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\begin{document}

\title{Analyzing Dependent Variables with Multiple Surrogates in Accounting
Research}



\author[1]{Enyi Enyi}%
\affil[1]{Babcock University}%


\vspace{-1em}



  
  \date{May 28, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
The paper contains details a research carried out to show that the use
of geometric mean to unify multivariate dependent variables in financial
performance studies gives better and more practical results than the
multiple abstraction analysis provided using advanced econometric tools
such as TLS, PLS, MCA, Canonical correlations etc.

The study used the logistic regression analysis to compare the a priori
expectations of 30 Ph.D research theses with their actual outcomes using
econometric tools and the actual outcome using geometric means. The
study used Ph.D theses in accounting and finance sourced from the
libraries of four universities in Nigeria.

The study was a desktop research using publicly available literary
resources and as such requires no ethical clearance.%
\end{abstract}%



\sloppy


Enyi Patrick Enyi

Babcock University

e.p.enyi@gmail.com

Department of Accounting, School of Management Sciences

Accounting and finance-based researchers often face the problem of using
multiple surrogates to capture the true essence of a dependent variable
in order to study its predictive relationship with explanatory
variables. The major pitfall with this, is the inability to directly
connect the study results with the major objective of the research
forming the topic. This study explores the various methods that can be
adopted to unify the engaging properties of the multiple parameters used
in identifying a dependent variable. Using logistic regression, the
study converted the \emph{a priori} expectations of 30 Ph.D research
theses in finance and accounting with four dependent surrogates into a
probabilistic log values and compared them with the individual surrogate
performance on the one hand and the surrogates geometric mean on the
other hand. While the geometric mean showed no significant difference
between itself and the probabilistic expectation (\selectlanguage{greek}\emph{β} \selectlanguage{english}=
.278,\emph{t\textsubscript{(30)}} = .695, \emph{R\textsuperscript{2}} =
.077,\emph{p} \textgreater{} .10), the individual surrogates results
revealed both combined and individual significant differences with the
theses\emph{a priori} expectations (\emph{Adj. R\textsuperscript{2}} =
.0291,\emph{F} \textsubscript{(4, 25)} = 22.598, \emph{p} \textless{}
.05). This paper recommends unifying multivariate dependent variables
with geometric means for successful financial performance relational
studies.

\emph{Keywords} : performance, dependent variable, surrogate, proxy,
logistic regression

Researchers and scholars in the social and management sciences are often
faced with the problem of identifying and operationalizing the main
ingredients forming the dependent or outcome variable in performance
assessment research. This is particularly a big issue when such a study
is extended in scope or necessitated by the requirements to fulfil the
conditions for the award of a degree. For those studying behavioral
traits and similar psychological phenomena that has no accounting or
financial data foundation, this will not present a problem as there are
several methods already developed to tackle the issue. Some of these
methods include the use of general linear model (GLM) multivariate and
repeated measures procedures using computer statistical software, while
others may include the use of canonical correlations and specially
constructed regression equations (Helwig, 2017; NCSS, 1989; Steiger,
n.d.). The use of means as a converging point was also advocated by
other researchers especially when multiple dependent variables represent
different measures of the same construct. When such differing variables
are measured on the same scale, researchers have the option of combining
them into a single measure of that construct. The use of binary response
model (BRM) was also in the picture, but as posited by Cameron (2015),
the description of the use of means looks more practical and less
ambiguous to comprehend (Cameron, 2015; Gruszczy, 2009; Price,
Jhangiani, \& Chiang, 2015). However, the imprecise and unsure nature of
the various methods in current use makes most research findings and
conclusions meaningless and unrelated to the major objective of the
research. This is very worrisome especially to graduate level research
students and their advisors and has proven to be of particular negative
implications in the fields of accounting and finance in management
sciences where precision in conclusions is of utmost importance in
guiding investors and decision makers correctly.

\textbf{Research objective}

The objective of this paper is to empirically investigate and determine
whether the present method of conducting, assessing and concluding
corporate performance researches using multiple surrogate findings on a
dependent variable is optimally satisfactory and capable of guiding
correct decision making on the basis of such study.

\textbf{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.

\emph{The use of Means}

When faced with two or more groups of data relating to surrogates with
values analogous to the measure of a dependent variable, the overall
mean can be computed as the average of the groups' means which then
assumes the responsibility of representing the dependent variable as a
single group which can now be regressed in an ordinary GLM against the
underlying independent variables (Carey, n.d.; Conference \& Pisa, 2007;
Fritz \& Berger, 2015; Fritz, Berger, Fritz, \& Berger, 2015). The use
of the mean as a unifying factor becomes inevitable in financial
performance studies involving multiple surrogates of a dependent
variable. However, the question remains - which type of mean do one
employ: the arithmetic mean or the geometric mean? To answer this
question, it is necessary to assess the effect of each type of mean.
The\emph{Arithmetic Mean (AM)} is a simple average derived by adding
all-inclusive elements which have numerical values together and diving
by the number of elements added. Despite its extensive use to report the
central tendency of a data distribution, it suffers from statistical
robustness because it is greatly influenced by outliers or extreme
values included in the distribution. The \emph{Geometric Mean (GM)} on
the other hand also measures the central tendency but it does so by
multiplying the numerical elements involved in the set and finding
the\emph{n} th root of their product. A geometric mean is often used to
find a single ``figure of merit'' for items with multiple properties
when comparing different items. It is also used to analyse a set of
numbers whose values are meant to be multiplied together or are
exponential in nature such as investment interest rate or human
population growth rate. It, however, applies only to positive numbers.
Nevertheless, the geometric mean (GM) is more respectful of the
intrinsic differences across all the dimensions of the data distribution
than the arithmetic mean (Transaction Processing Performance Council,
2011; UNDP, 2011). For the reasons as earlier adduced, the use of
geometric mean, is, therefore, favoured and will be used to unify the
multiple surrogates of the dependent variables studied in this work.

\emph{Accounting and financial performance indicators}

Accounting and general financial performance indicators are usually
expressed as ratios derived from information contained on corporate
financial statements. While ratios such as return on assets (ROA),
return on equity (ROE), return on capital employed (ROCE), debt equity
ratio (DER), net profit margin (NOM), gross profit margin (GPM), and
inventory turnover rate (ITR) are fractional ratios that can be
expressed as mere fractions or in percentages, others such as earning
per share (EPS), receivable turnover ratio (RTR) or average collection
period (ACP) and others may be expressed in monetary or time denominated
terms as kobo or cents per share or days. The objective of whichever
form the ratio takes is to convey a useful information to the recipient
of such information.

The knotty point in the use of accounting ratios, however, is the fact
that accounting performance data may include different elements in its
composition, such as fractional values, days and monetary denominations
which must be fused together to obtain the geometric mean. For instance,
supposing a researcher wants to study the relationship between a
company's performance as proxied with ROCE, ROA, EPS, and ACP surrogates
over a 20-year period, and the personnel (PER), administrative (ADM),
financial (FIN), and marketing (MKT) costs; the researcher has the
option of studying the relationship between each surrogate of the
performance variable and the four independent variables of PER, ADM,
FIN, and MKT or combining the four surrogates into one using a geometric
mean. If he decides to study them individually, he will end up with four
models and four conclusions, which might conflict with one another
thereby rendering the process an exercise in futility. However, if he
decides to unify them with a mean, he will have to deal with the problem
of bringing all the variables under a common denominator since ROCE and
ROA will be in fractions while EPS will be either book value or market
value denominated, and ACP will be time denominated as ACP is always
expressed in days.

To resolve the issue, the EPS and the ACP must be converted to fractions
in line with ROCE and ROA. To convert the EPS into a fraction, it is
necessary to divide the EPS with the market value of the share of the
firm, if it is market regulated or with the par/book value of the share
if the firm is not listed or quoted. To convert the ACP to fraction, two
steps must be followed -- the first step is to divide the ACP with 365,
the number of days in a year whilst the second step is to deduct the
resulting fraction away from one. This two-prong approach to convert ACP
to fraction is necessary because efficiency in credit administration
relies much on the shortness of the debtors' collection period. The
shorter the period, the more efficient the firm's credit administration
is adjudged. When a relatively short ACP is converted to a fraction with
the first step, it will show a small value which will be suboptimal when
used in a regression analysis, but when this value is deducted from one,
it will reveal the true fraction or percentage of efficiency achieved in
credit administration by the firm. For instance, assuming companies A
and B achieved 32- and 45-days ACP respectively, at first step
fractional conversion, company A will have ACP fraction of 0.0877
(8.77\%) while company B will return ACP fraction of 0.1233 (12.33\%)
which is indeed confusing and totally incorrect because from the face
value of it, company A performed better than B in credit control, and
not the other way round. In order to correct this anomaly, it will be
necessary to take away the earlier computed fractions from one, such
that the new ACP fractions become 0.9123 (91.23\%) for company A and
0.8767 (87.67\%) for company B which echoes the reality of credit
control events in the two firms. Succinctly, the formula for the EPS and
ACP fractional conversions are given in equations (1) and (2) below:

EPS (in fraction) = \(\frac{\text{EPS}}{\text{Share\ Price}}\) (1)

ACP (in fraction) = \(1-\ \frac{\text{ACP}}{365}\) (2)

To complete our sample analysis, it is necessary to bring all the four
surrogates of the financial performance dependent variable into one
using the geometric mean formula as follows:

FP = \(\sqrt[4]{\text{ROCE}}\text{\ x\ ROA\ x\ EPS\ x\ ACP}\) (3)

The number 4 in the formula (equation 3) was used there because the
number of elements requiring a geometric mean is four. That is to say
that the geometric mean of the product of the four elements is the
fourth (4\textsuperscript{th}) root. If the number is five, then the
geometric mean will be the fifth (5\textsuperscript{th}) root, and so
on.

Where,

FP = Financial Performance ROCE, ROA, EPS, and ACP as previously
defined.

With the variables now defined and brought under a uniform measurement
platform, we can now fit the ordinary GLM as follows:

FP = \selectlanguage{greek}β\selectlanguage{english}\textsubscript{0} + \selectlanguage{greek}β\selectlanguage{english}\textsubscript{1}PER + \selectlanguage{greek}β\selectlanguage{english}\textsubscript{2}ADM
+ \selectlanguage{greek}β\selectlanguage{english}\textsubscript{3}FIN + \selectlanguage{greek}β\selectlanguage{english}\textsubscript{4}MKT + \selectlanguage{greek}ε \selectlanguage{english}(4)

With this overall unified dependent variable GLM regression model, it
will be easy to predict the impact of each of the four cost elements on
the overall fortunes or profitability of the company for the 20-year
period under review.

\textbf{Methodology}

The study employed comparative and empirical literature review to
compare the methods adopted by 30 Ph.D researchers selected from
concluded studies in finance and accounting from four universities in
Nigeria. Sample selection targeted only studies on financial performance
with four dependent-variable surrogates. Logistic regression was used to
convert the \emph{a priori} expectations of the 30 Ph.D research theses
into a probabilistic log values' data. The probability values ranged
from 0.24 to 0.99 in accordance with the expressed expectation to the
actual expectation. The log values were then compared with the
individual surrogate performance on the one hand and the surrogates'
geometric means on the other hand using ANOVA and logistic regression
analysis.

\textbf{Data Analysis, Results and Discussions}

Table 1 below shows how the final results of the theses agreed with
their pre-study \emph{a priori} expectations.

Table 1: Agreement with Theses \emph{A Priori} Expectations\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Level Achieved & Number of Theses & Percentage\tabularnewline
\midrule
\endhead
100\% & 5 & 16.67\tabularnewline
75\% & 8 & 26.67\tabularnewline
50\% & 11 & 36.66\tabularnewline
25\% & 6 & 20.00\tabularnewline
\bottomrule
\end{longtable}

\emph{Source: Multiproxy by Enyi, 2018}

Table 1 shows that only five of the thirty theses analysed representing
16.67\% achieved 100\% of their pre-study expected conclusions, while 11
representing 36.66\% achieved only 50\% of their \emph{a
priori}expectations. Eight or 27\% were able to achieve 75\%; 6 or 20\%
achieved only 25\% of their pre-study conclusions while none had a zero
agreement. Since the researchers of the theses under study carried out
their analyses with the individual surrogates of the multivariate
dependent variables, the level achieved was based on the number of the
surrogates that agreed with their pre-study \emph{a priori} .

Table 2: Summary Statistics\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Item & Logit & Ln(ROA) & Ln(ROE) & Ln(ROCE) & Ln(EPS) &
Ln(Unified)\tabularnewline
\midrule
\endhead
Mean & 0.9 & 2.12 & 1.63 & 1.98 & 2.89 & 2.15\tabularnewline
Median & 0.08 & 1.96 & 1.36 & 1.96 & 2.87 & 2.04\tabularnewline
Max & 4.6 & 3.69 & 2.73 & 3.36 & 3.3 & 3.27\tabularnewline
Min & -1.15 & -0.13 & -1.97 & -0.21 & 2.17 & 0.14\tabularnewline
Std Dev & 1.771 & 0.909 & 1.091 & 0.863 & 0.59 & 0.774\tabularnewline
Obs & 30 & 30 & 30 & 30 & 30 & 30\tabularnewline
\bottomrule
\end{longtable}

\emph{Source: IBM-SPSS 25 Analysis by Enyi, 2018}

The resulting models from the data analysis using GLM regression are
expressed as follows:

Logit1 = -0.678 + 0.734Ln(Unified) + \selectlanguage{greek}ε \selectlanguage{english}(5)

Logit2 = -2.99 -- 2.538Ln(ROA) + 1.097Ln(ROE) + 1.709Ln(ROCE) +
1.427Ln(EPS) + \selectlanguage{greek}ε \selectlanguage{english}(6)

Table 3: Comparative Analysis of Logit1 and Logit2 using IBM-SPSS 25
Output\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Performance Parameter Proxies & Influence & Beta Coefficient & t -
Statistics & t - Statistics & F -- Statistics & F --
Statistics\tabularnewline
\midrule
\endhead
& & & Value & Sig & Value & Sig\tabularnewline
Unified Perf. Variable & 0.734 & 0.278 & 0.695 & \textgreater{} .10 &
2.426 & \textgreater{} .05\tabularnewline
ROA & -2.538 & -1.183 & -1.342 & \textless{} .10* & 22.598 & \textless{}
.05**\tabularnewline
ROE & 1.097 & 0.653 & -0.790 & \textgreater{} .10 & 22.598 & \textless{}
.05**\tabularnewline
ROCE & 1.709 & 0.760 & -1.183 & \textless{} .10* & 22.598 & \textless{}
.05**\tabularnewline
EPS & 1.427 & 0.215 & -2.198 & \textless{} .10* & 22.598 & \textless{}
.05**\tabularnewline
\bottomrule
\end{longtable}

* significant at 10\% confidence level ** significant at 5\% confidence
level

\emph{Source: IBM-SPSS Analysis by Enyi, 2018}

Table 4: ANOVA Test for Unified Performance Variable (Logit1)\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Model & Sum of Sqrs & Df & Mean Sqrd & F & Sig\tabularnewline
\midrule
\endhead
Regression & 7.196 & 1 & 7.196 & 2.342 & .137\tabularnewline
Residual & 86.039 & 28 & 3.073 & &\tabularnewline
Total & 93.236 & 29 & & &\tabularnewline
\bottomrule
\end{longtable}

R\textsuperscript{2} = 0.0772

Adj. R\textsuperscript{2} = 0.0442

Durbin-Watson Statistics = 2.383

\emph{Source: IBM-SPSS Analysis by Enyi, 2018}

Table 5: ANOVA Test for Individual Surrogate Dependent Variables
(Logit2)\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Model & Sum of Sqrs & Df & Mean Sqrd & F & Sig\tabularnewline
\midrule
\endhead
Regression & 15.202 & 4 & 3.800 & 1.216 & .328\tabularnewline
Residual & 78.034 & 25 & 3.121 & &\tabularnewline
Total & 93.236 & 29 & & &\tabularnewline
\bottomrule
\end{longtable}

R\textsuperscript{2} = 0.163

Adj. R\textsuperscript{2} = 0.0291

Durbin-Watson Statistics = 2.432

\emph{Source: IBM-SPSS Analysis by Enyi, 2018}

Discussions

The results of the foregoing analyses have been quite revealing. It is
not surprising that the results of the empirical analysis agree largely
with the findings from the literature review process. While the use of
geometric mean to unify all performance parameter proxies showed no
significant difference between itself and the \emph{a
priori}expectations or the theses researchers' pre-study perceptive
conclusions indicated in the analysed theses, using 10\% level of
significance (\selectlanguage{greek}\emph{β} \selectlanguage{english}\textsubscript{(30)} = .278, \emph{t}
\textsubscript{(30)} = .695, \emph{R\textsuperscript{2}} = .0772,
\emph{p} \textgreater{} .10), all the individual surrogate variables
excepting ROE returned significant figures for t at the 10\% significant
level. Buttressing the t statistics findings with F statistics, the
geometric mean unified variable result was also not significant both at
the 5\% and 10\% levels of significance (\emph{Adj.
R\textsuperscript{2}} = .0442, \emph{F} \textsubscript{(1, 28)} = 2.426,
\emph{p} \textgreater{} .05), as against the test for the individual
performance parameter surrogates which returned overall significant
difference in relationship with the analysed theses pre-study
expectations (\emph{Adj. R\textsuperscript{2}} = .0291,\emph{F}
\textsubscript{(4, 25)} = 22.598, \emph{p} \textless{} .05).

In other words, what the results of the various analysis is telling us
is that the theses researchers' pre-conceived conclusions were no
different from the results obtained using the geometric mean unified
dependent variables. Looking at the figures on table 3, it will be
interesting to note that while the geometric mean unified performance
variable maintained a positive relationship with the theses \emph{a
priori} expectations, one out of the four surrogate variables (ROA)
showed strong negative relationship indicating that its individual
influence inhibits the positive pull of the other variables, thereby
distorting logic of joint conclusion. This trait was also exhibited on
table 2 (summary statistics) which showed all the figures of the unified
variable as positive but three of the individual surrogate variables
returned negative minimum figures.

Summary, Conclusion and Recommendations

There is no doubt that this paper has been able to adequately address
the objectives it set out to achieve. It started by introducing the
subject of study and identifying the problem it set out to tackle. While
reviewing extant literature frameworks on the subject of multivariate
dependent variables, the paper introduced the various methods and
formula adaptations that can be employed to unify financial performance
data for the purpose of relational research analysis. From the
literature review and the earlier discussions of the results of research
data analysis, it is evident that financial performance research
utilizing multivariate dependent variable has very little space to
maneuver with the existing econometric methods of multivariate data
analysis. Financial and accounting information are made up of already
processed and validated economic data and values which require careful
and exact practical treatment which the abstract assumptions of most
econometric measurements and analysis may not adequately handle,
resulting in the need to adopt a more practical and less abstraction
assumptions and methods to manipulate them. The use of geometric means
to unify multivariate dependent variables into a single variable is
considered the best way to effectively execute a financial performance
relational research because, according to Transaction Processing
Performance Council (2011), the geometric mean presents a single figure
of merit which respects the intrinsic differences across all dimensions
of the data distribution (UNDP, 2011).

In view of the aforementioned findings, this paper recommends that more
attention be paid to the peculiar nature of financial performance
research and the important role that such researches ought to play in
the economy of every nation when deciding on the method and tool of
analysis to adopt. It will not be out of place if we have a statistical
analysis type that takes the peculiar interest of accounting and finance
into consideration. If chemistry can develop a special branch of
statistics called \emph{chemometrics} , it is possible to have
either\emph{finometrics} or \emph{accometrics} .

\textbf{References}

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latent structure regression (PLS-Regression). \emph{Wiley
Interdisciplinary Reviews: Computational Statistics} , \emph{2} ,
97--106. https://doi.org/10.1002/wics.51

Afthanorhan, W. M. A. B. W. (2013). A comparison of Partial Least Square
Structural Equation Modeling (PLS-SEM) and Covariance Based Structural
Equation Modeling (CB-SEM) for confirmatory Factor
Analysis.\emph{International Journal of Engineering Science and
Innovative Technology (IJESIT)} , \emph{2} (5).

Bu, D. (2007). Bridging the Gap between the State and Measurement of a
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