Theoretical framework
As stated earlier, there are many ways to deal with multi-surrogate
dependent variables (DV) when analyzing cause-and-effect relationships
in research studies that bothers more on behavioral phenomena than
real-life business-related problems. This is premised on the fact that
business and applied economic problems demand the use of past
transaction data not based on assumptions or mere conjecture in setting
relational models that can be used to direct the affairs of an
organization. To deal with the issues of behavioral phenomenon with more
than one DV surrogate, it was suggested in a community of online
discussants that one could run two separate regression equations in a
case where there are two DV surrogates; one for each DV, but the general
concern is that such treatment might likely not capture the
interspersing relationship between all the DV surrogates. Also, fitting
all surrogates’ regressions separately will indeed be equivalent to
formulating multivariate relationships with a matrix of dependent
variables (Transaction Processing Performance Council, 2011). However,
if one is interested in describing a two-block structure, this could be
done using partial least square regression (PLS). Partial least square
is a regression framework which relies on the idea of building
successive (orthogonal) linear combinations of the variables belonging
to each block such that their covariance is maximal. It is a method for
relating two data matrices, X and Y, by a linear multivariate model but
goes beyond traditional regression in that it models also the structure
of X and Y and also derive its usefulness from its ability to analyse
data with many, noisy, collinear, and even incomplete variables in both
X and Y (Wold, Sjostrom, & Erikkson, 2001).
Many social scientists on the other hand, prefer the use of the GLM
multivariate and repeated measures ANOVA to fit the multiple equations
resulting from the use of more than one dependent variable into a single
equation for the purpose of getting a unified analytical result;
however, a number of others prefer the use of more exotic methods such
as binary response model (BRM), multiple classification analysis (MCA),
and canonical correlation among others, to obtain the same effect.
Particularly, the GLM Multivariate procedure allows the analyst to model
the values of multiple dependent scale variables, based on their
relationships to categorical and scale predictors. In a case of ordinary
GLM, there is always a single dependent variable, with a prediction mean
error of zero (0) and a variance that can be computed after the GLM is
fitted. But when there are multiple dependent variables, each of the
dependent variables will have a prediction error (Helwig, 2017; NCSS,
1989; Steiger, n.d.).
In chemometrics analysis, the use of PLS is favoured because of the
multiplicity of the inputs and outputs of most chemical processes.
Chemometrics is the use of mathematical and statistical methods to
improve the understanding of chemical information and to correlate
quality parameters or physical properties to analytical instrument data
(Bu, 2007). Chemometrics analysis is a fascinating one because it is
interdisciplinary and employs the extensive use of such tools as
principal components analysis (PCA), multivariate statistics, three-pass
regression, LPLS regression, latent structure regression, partial least
square structural equation modeling (PLS-SEM), covariance based
structural equation modeling (CB-SEM), and shrinkage structure analysis
(Abdi, 2010; Afthanorhan, 2013; Helland, 1990; Kelly & Pruitt, 2015;
Lingjaerde & Christophersen, 2000; Saeboa, Almoya, Flatbergb,
Aastveita, & Martens, 2008). Chemometrics also employ the use of total
least square (TLS) and Deming regression in analyzing multiple dependent
variables because of the reasons earlier adduced. TLS is a method of
fitting that is appropriate when there are errors in both the
observation vector and in the data matrix (Golub & Van Loan, 1980).
Deming regression on the other hand is a special case of TLS which
allows for any number of predictors and complicated error structure to
be analyzed (Jensen, 2007).
Though, most of the analytical tools enunciated above employ techniques
that will eventually end in bringing out the mean values that will be
used to fit the final model of the intended research relationship, such
may not readily or necessarily suit the secondary nature of the data
usually extracted for financial performance analysis. Besides, the
average accountant or financial analyst are not expected to acquire the
deep knowledge of econometric and statistical analysis necessary to
undertake such intricate computations in the absence of a computer
software. These are, however, the least of the problems.
In accounting and finance, ratios are used to convey performance
information to stakeholders in a business atmosphere. These ratios are
often relational in nature, meaning that they try to tell us what
fraction, level or percentage of efficiency was achieved in the use of
certain resources; in other cases, the ratios might be engaged to do
comparative/differential analysis between one period’s transactions and
another’s or even to compare the performance of different projects or
activities. These are the kinds of information that investors and
management need to guide them in their daily decisions and divisional
performance evaluation exercises - not the abstraction thinking involved
in advanced econometric measurements which have no legal substance in
business and commercial transactions. In addition, the measurements used
in arriving at financial and accounting ratios are ways different from
the means, errors, variations and covariations produced and fitted into
most econometric and statistical models of measurement by other social
science researchers. Though, means and averages can be employed in
financial and accounting performance measurements, the way and mode of
their employment will vary significantly with those used for pure
econometrics studies.