INTRODUCTION
It is becoming increasingly difficult to ignore the existence of soft drink
in today’s markets. Since the inception of soft drink in the 1830's, its
consumption has steadily increased with technological advances in production
and increased product availability. Recent statistics from the United States
Department of Agriculture reported a per capita increase in regular soft drink
consumption from 28 gallons per person in 1986 to 41 gallons per person in 1997
(Yule, 2002). In Malaysia, with the same trend it was
reported that the number of people consumes soft drink is very high up to 1000
cans per minute (Bernama, 2007). Soft drink products have
been well accepted by consumers and gradually overtaking hot drinks as the biggest
beverage sector in the world. In the midst of the rapidly growing soft drink
demand, the industry on the whole is encountering new opportunities and challenges.
Changing consumer demands and preferences require new ways of maintaining current
customers and attracting new ones. Amid everincreasing competition, beverage
companies must intensely court customers, offer high quality products, efficiently
distribute them, ensure safety and keep prices low all while staying nimble
enough to exploit new markets by launching new products.
In order to survive in this environment, manufacturers must consider the market
trends that will likely shape the industry over the next few years. This will
help soft drink companies to understand the challenges they will encounter and
to turn them into opportunities for improvement, enhanced flexibility and, ultimately,
greater profitability. Market trends for the soft drink industry can be characterized
by six fundamental themes (Doilette, 2007). Out of six
themes, there is one that directly focuses to consumers preferences. This is
the one out of many challenges that has to be faced by manufacturers. Recent
developments in soft drink consumption and challenges in marketing have heightened
the need for searching the consumers’ needs and preferences. In food industry,
taste and other sensory characteristics of foods occupy a key position. Taste
has to be faultless since it strongly influences food choices (Arvola
and Tuorila, 1999), in many cases surpassing health issues (Glanz
et al., 1999; Tepper and Trail, 1998). However,
it is still unclear whether these factors also affect consumers’ acceptability
of soft drink.
Consumer preferences have been studied across food categories from beverages
to fast food with a number of methods. In a study conducted by Nelson
et al. (2005), three attributes of roasted peanuts were evaluated
using conjoint analysis. The three predetermined attributes were dryhoney roasted,
country of origin and price. In another study to understand consumer attitudes
and preferences for chocolate milk, again the predetermined attributes such
as visual, flavour and mouth feel were differentiated between a group of adults
and children using descriptive statistics (Thompson
et al., 2007). Another example of predetermined attributes of mandarins
was studied by Wei et al. (2003). The attributes
include the appearance, taste, texture and overall quality of fruit segments
and skin colour were considers to determine consumer preferences and compared
between domestic and imported mandarins. All these studies used predetermined
attributes or factors to determine consumer preferences. Furthermore, statistical
approaches mainly descriptive and inferential statistics were tabled and tested
to meet the objectives. The problem of determining factors that influenced consumer
preferences has been given somewhat less attention. One of the methods in multivariate
analysis that meant for extracting variables or attributes is factor analysis.
Thus, the present study focuses on statistical evidence provided by factor analysis
in describing consumer preferences with respect to the choices of a soft drink
product at a small town in Malaysia. These latent variables will help us to
identify consumer preferences of a soft drink product.
FACTOR ANALYSIS MODEL AS MEASURING CONSUMER PREFERENCES
Factor analysis is a set of techniques for determining the extent to which
variables that are related can be grouped together so that they can be treated
as one combined variable or factor rather than as a series of separate variables.
Perhaps the most common use of factor analysis in the social and behavioural
sciences is to determine whether the responses to a set of items used to measure
a particular concept can be grouped together to form an overall index of that
concept (Duncan, 2003). Factor analysis is often used
in the empirical research in social sciences (Harman, 1976;
Kim and Mueller, 1990; Hatcher, 1994).
Political scientists, when comparing the attributes of nations in terms of a
variety of political and socioeconomic variables, have applied factor analysis
in an attempt to determine characteristics that are the most important in classifying
nations (Rummel, 1979). Alternatively, sociologists have
determined friendship groups' by examining which people associate most frequently
with each other (Asher, 1976). In addition, psychologists
have used this statistical technique so as to study a given individual's intelligence
dimensions (Thomson, 1951) and to assess how people perceived
different stimuli and categorize them into different response sets (Stukat,
1958). Finally, economists have used factor analysis in the study of consumer
behavior, namely in assessing the individual consumer living standards and individual
consumer charity behaviour (Schokkaert and van Ootegem, 1990).
These are among the examples of the broad range applications of factor analysis.
A brief theoretical view of factor analysis model is relevant in explaining
how factors can extracted from considerable numbers of latent variables.
FACTOR ANALYSIS MODEL
Factor analysis begins with number of variables X_{1}, X_{2},...,X_{p}.
Equation 1 can be simplified in matrix form:
where, X_{1}, X_{2},...,X_{p} are known variables, l_{ij} is a constant represents loading for ith and jth factor. λ_{j} is jth factor.
Similarly, the Eq. 2 can be expressed in the matrix notation:
Where:
Λ 
= 
{l_{ij}} is a p x k matrix of constants, called
the matrix of factors loadings 
f 
= 
Random vector representing the k common factors 
e 
= 
Random vector representing p unique factors associated with the original
variables 
The common factors f_{1}, f_{2},….., ,f_{k} are
common to all X variables and are assumed to have mean = 0 and variance = 1.
The unique factors are unique to Xi. The unique factors are also assumed to
have mean = 0 and are uncorrelated to the common factors.
Equivalently, the covariance matrix Σ can be decomposed into a factor covariance matrix and an error covariance matrix:
where:
^{T
}is the transpose of 
The diagonal of the factor covariance matrix is called the vector of communalities
where:
The factor loadings are the correlation coefficients between the variables and factors. Factor loadings are the basis for imputing a label to different factors. Analogous to Pearson's r, the squared factor loading is the percentage of variance in the variable, explained by a factor.
The sum of the squared factor loadings for all factors for a given variable is the variance in that variable accounted for by all the factors and this is called the communality. The factor analysis model does not extract all the variance; it extracts only that proportion of variance, which is due to the common factors and shared by several items. The proportion of variance of a particular item that is due to common factors (shared with other items) is called communality. The proportion of variance that is unique to each item is then the respective item's total variance minus the communality.
The solution of Eq. 4 is not unique (unless the number of factors = 1), which means that the factor loadings are inherently indeterminate. Any solution can be rotated arbitrarily to obtain a new factor structure. The goal of these rotation strategies is to obtain a clear pattern of loadings, i.e., the factors are somehow clearly marked by high loadings for some variables and low loadings for other variables.
Rotation factors can be found as follows:
is an element of eigenvector in correlation matrix.
Due to orthogonal tansformation from Xscore to Zscore, the Eq. 5 becomes:
With only extracting m principle components, Eq. 6 yields:
is a linear combination of principle components Z_{m+1} to Z_{p}.
is a new factor and b_{ij} is a new loading factor.
The eigenvalue for a given factor reflects the variance in all the variables, which is accounted for by that factor. A factor's eigenvalue may be computed as the sum of its squared factor loadings for all the variables. The ratio of eigenvalues is the ratio of explanatory importance of the factors with respect to the variables. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored.
In finding eigenvalue, consider the Eq. 8:
where,
By finding the determinant of matrix (AλI)x = 0, then λ can be determined and it is an eigenvalue of A. An empirical example is presented to find eigenvalue, loading factors and new factors.
AN EMPIRICAL STUDY
In this empirical study, an application of factor analysis to identify consumers’
preferences with respect to the choices of a soft drink will be explored. In
other words, understanding and listing of consumer valuation for the choices
of a soft drink are proposed. The present survey instrument contains a list
of 23 attitudinal items were given out to 190 respondents at Sabak Bernam, Selangor,
Malaysia. Each item was represented by a sentence as presented in the instrument
survey. The respondent expresses her opinion towards a soft drink product by
classifying each sentence using a five point semantic differential or Likert
scale: I completely disagree, I disagree, Sometimes I agree, sometimes I disagree,
I agree and I completely agree. Formally, the factor analysis model that confined
to the following steps was employed. In the empirical work, two major analyses
steps were taken. In the first analysis an extraction of the initial common
preferential factors were performed. In the second analysis, a loading factor
for each common preferential factor was provided. The Eq. 18
were used in the two analyses. Calculations were made with the used of SPSS
11.0.
EXTRACTION OF THE INITIAL COMMON PREFERENTIAL FACTORS
The first step in the empirical analysis consists in extracting of a latent
preferential construct with factors. Since the object of factor analysis is
to reduce the number of variables that to be handled, this would not be achieved
if all of them were used. Consequently, the next step is to decide how many
factors should be kept. This really is a question of how many of the smaller
factors should be retained, since the first few which explain most of the variance
would be kept. The first factor will always explain the largest proportion of
the overall variance; the second factor will explain the next largest proportion
of variance that is not explained by the first factor and so on, with the last
factor explaining the smallest proportion of the overall variance. Each variable
is correlated with or loads on each factor. Because the first factor explains
the largest proportion of the overall variance, the correlations or loadings
of the variables will, on average, be highest for the first factor, next highest
for the second factor and so on. To calculate the proportion of the total variance
explained by each factor, the loadings of the variables on that factor is squared,
add the squared loadings to give the eigenvalue or latent root of that factor
and divide the eigenvalue by the number of variables. As there are as many components
as variables, some criterion needs to decide how many of the smaller factors
should be ignored, as these explain the least amount of the total variance.
One of the main criteria used is the Kaiser or KaiserGuttman criterion, which
is that factors that have eigenvalues of one or less should be ignored. As the
maximum amount of variance that can be explained by one variable is one, these
factors effectively account for no more than the equivalent of the variance
of one variable.
Table 1: 
Kaiser test 

The rationale for the Kaiser test is as follows: each observed variable contributes
one unit of variance to the total variance in the data set. Thus, any component
that displays an eigenvalue greater than one accounts for a greater amount of
variance than had been contributed by one variable. In addition, a component
that displays an eigenvalue less than one accounts for less variance than had
been contributed by one variable.
Since, the purpose of the factor analysis is to assess a number of reduced components (or factors), this cannot be effectively achieved if one retains factors that account for less variance than had been contributed by individual variables. According to the estimation results, it is sufficient to retain five factors since Δ_{6} = 0.983 <1 (Table 1).
Furthermore, the pattern of loadings of the retained fivefactor model shows a common conceptual meaning.
ROTATIONAL FACTORS
In the first step of factor analysis, the extraction (or identification) of
the preferential factors is preceded. At this stage the number of factors to
be rotated is not specified. Since the final objective is the reproduction of
the covariances and correlations, the sample correlation matrix of rotated factor
loadings as the primary data to be used in the analysis is accounted. Estimation
results are presented in Table 2. Printed results are multiplied
by 100 and rounded to the nearest integer. The values of below 0.50 are omitted
(Lazim et al., 2005; Lazim
and Kamaludin, 2007). This matrix represents the productmoment correlation
between the observable variable and the underlying factor. The factor loadings
are analogous to the standardized regression coefficients as obtained in regression
analysis. In other words, dropping an attitudinal item that does not score above
0.50 (assumed as the minimum correlation bound) means that an exploratory rule
based on the magnitude of the estimated regression coefficients, which is characterized
by rejecting all the items which indicate low correlations with the common factors
are followed.
As can be seen from Table 2, the factor model specification
is characterized by five common factors: Factor 1, 2, 3, 4 and 5. A closer inspection
to the attitudinal items polled under the factor 5 reveals that they do not
share any common conceptual meaning: M23 focuses on the trend in choosing soft
drink of the days; M6 and M5 focus on the accessibly in the market.
Table 2: 
Rotated factor pattern (five common factors) 

The M23, M6 and M5 are interpreted as not being pure measures underpinning
any common latent construct. Therefore, whether a fourfactor model performs
an adequate representation of the data is tested.
Factor 1 collects a number of items related to the respondent's general attitude with respect to promotions and popularity of the product. Therefore this latent construct can be labelled as branding. A higher number of items in this factor indicate a strong trustworthiness to brand.
Factor 2 collects a number of items that are related to respondent's belief toward certification by authority and also confirmation of prices that comparable to other brands. Therefore this factor is labelled as the validation and prices. A high score on this factor reveals that the respondent experiences good value for money that makes them feel happy with the product.
Factor 3 collects a number of items that related to the physical appearance of the product. For this reason the third factor is labelled as the packaging. Respondents who score high on packaging have strong beliefs with respect to the well presented and palatable product.
Factor 4 collects two items that related to the tasty of the product. Item M13 and item M1 focus on the taste of the product. Therefore, this factor is labelled as taste. A higher score in the item M13 of thirst quencher was due to the strong belief consumers in taste of the product.
These statistical evidences provide a robust tool in identifying four conceptual factors and loading for each item in describing consumers preferences toward choice of a soft drink.
CONCLUSION
The results successfully showed the application of factor analysis model in extracting new factors together with their respective loading factors. These results have important implications not only to manufacturers and marketers but also to the researchers. First, one can conclude that any policy action in marketing strategy must consider the four factors. Secondly, the evaluation results clearly indicate that the Malaysian customers prefer to keep branding as the first priority. The other factors are also important but with a slight reduction in the degree of importance. These results can positively be transferred to other areas of marketing policy. Indeed, identification and characterization of consumer preferences are expected to play a crucial role in stimulating consumer awareness for worth value products. Summarily factor analysis model have proven its applicability in identifying factors influencing customers and surely could be extended into other areas where factors extracting is highly needed.