT requires no such assumptions.
Measuring Tools
Special computer program developed for MS and FT: e.g. Multiple Scaling by Partial-Order
Scalogram Analysis (POSA), Smallest Space Analysis (SSA) and Multidimensional Scaling
(MS), for the discovery of lawfulness and scientific measurement in complex systems. Thus,
the hypotheses stated in the mapping sentence can then be tested by relating the conceptual
structure of observations on the universe to features of the empirical structure of observations
on that universe, using SSA (also referred to as Similarity Structure Analysis) (e.g. Borg and
Meir, 2017; Borg et al. 2020; Hetsroni, 2000; Hornik 1996; Solomon and Huse, 2019).
Summary
The MS constitutes a visual guide for researchers to design flexible research tools to address
multifaceted research topics. The conceptual framework of the MS, coupled with nonmetric
data-analysis techniques, can solve major empirical problems faced continuously during the-
oretical and applied research. The following appendix are two illustrations of MS – Figures
2 and 3.
Appendix
6

Figure 2: Mapping sentence for the relationships between ads and appeal for cross-cultural
analyses
7

Figure 3: Mapping sentence for attitudes toward digital marketing
8

References:
Borg, I., Hertel, G., Krumm, S., & Bilsky, W. (2019). Work values and facet theory: From
intercorrelations to individuals. International Studies of Management & Organization, 49(3),
283-302.
Borg. I. Meir, P @ Cetron, J (2020). Facet Theory and Multidimensional scaling, A
Revised Facet Theory. 211-237.
Borg, I. & Mair, P. (2017). The choice of initial configurations in multidimensional scal-
ing: Local minima, fit, and interpretability. Austrian Journal of Statistics, 46, 19–32.
Hackett, P. M. (2017). A Mapping Sentence for Understanding the Genre of Abstract Art
Using Philosophical/Qualitative Facet Theory. Frontiers in psychology, 8, 1731.
Hackett, P.M., & Y Fisher. “Advances in Facet Theory Research: Developments in Theory
and Application and Competing Approaches.” Frontiers in psychology 10 (2019): 1642.
Hackett, P. M. (2021). The Declarative Mapping Sentence and Qualitative Facet Theory
Research. In Facet Theory and the Mapping Sentence 121
Hetsroni, A. 2000. The relationship between values and appeals in Israeli advertising: A
smallest space analysis. Journal of Advertising 29, no. 3: 55–68.
Hetsroni, A. 2001. A smallest space analysis of values and appeals in advertising and the
distorted mirror phenomenon. Proceedings of the Facet Theory Conference 7, 127–39.
Hornik, J & Feldman L, (1981). The use of time: An integrated conceptual model. Jour-
nal of consumer research, 7(4), 407-419.
Hornik, J. 1982. Impact of pre-call request from and gender interaction on response to
mail
survey. Journal of Marketing Research 19 (February): 144–53.
Hornik, J. (1996). A circumplex model for the behavioral constructs towards television
advertising. Journal of the Academy of Marketing Science, 4(1), 484-503.
Hornik, J., Cohen, E. H., & Amar, R. (2009). Theory construction and data analysis in
marketing communication: A facet analytical approach. Journal of Marketing Communica-
tions, 15(1), 35-54.
Hornik, J., Shaanan Satchi, R., & Rachamim, M. (2019). The joy of pain: A gloating
account of negative electronic word-of-mouth communication following an organizational
setback. Internet Research, 29(1), .82-103
Leue, A, & A. Beauducel (2021) “A facet theory approach for the psychometric measure-
ment of conflict monitoring.” Personality and Individual Differences 171, 110479.
Rose, G. (2011). Visual Methodologies, an introduction to researching with visual mate-
rials. 3. ed. London, Sage Publications.
9

Solomon, E., & Huse, M. (2019). Corporate governance and paradoxical tensions: Lead-
ership dynamics through facet theory. International Studies of Management & Organization,
49(3), 320-339.
Van Dijck, J. (2013). The Culture of Connectivity: A Critical History of Social Media.
Oxford University Press.
10

Visual mapping sentence_a_methodological (1)

Recommended

Recommended

More Related Content

What's hot

What's hot (15)

Similar to Visual mapping sentence_a_methodological (1)

Similar to Visual mapping sentence_a_methodological (1) (20)

Recently uploaded

Recently uploaded (20)

Visual mapping sentence_a_methodological (1)