chapter 4 data analysis and interpretation...
Post on 22-May-2020
118 Views
Preview:
TRANSCRIPT
106
CHAPTER 4
DATA ANALYSIS AND INTERPRETATION
INTRODUCTION
This chapter the results of the statistical analysis done for testing
hypothesis are presented and interpreted. The analysis was done with
SPSS 15.0 & AMOS 7.0 software packages.
The first section presents the results of various relationships between the
demographic and purchase motivating factors and testing of inter-
correlation matrix.
The second section presents the construction and validation of Structural
Equation Model of SEM-CPD mediated model with the dimensions
Affordability, Attributes, Sales Support, the mediating parameter
external factors and the outcome of the purchase decision. And also the
SEM-CPD mediated model is tested with Bayesian testing and
estimation.
4.1 ANALYSIS OF VARIOUS RELATIONSHIP BETWEEN
DEMOGRAPHIC, CONSUMER PREFERENCES,
PRIORITIES AND THE STUDY VARIABLE
In order to understand the relationship between the demographic
variables and the study variables i.e., the dimensions of purchase
107
decisions, empirically tested. The summary of the analyses and the
interpretation thereon is set out in the following sections.
4.1.1 ANALYSIS OF VARIOUS RELATIONSHIPS AMONG
DEMOGRAPHIC VARIABLES
Table 4.1: Cross Tabulated Relationship among Age & Family
Size
Personal Information
FAMILY SIZE
2-3 4-5 6-7 8-9 <9
AGE
21-25
Count 66 151 26 5 2
% 9.8% 22.5% 3.9% 0.7% 0.3%
26-35
Count 71 95 25 4 4
% 10.6% 14.1% 3.7% 0.6% 0.6%
36-45
Count 39 31 11 3 4
% 5.8% 4.6% 1.6% 0.4% 0.6%
45-50 Count 14 28 7 6 3
% 2.1% 4.2% 1.0% 0.9% 0.4%
Above
50
Count 14 35 13 9 6
% 2.1% 5.2% 1.9% 1.3% .9%
SPSS15.0 OUTPUT Source: primary data
The table 4.1 reveals that the age group of 21-25 having a family size of
four to five members, 2-3 and 6-7 members has greatest inclination of
purchasing a motorbike in that order. Consumers in the age group of 26-
35 closely follow the similar trend but with a variation of high relative
frequency in the family size of 6-7 members. The trend observed from
the table 4.1 is that younger, the consumers and medium their family
size, their inclination towards possession of motorbike is greater.
108
Targeting such an age group and delivering product to meet their needs
will be helpful in gaining reasonable market share for manufacturers.
Table 4.2: Cross Tabulated Relationship among Age & Income
Personal Information
INCOME
>50000 50001-100000
100000-150000
150000-200000 >200000
AGE
21-25
Count 38 62 52 27 71
% 5.7% 9.2% 7.7% 4.0% 10.6%
26-35
Count 14 26 46 36 77
% 2.1% 3.9% 6.8% 5.4% 11.5%
36-45
Count 9 17 20 9 33
% 1.3% 2.5% 3.0% 1.3% 4.9%
45-50
Count 8 13 16 8 13
% 1.2% 1.9% 2.4% 1.2% 1.9%
Above 50
Count 7 9 15 11 35
% 1.0% 1.3% 2.2% 1.6% 5.2%
SPSS15.0 OUTPUT Source: primary data
The table 4.2 reveals that the age group of 21-25 having an annual
income of more than 200 thousands have greatest inclination for
possessing a two wheeler followed by those in the income group
between 50 thousands to 150 thousands. Another significant age group
following the similar trend is the age group of 26-35 with a little
variation of having higher relative frequency in income group of 100 –
150 thousands. The trend observed from the table 4.2 is that younger the
age of consumers and higher their annual income, their inclination
towards possession of motorbike is greater. The inclination for
possession of two-wheeler decreases with the increase in age and/or
109
decrease in income. Targeting such an age group and delivering product
to meet their needs will be helpful in better product positioning.
Table 4.3: Cross Tabulated Relationship among Age &
Employment
Personal Information
EMPLOYMENT
GOVT SECTOR
PVT SECTOR PROFESSIONALS
SELF/ BUSINESSMEN OTHERS
AGE
21-25
Count 12 57 96 21 64
% 1.8% 8.5% 14.3% 3.1% 9.5%
26-35
Count 8 60 105 17 9
% 1.2% 8.9% 15.6% 2.5% 1.3%
36-45
Count 7 38 24 7 12
% 1.0% 5.7% 3.6% 1.0% 1.8%
45-50
Count 9 12 11 17 9
% 1.3% 1.8% 1.6% 2.5% 1.3%
Above 50
Count 17 16 13 15 16
% 2.5% 2.4% 1.9% 2.2% 2.4%
SPSS15.0 OUTPUT Source: primary data
The table 4.3 reveals that the professionals in the age groups of 21-25,
26-35 are more interested in making motorbikes purchase decision.
Significantly, those employed in the private sector in above age groups
are inclined in possessing the motorbikes. Another group, that is making
interesting decision of possessing is others, which include self
employed, students and others. Students make up the major portion of
those in the group others. Those in business and government sector do
not respond positively to the purchase decision-making. Consumerism
of motorcycle is quite high in respect of those employed privately and in
independent profession.
110
Table 4.4: Cross Tabulated Relationship among Age &
Qualification
Personal Information QUALIFICATION
SCHOOLING GRADUATE
- UG GRADUATE
- PG PROFESSIONALS
AGE
21-25
Count 3 68 125 54
% .4% 10.1% 18.6% 8.0%
26-35
Count 3 46 87 63
% .4% 6.8% 12.9% 9.4%
36-45
Count 6 22 32 28
% .9% 3.3% 4.8% 4.2%
45-50
Count 11 17 17 13
% 1.6% 2.5% 2.5% 1.9%
Above 50
Count 12 23 28 14
% 1.8% 3.4% 4.2% 2.1%
SPSS15.0 OUTPUT Source: primary data
Interestingly, the table 4.4 reveals that those possessing educational
qualification of masters and professionally qualified form the significant
portion of the consumers of the motorcycle. Another interesting
revelation is that those having college education are inclined in the
possession of the product under study. As the level of education
increased, notable rise in the consumer’s inclination towards purchasing
an automobile increases. In the group of those less educated the increase
in age has positive influence in the purchase decision. Targeting those
with reasonable educational qualification will boost the sales of the
companies.
111
Table 4.5: Cross Tabulated Relationship among Employment &
Income
Personal Information
INCOME
>50000 50001-100000
100000-150000
150000-200000 <200000
EMPLOYMENT
GOVT
Count 7 9 16 9 12
% 1.0% 1.3% 2.4% 1.3% 1.8%
PVT
Count 19 37 46 17 64
% 2.8% 5.5% 6.8% 2.5% 9.5%
PROFESSIONALS
Count 21 31 43 45 109
% 3.1% 4.6% 6.4% 6.7% 16.2%
SELF
Count 7 17 23 11 19
% 1.0% 2.5% 3.4% 1.6% 2.8%
OTHERS
Count 22 33 21 9 25
% 3.3% 4.9% 3.1% 1.3% 3.7%
SPSS15.0 OUTPUT Source: primary data
The table 4.5 reveals an interesting angle. It reveals that the respondents
employed in government sector are drawing salary between Rupees
100-150 thousands, above 200 thousands. These sections of government
employees have inclination of purchase of motorbikes than those in
other compensation package. Interestingly, the professionals and private
sector employees receiving an annual compensation above Rupees 200
thousands have notable inclination of purchase of motorbikes. Self-
employed in the annual income between 150-200 thousands are likely to
purchase or already purchased motorbikes. The table is quite interesting
that the consumers who receive an annual compensation more than
Rupees 200 thousands think that the motorbikes are affordable to them.
Hence, the motorbikes can be positioned for this segment of consumers.
112
Table 4.6: Cross Tabulated Relationship among Employment &
Family Size
Personal Information
FAMILYSIZE
2-3 4-5 6-7 8-9 <9
EMPLOYMENT
GOVT
Count 18 25 8 2 0
% 2.7% 3.7% 1.2% .3% .0%
PVT
Count 59 96 18 7 3
% 8.8% 14.3% 2.7% 1.0% .4%
PROFESSIONALS
Count 86 116 32 7 8
%
12.8% 17.3% 4.8% 1.0% 1.2%
SELF
Count 14 41 14 7 1
% 2.1% 6.1% 2.1% 1.0% .1%
OTHERS Count 27 62 10 4 7
% 4.0% 9.2% 1.5% .6% 1.0%
SPSS15.0 OUTPUT Source: primary data
The table 4.6 reveals that the professionals in the age groups of 21-25,
26-35 is more interested in making the motorbike purchase decision.
Significantly, those employed in the private sector in above age groups
are inclined in the possessing the motorbikes. Another group, that is
making interesting decision of possessing is others, which include self
employed, students and others. Students make up the major portion of
those in the group others. Those in business and government sector do
not respond positively to the purchase decision-making. Consumerism
of motorcycle is quite high in respect of those employed privately and in
independent profession.
113
Table 4.7: Cross Tabulated Relationship among Employment &
Qualification
Personal Information QUALIFICATION
SCHOOLING GRADUATE -
UG GRADUATE
- PG PROFESSIO
NALS
EMP LOY MEN T
GOVT
Count 6 15 26 6
% .9% 2.2% 3.9% .9%
PVT
Count 8 63 85 27
% 1.2% 9.4% 12.6% 4.0%
PROFESSIONALS
Count 5 43 90 111
%
.7% 6.4% 13.4% 16.5%
SELF
Count 10 27 26 14
% 1.5% 4.0% 3.9% 2.1%
OTHERS
Count 6 28 62 14
% of Total .9% 4.2% 9.2% 2.1%
SPSS15.0 OUTPUT Source: primary data
Like the table 4.4, the table 4.7 reveals that many of the employed
consumers are either undergraduate or post-graduate. But the need for
higher education diminishes as the consumers become employed in
government sector. Obviously, those in the private sector are more
qualified educationally than those in other sectors. Self employed
display professionalism in their skills. The advertising campaign shall
be directed keeping these dimensions in mind.
114
Table 4.8: Cross Tabulated Relationship among Income &
Family Size
Personal Information
FAMILY SIZE
2-3 4-5 6-7 8-9 <9
INCOME
>50K
Count 22 34 17 2 1
% 3.3% 5.1% 2.5% .3% .1%
50K – 100K
Count 39 63 13 8 4
% 5.8% 9.4% 1.9% 1.2% .6%
100K -150K
Count 30 81 27 7 4
% 4.5% 12.1% 4.0% 1.0% .6%
150K -200K
Count 24 49 11 5 2
% 3.6% 7.3% 1.6% .7% .3%
<200K
Count 89 113 14 5 8
% 13.2% 16.8% 2.1% .7% 1.2%
SPSS15.0 OUTPUT Source: primary data
The table 4.8 reveals that the level of annual compensation received
determines the size of the family. Higher the level of annual income,
higher the size of the family going well with the popular notion that the
wealthy will have moderate sized family i.e., between 2-5 membership.
The uniqueness observed in Kancheepuram district is that the family
system is joint family system. But the increase in annual compensation
is not a matter as far as having a family size above 5 members. The
increasing awareness of family planning and birth control besides the
economic well-being is the reason for this trend. The manufacturers,
therefore, has to be target the consumers having family size of 4-5
members. Because the increasing need of ease of transportation compels
the low sized family, they may also be targeted.
115
Table 4.9: Cross Tabulated Relationship among Income &
Qualifications
Personal Information
QUALIFICATIONS
SCHOOLING GRADUATE
- UG GRADUATE
- PG PROFESSIONA
LS
INCO ME
>50K
Count 8 18 37 13
% 1.2% 2.7% 5.5% 1.9%
50K – 100K
Count 8 40 60 19
% 1.2% 6.0% 8.9% 2.8%
100K -150K
Count 11 41 67 30
% 1.6% 6.1% 10.0% 4.5%
150K -200K
Count 3 26 35 27
% .4% 3.9% 5.2% 4.0%
<200K
Count 5 51 90 83
% .7% 7.6% 13.4% 12.4%
SPSS15.0 OUTPUT Source: primary data
The table 4.9 signifies that the higher qualification is high rewarding
ones. Those having more than Rupees 200K are mostly either master
degree holders or professionally qualified. Those who are qualified less
than under-graduation receive lower annual income. The consumers
who can afford motorbikes are in group of graduate or higher with an
annual income of more than Rupees 50 K and less than 150 K.
Therefore, the potential consumers lie in this group, which is the middle
class consumers of India and form major consumer base for the
consumer durables and automobiles.
116
Table 4.10: ONE WAY ANALYSIS OF VARIANCE OF AGE
AMONG PURCHASE DECISION DIMENSIONS
Sum of
Squares df Mean
Square F Sig.
Statistical Inference
Affordability
Between Groups
835.499 4 208.875 1.421 0.225 Insignificant
Within Groups
98014.714 667 146.949
Total 98850.213 671
Attributes
Between Groups
719.704 4 179.926 .831 0.506 -do=
Within Groups
144375.295 667 216.455
Total 145094.999 671
Sales Support
Between Groups
258.478 4 64.619 1.565 0.182 -do-
Within Groups
27543.141 667 41.294
Total 27801.619 671
External Factors
Between Groups
164.133 4 41.033 .684 .603 -do-
Within Groups
40023.080 667 60.005
Total 40187.213 671
Purchase Decision
Between Groups
45.968 4 11.492 .295 .881 -do-
Within Groups
25980.245 667 38.951
Total 26026.213 671
SPSS 15.0 OUTPUT Source: primary data
Table 4.10 reveals the significant difference on the various purchase
decisions dimensions with respect to age of the respondents. From the
above table, it is evident that there is no significant difference of age of
the respondents with regard to Affordability, Attributes, Sales Support,
External Factors and overall purchase decision. Purchase is an outcome
of various dimensions of consumer behavior in India, but the researcher
found out that there were quite significant differences among the
117
respondents with respect to age. The researcher identified the following
reasons as the cause; the influence of the peers, family and friends and
also the availability of credit, consumers’ sensitivity to consumption of
fuel, information on spare price across all ages. The above stated factors
are influencing various dimensions of purchase decision- making under
study.
Table 4.11: ONE WAY ANALYSIS OF VARIANCE OF
OCCUPATION AMONG PURCHASE DECISION
DIMENSIONS
Sum of
Squares df Mean
Square F Sig.
Statistical Inference
Affordability
Between Groups
6371.324 4 1592.831 11.488 .000 Significant
Within Groups
92478.889 667 138.649
Total 98850.213 671
Attributes
Between Groups
1596.275 4 399.069 1.855 .117 Insignificant
Within Groups
143498.724 667 215.141
Total 145094.999 671
Sales Support
Between Groups
283.916 4 70.979 1.720 .144 Insignificant
Within Groups
27517.703 667 41.256
Total 27801.619 671
External Factors
Between Groups
607.708 4 151.927 2.560 .038 Significant
Within Groups
39579.505 667 59.340
Total 40187.213 671
Purchase Decision
Between Groups
269.292 4 67.323 1.743 .139 Insignificant
Within Groups
25756.921 667 38.616
Total 26026.213 671
SPSS 15.0 OUTPUT Source: primary data
118
Table 4.11 reveals the significant difference on the various purchase
decisions dimensions with respect to employment or occupation of the
respondents. From the above table, it is evident that there is no
significant difference of employment status of the respondents with
regard to Affordability, External Factors. From the above table, there is
no significant difference among employment status with regard to
purchase decisions as it is dependent upon individual dimensions of
purchase behavior of consumers in India, but the researcher found out
that there were quite significant differences among the respondents with
respect to occupation. The research identified the following reasons as
the causes: the cost of fuel, geographical diversity, cultural bias, rural-
urban divergence, standard of education acquired which spread across
almost all types of employment. The above stated factors are
influencing various dimensions of purchase decision- making under
study.
119
Table 4.12: ONE WAY ANALYSIS OF VARIANCE OF
INCOME AMONG PURCHASE DECISION DIMENSIONS
Sum of
Squares df Mean
Square F Sig.
Statistical Inference
Affordability
Between Groups
1593.689 4 398.422 2.732 0.028 Significant
Within Groups
97256.524 667 145.812
Total 98850.213 671
Attributes
Between Groups
2997.751 4 749.438 3.518 0.007 Significant
Within Groups
142097.247 667 213.039
Total 145094.999 671
Sales Support
Between Groups
480.044 4 120.011 2.930 0.020 Significant
Within Groups
27321.575 667 40.962
Total 27801.619 671
External Factors
Between Groups
196.192 4 49.048 .818 0.514 Insignificant
Within Groups
39991.021 667 59.957
Total 40187.213 671
Purchase Decision
Between Groups
1665.317 4 416.329 11.399 0.000 Significant
Within Groups
24360.896 667 36.523
Total 26026.213 671
SPSS 15.0 OUTPUT Source: primary data
Table 4.12 reveals the significant difference on the various purchase
decisions dimensions with respect to level of annual income of the
respondents. From the above table, it is evident that there is significant
difference of level of annual income of the respondents with regard to
Affordability, Attributes, Sales Support and Purchase decision. From
the above table, there is no significant difference of level of annual
income with regard to external factors such as advertising, word of
mouth in India, but the researcher found out that there were quite
120
significant differences among the respondents with respect to annual
income. The research identified the following reasons as the causes: the
needs such as neighbor’s possession and maintenance requirements. The
above stated factors are influencing various dimensions of purchase
decision- making under study.
Table 4.13: ONE WAY ANALYSIS OF VARIANCE OF
FAMILY SIZE AMONG PURCHASE DECISION
DIMENSIONS
Sum of
Squares df Mean
Square F Sig.
Statistical Inference
Affordability Between Groups
2429.358 4 607.339 4.201 .002 Significant
Within Groups
96420.855 667 144.559
Total 98850.213 671
Attributes Between Groups
4085.872 4 1021.468 4.832 .001 -do-
Within Groups
141009.126 667 211.408
Total 145094.999 671
Sales Support
Between Groups
317.470 4 79.368 1.926 .104 Insignificant
Within Groups
27484.149 667 41.206
Total 27801.619 671
External Factors
Between Groups
1196.566 4 299.141 5.117 .000 Significant
Within Groups
38990.647 667 58.457
Total 40187.213 671
Purchase Decision
Between Groups
1512.613 4 378.153 10.289 .000 -do-
Within Groups
24513.600 667 36.752
Total 26026.213 671
SPSS 15.0 OUTPUT Source: primary data
121
Table 4.13 reveals the significant difference on the various purchase
decisions dimensions with respect to size of the family of the
respondents. From the above table, it is evident that there is significant
difference of size of the family of the respondents with regard to
Affordability, Attributes, External Factors and Purchase decision. From
the above table, there is no significant difference of size of the family
with regard to Sales Support such as dealer network, number of service
stations in India, but the researcher found out that there were quite
significant differences among the respondents with respect to size of the
family. The research identified the following reasons as the causes:
Location, Trained Service Personnel and neighborhood help. The above
stated factors are influencing various dimensions of purchase decision-
making under study.
122
Table 4.14: ONE WAY ANALYSIS OF VARIANCE OF
EDUCATIONAL QUALIFICATIONS AMONG PURCHASE
DECISION DIMENSIONS
Sum of
Squares df Mean
Square F Sig.
Statistical Inference
Affordability Between Groups
41217.376 3 13739.125 159.245 .000 Significant
Within Groups
57632.836 668 86.277
Total 98850.213 671
Attributes Between Groups
1383.919 3 461.306 2.144 .093 Insignificant
Within Groups
143711.079 668 215.136
Total 145094.999 671
Sales Support
Between Groups
351.898 3 117.299 2.855 .036 Significant
Within Groups
27449.721 668 41.092
Total 27801.619 671
External Factors
Between Groups
458.335 3 152.778 2.569 .050 Significant
Within Groups
39728.878 668 59.474
Total 40187.213 671
Purchase Decision
Between Groups
647.644 3 215.881 5.682 .001 Significant
Within Groups
25378.569 668 37.992
Total 26026.213 671
SPSS 15.0 OUTPUT Source: primary data
Table 4.14 reveals the significant difference on the various purchase
decisions dimensions with respect to level of education received of the
respondents. From the above table, it is evident that there is significant
difference of size of the family of the respondents with regard to
Affordability, Sales Support, External Factors, Overall Possession needs
and Purchase decision. From the above table, there is no significant
difference of level of education received with regard to Attributes of the
product such as product features, style, price and road conditions in
123
India, but the researcher found out that there were quite significant
differences among the respondents with respect to level of education
received. The research identified the following reasons as the causes:
Word of mouth of friends, neighbors, highest reach of advertising,
proximity of the study area with largest metropolitan city in the state
and need for self esteem. The above stated factors are influencing
various dimensions of purchase decision- making under study.
4.2 REGRESSION MODEL OF THE SQM-HEI MEDIATED
STRUCTURAL EQUATION MODEL
In hierarchical regression, the predictor variables are entered in sets of
variables according to a pre-determined order that may infer some
causal or potentially mediating relationships between the predictors and
the dependent variable (Francis, 2003). Such situations are frequently of
interest in the social sciences. The logic involved in hypothesizing
mediating relationships is that “the independent variable influences the
mediator which, in turn, influences the outcome” (Holmbeck, 1997).
However, an important pre-condition for examining mediated
relationships is that the independent variable is significantly associated
with the dependent variable prior to testing any model for mediating
124
variables (Holmbeck, 1997). Of interest is the extent to which the
introduction of the hypothesized mediating variable reduces the
magnitude of any direct influence of the independent variable on the
dependent variable.
Hence the researcher empirically tested the hierarchical regression for
the model conceptualized in the figure 4.1, with in the AMOS graphics
environment. The path diagram for the hypothesized mediated model is
given in the path diagram (see Figure 4.1).
Figure 4.1: Hypothesized mediated model specification for AMOS
graphics input
M1, V1
Attributes
M2, V2
Affordability
M3, V3 Sales
Support
I1
External Factors
I2 Purchase
Decision
W1
W2
W3
W4
W5
W6
W7
C1
C2
C3
e1
e2
STANDARDIZED PARAMETER ESTIMATES FOR
MEDIATED SEM – CPD Overall MODEL
125
The analyses are conducted; the parameter estimates are then viewed
within AMOS graphics. Figure 4.2 displays the standardized parameter
estimates.
FIGURE 4.2: STANDARDIZED PARAMETER ESTIMATES FOR MEDIATED SEM-CPD Overall MODEL
The regression analysis revealed that the student’s perception on the
various dimensions of purchase decision, attributes explained 0.10 of
the purchase decision, followed by affordability which explains -0.01 of
the purchase decision. The R2
value of 0.42 is displayed above the box
101.00, 215.92
Attributes
56.95, 168.34
Affordability
32.98, 41.37
Sales Support
4.17
External Factors
.42
Purchase Decision
.23
.06
.17
.11
-.01
.08
.10
64.74
20.46
61.46
e1
e2
126
purchase decision in the AMOS graphics output. The visual
representation of results suggest that the relationships between the
dimensions of purchase motives and the mediated factor. The Attributes
results a significant impact on the mediated factor, External Factors.
The Affordability results very limited negative influence on the
purchase motives. It shows that the consumer attitude towards the
affordability issues like credit facility, influence of the environment
towards the outcome of affordability is insignificant; where as the
impact of the same is very high on the mediating variable. The
covariance is quite significantly high between affordability and sales
support, which shows that consumer, requires high level of after sales
service and support from the dealer to buy the motorbikes and for
advice on maintenance. The covariance between affordability and
attributes is moderate, which means that the affordability and attributes
play a modest yet key role in the decision-making process towards
purchase. According to Hoyle, (1995) a model is a statistical statement
about the relation among variables, in the present study reveals the
relationship among the various dimensions of purchase motives & the
outcome of the purchase decision.
127
4.2.1 BAYESIAN ESTIMATION AND TESTING FOR
REGRESSION MODEL OF SEM-CPD MEDIATED
STRUCTURAL EQUATION MODEL
The research model is a SEM, while many management scientist are
most familiar with the estimation of these models using software that
analyses covariance matrix of the observed data ( e.g. LISREL,
AMOS, EQS), the researcher adopt a Bayesian approach for
estimation and inference in AMOS 7.0 environment((Arbuckle &
Wothke, 2006). Since it offers numerous methodological and
substantive advantages over alternative approaches.
TABLE 4.15: BAYESIAN CONVERGENCE DISTRIBUTION FOR
SEM-CPD REGRESSION MODEL
Mean S.E. S.D. C.S. Median
95%
Lower
bound
95%
Upper
bound
Skewness Kurtosis Min Max Name
Regression
weights
External
Factors<--
Attributes
0.235 0.000 0.023 1.000 0.235 0.190 0.280 -0.014 -0.018 0.140 0.322 W1
External
Factors<--
Affordability
0.062 0.000 0.020 1.000 0.062 0.024 0.101 0.019 0.026 -0.016 0.140 W2
External
Factors<--
Sales Support
0.167 0.000 0.051 1.000 0.166 0.066 0.267 0.010 -0.039 -0.036 0.363 W3
Purchase
Decision<--
External
Factors
0.113 0.000 0.017 1.000 0.113 0.079 0.147 0.008 0.008 0.044 0.189 W4
Purchase
Decision<--
Affordability
-0.009 0.000 0.009 1.000 -0.008 -0.026 0.009 -0.004 -0.016 -0.047 0.027 W5
Purchase
Decision<--
Sales Support
0.080 0.000 0.023 1.001 0.080 0.035 0.126 0.012 -0.012 -0.021 0.176 W6
128
Purchase
Decision<--
Attributes
0.103 0.000 0.011 1.000 0.103 0.082 0.125 0.002 0.011 0.056 0.149 W7
Means
Attributes 101.000 0.004 0.574 1.000 100.999 99.873 102.118 0.002 -0.017 98.825 103.217 M1
Affordability 56.938 0.004 0.506 1.000 56.939 55.940 57.921 -0.027 -0.009 54.966 58.877 M2
Sales Support 32.977 0.002 0.252 1.000 32.978 32.482 33.468 -0.013 -0.024 32.011 33.935 M3
Intercepts
External
Factors 4.177 0.019 1.782 1.000 4.179 0.696 7.652 -0.009 0.026 -3.795 11.255 I1
Purchase
Decision 0.417 0.008 0.795 1.000 0.416 -1.154 1.980 -0.008 -0.008 -3.028 3.612 I2
Covariances
Attributes<-
>Sales Support 65.582 0.037 4.532 1.000 65.427 57.275 75.041 0.241 0.089 49.959 85.090 C1
Affordability<-
>Sales Support 20.697 0.035 3.371 1.000 20.652 14.318 27.518 0.093 0.040 8.215 35.579 C2
Attributes<-
>Affordability 62.202 0.071 7.928 1.000 61.960 47.355 78.499 0.172 0.086 31.443 99.828 C3
Variances
Attributes 218.843 0.089 12.059 1.000 218.369 196.601 243.732 0.236 0.047 179.028 272.712 V1
Affordability 170.638 0.123 9.424 1.000 170.301 153.170 190.083 0.224 0.120 137.190 211.322 V2
Sales Support 41.901 0.018 2.312 1.000 41.805 37.634 46.676 0.243 0.108 33.632 52.675 V3
e1 39.353 0.022 2.161 1.000 39.281 35.334 43.791 0.203 0.064 31.502 49.552 V4
e2 7.789 0.004 0.425 1.000 7.774 6.998 8.666 0.206 0.042 6.347 9.568 V5
The table 4.8 shows the Bayesian convergence distribution of the SEM-
CPD mediated regression model. In this research the researcher has
adopted for the procedure of assessing convergence of MCMC (Markov
Chain Monte Carlo) algorithm of maximum likelihood. To estimate the
MCMC convergence the researcher has adopted two methods namely,
convergence in distribution, convergence of posterior summaries. The
values of posterior mean accurately estimate the SEM-CPD mediated
SEM model. From the above table the highest value of Convergence
129
Statistics (C.S) is 1.001 which is less than the 1.002 conservative
measures (Gelman et al. 2004).
4.2.2 POSTERIOR DIAGNOSTIC PLOTS OF SQM-HEI
MEDIATED REGRESSION MODEL
To check the convergence of the Bayesian MCMC method the posterior
diagnostic plots are analyzed. The following figures (figure 4.3 to 4.9)
shows the posterior frequency polygon of the distribution of the
parameters across the 60,000 samples. The Bayesian MCMC diagnostic
plots reveals that for all the figures the normality is achieved, so the
structural equation model fit is accurately estimated.
Figure 4.3: Posterior frequency polygon distribution of the External
Factors and Attributes, regression weight (W1)
130
Figure 4.4: Posterior frequency polygon distribution of the External
Factors and Affordability, regression weight (W2)
Figure 4.5: Posterior frequency polygon distribution of the External
Factors and Sales Support, regression weight (W3)
131
Figure 4.6: Posterior frequency polygon distribution of the Purchase
Decision and External Factors, regression weight (W4)
Figure 4.7: Posterior frequency polygon distribution of the Purchase
Decision and Affordability, regression weight (W5)
Group number 1
Purchase Decision<--External Factors (W4) 0.1 0.2 0.3
F r e q u e n c y
132
Figure 4.8: Posterior frequency polygon distribution of the Purchase
Decision and Sales Support, regression weight (W6)
Figure 4.9: Posterior frequency polygon distribution of the Purchase
Decision and Attributes, regression weight (W7)
133
To ensure that Amos has converged to the posterior distribution is a
simultaneous display of two estimates of the distribution, one obtained
from the first third of the accumulated samples and another obtained
from the last third. The following figures (Figure 4.10 to Figure 4.12)
show the simultaneous display of two estimates of the distribution for
the mediated factor External Factors with the other dimensions across
50,000 samples. From the three figures, it is observed that the
distributions of the first and last thirds of the analysis samples are
almost identical, which suggests that Amos has successfully identified
the important features of the posterior distribution of the relationship
between the mediated factor External Factors and other purchase
decision dimensions.
134
Figure 4.10 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediated factor External Factors and Attributes
Figure 4.11 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediated factor External Factors and Affordability
135
Figure 4.12 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediated factor External Factors and Sales Support
\
The trace plot also called as time-series plot shows the sampled values
of a parameter over time. This plot helps to judge how quickly the
MCMC procedure converges in distribution. The following figures
(figure 4.13 – figure 4.15) shows the trace plot of the SEM-CPD model
for the mediated factor External Factors with other dimensions across
60,000 samples. All the three figures exhibit rapid up-and-down
variation with no long-term trends or drifts. If we mentally break up this
plot into a few horizontal sections, the trace within any section would
not look much different from the trace in any other section. This
136
indicates that the convergence in distribution takes place rapidly. Hence
the SEM-CPD MCMC procedure very quickly forgets its starting
values.
Figure 4.13 Posterior trace plot of the SEM-CPD regression model
for the mediated factor External Factors and Attributes
137
Figure 4.14Posterior trace plot of the SEM-CPD regression model for
the mediated factor External Factors and Affordability
Figure 4.15Posterior trace plot of the SEM-CPD regression model for
the mediated factor External Factors and Sales Support
138
To determine how long it takes for the correlations among the samples
to die down, autocorrelation plot which is the estimated correlation
between the sampled value at any iteration and the sampled value k
iterations later for k = 1, 2, 3,…. is analyzed for the SEM-CPD
regression model. The figures (figure 4.16 to figure 4.18) shows the
correlation plot of the SEM-CPD model for the mediated factor External
Factors with other dimensions across 60,000 samples. The three figures
exhibits that at lag 90 and beyond, the correlation is effectively 0. This
indicates that by 90 iterations, the MCMC procedure has essentially
forgotten its starting position. Forgetting the starting position is
equivalent to convergence in distribution. Hence, it is ensured that
convergence in distribution was attained, and that the analysis samples
are indeed samples from the true posterior distribution.
139
Figure 4.16 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor External Factors and Attributes
Figure 4.17 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor External Factors and Affordability
.
140
Figure 4.18 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor External Factors and Sales Support
Even though marginal posterior distributions are very important, they do
not reveal relationships that may exist among the two parameters. The
summary table given in table 4.8 and the frequency polygons given in
the figure 4.3 to figure 4.9 describe only the marginal posterior
distributions of the parameters. Hence to visualize the relationships
among pairs of Parameters in three dimensional the following figures
(figure 4.19 to figure 4.21) provide bivariate marginal posterior plots of
the SEM-CPD model for the mediated factor External Factors with
other dimensions across 60000 samples. From the three figures it
reveals that the three dimensional surface plots also signifies the
141
interrelationship between the mediating variable External Factors with
the other dimensions Attributes, Affordability and Sales Support
Figure 4.19: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor External Factors with the
Attributes & Sales Support
142
Figure 4.20: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor External Factors with the
Attributes & Affordability
Figure 4.21: Three-dimensional surface plot of the marginal posterior
distributions of Attributes with Purchase Decision & Affordability
143
The following figures (figure 4.22 to figure 4.24) display the two-
dimensional plot of the bivariate posterior density across 50000
samples. The plot shows range of darkness from dark to light. The three
shades of gray represent 50%, 90%, and 95% credible regions
respectively. From the three figures, it reveals that the sample
respondent’s responses are normally distributed.
Figure 4.22: Two-dimensional plot of the bivariate posterior density
for the regression weights External Factors to Attributes and
Attributes to Sales Support
144
Figure 4.23: Two-dimensional plot of the bivariate posterior density
for the regression weights External Factors to Attributes and
Attributes to Affordability
Figure 4.24 Two-dimensional plot of the bivariate posterior density
for the regression weights Purchase Decision to Attributes and
Attributes to Affordability
145
The reliability of the data has been carried out in the SPSS 15.0 and the
worthwhileness of the data is proved. The Cronbach’s Alpha value for
the sample data is 0.896, which is very close to 0.90. The value below
1.0 is accepted. That proves the sample data is reliable for analysis and
the results based on those analysis are statistically accepted. The
Cronbach’s Alpha of 0.896 signifies the sample, size of which is small,
validity of the data is most significant than similar yet larger sample.
4.3 STRUCTURAL EQUATION MODELING OF MEDIATED
SEM-CPD MODEL
Since the purchase decision is a theoretical construct, researcher has
defined its dimension based on the setting used to explore the construct.
If Mediated SEM-CPD Model is to be applicable in the Indian context,
the dimensions and the sub dimensions on purchase decision/motives
have to be reliable and valid in measuring consumer purchase behavior.
The model examines the relative importance of dimensions of
possession to overall purchase behavior of motorbikes and/or any
automobiles in India especially urbanized geographical area with
abutting rural pockets.
146
The SEM-CPD Model examines the relative importance of External
Factors as a mediating factor for motorbike purchase behavior in India.
The SEM-CPD model includes the measurement of sub dimensions of
purchase behavior as follows Needs, Features, After Sales Service and
Support (Support), Advertising Media (AdMedia), Price, Availability of
Credit Facility (CreditFaci), Infrastrcture, Maintenance (ServiceInfra),
Referral and finally the measure of Purchase Decision. Needs dimension
include lifestyle, cost of transportation, journey time, job compulsions
and influence of family, friends and others. Features dimension include
product color, style, fuel consumption, torque, transmission, comfort
and stability (at high speed & bends), Sales Service and Support
dimension include service quality, spare availability, spare price, trained
service personnel, timeliness of delivery and instructions. Advertising
Media dimension include newspaper, television, internet, magazine,
showroom and radio. Price dimension include economicality,
exorbitancy, normal and high quotes. Availability of Credit Facility
include flexible of credit (installment), rate of interest, initial
commitment and ease of documentation. Infrastructure and maintenance
dimension include road condition, ease of riding, mobility and space
requirements. The individual variables of sub dimensions are
147
considered not necessary for inclusion in the model as the sub
dimension to which they belong take care of it. The measure of purchase
decision includes convenience, handling, and economics of price,
parking ease and maintenance ease are grouped as single observed
variable. After identifying a potential model that best explains the data
in terms of theory and model fit, a confirmatory factor analysis (CFA)
using structural equation modeling (SEM) was used to test the
invariance of the factorial model. All tests of model invariance begin
with a global test of the equality of covariance structures across groups
(Joreskog, 1971). The data for all groups were analyzed simultaneously
to obtain efficient estimates (Bentler, 1995). The constraints used
include, from weaker to stronger: (1) model structure, (2) model
structure and factor loadings, and (3) model structure, factor loadings,
and unique variance.
Evaluation of Model Fit
Several well-known goodness-of-fit indices were used to evaluate
model fit: the chi-square χ2
, the comparative fit index (CFI), the
unadjusted goodness-of-fit indices (GFI), the normal fit index (NFI), the
Tucker-Lewis Index (TLI), the root mean square error of approximation
(RMSEA) and the standardized root mean square error residual
148
(SRMR).
Goodness-of-fit (GOF) indices provide “rules of thumb” for the
recommended cutoff values to evaluate data-model fit. Hu and Bentler
(1999) recommend using combinations of GOF indices to obtain a
robust evaluation of model fit. The criterion values they list for a
model with good fit are CFI > 0.95, TLI > 0.95, RMSEA < 0.06, and
SRMR < 0.08 for assessing fit in structural equation modeling. Hu and
Bentler offer cautions about the use of GOF indices, and current
practice seems to have incorporated their new guidelines without
sufficient attention to the limitations noted by Hu and Bentler.
Moreover, some researchers (Beauducel & Wittmann, 2005; Fan &
Sivo, 2005; Marsh, Hau, & Wen, 2004; Yuan, 2005) believe that these
cutoff values are too rigorous and the results by Hu and Bentler may
have limited generalizability to the levels of misspecification
experienced in typical practice. In general practice, a “good enough”
or “rough guideline” approach is that for absolute fit indices and
incremental fit indices (such as CFI, GFI, NFI, and TLI), cutoff values
should be above 0.90 (0.90 benchmark) and for fit indices based on
residuals matrix (such as RMSEA and SRMR), values below 0.10 or
0.05 are usually considered adequate. All analyses were conducted
149
using AMOS 7.0 (Arbuckle & Wothke, 2006).
Figure 4.25 shows Amos’s path diagram output for the final SEM-CPD
Structural Equation model. One can see that the Affordability had needs
(eleven sub dimensional variables), credit facility (four sub dimensional
variables), attributes had price (four sub dimensional variables), features
(ten sub dimensional variables) and infrastructure (four sub dimensional
variables), Sales Support (six sub dimensional variables), External
factors had Advertising Media (six sub dimensional variables), mediated
factor referral (one sub dimensional variable) and overall possession
(Purchase Decision) had five sub dimensional variables. For the latent
variable purchase behavior, “e1” is the residual for the latent variable.
The RMSEA fit statistics for the model was 0.050, which is considered
as a most appropriate fit model (Brown and Cudeck, 1993;
Diamantopoulos and Siguaw, 2000). The path diagram shows the
referral is the mediating factor for purchase decision. The regression co-
efficient 0.66 signifies the impact of mediating factor referral on the
other dimensions towards the purchase decision-making.
150
STANDARDIZED PARAMETER ESTIMATES FOR
MEDIATED SEM – CPD (WOM) MODEL
Figure 4.25: Hypothesized mediated model specification for
AMOS graphics input
M1, V1
Needs
M2, V2
Features
M3, V3
Support
M4, V4
AdMedia
M5, V5
CreditFaci
M6, V6
ServiceInfra
M7, V7
Price
I1
Referral
I2
Purchase Decision
W1
W2
W3
W4
W5
W6
W7
W8
W9
W10
W11
W12
W13
W14
W15
0, V1
e1 1
0, V2
e2
1
C1
C2
C3
C4
C5
C6
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
C1
151
Fig 4.26: STANDARDIZED PARAMETER ESTIMATES FOR
MEDIATED SEM– CPD (WOM) MODEL
Among the dimensions of purchase decision of consumer in the SEM-
CPD (WOM) Model above, the needs sub dimension has a regression
weight of -0.02. It signifies that need for life style change, savings on
45.97, 87.76
Needs
60.66, 41.55
Features
32.98, 31.77
Support
31.57, 39.10
AdMedia
21.78, 32.36
CreditFaci
21.36, 26.29
ServiceInfra
24.32, 24.70
Price
.76
Referral
.83
Purchase Decision
.01
-.02
.01
.13
.13
.12
.39
.09
.03
.03
.03
.01
.01
.66
0, 87.76
e1 1
0, 41.55
e2
1
10.24
16.61
10.03
8.63
15.05
8.53
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
10.24
.08
152
transport, influence of family and others is quite negligible towards
purchase behavior of motorcycle consumer in study geographical area.
While the credit facility sub dimension has a regression weight of 0.12,
which reveals that the rate of interest, flexibility in repayment and ease
of documentation is the key for making purchase decision. As the study
area is a rural-urban conglomeration, the availability of credit at a
reasonable rate with the flexible terms influences purchase decision
when the affordability is broken down into sub dimensions. Individual
variables loses its significance in view of the major sub-dimensions are
themselves self explanatory.
Features dimension of the motorcycles have a less significant regression
weight of 0.01. Though the features dimension have positive impact on
purchase decision outcome, it does not have significant impact to
change the consumers’ behavior. Whereas the Infrastructure (available
for servicing) and maintenance dimension have very significant
regression weight of 0.39. It is this requirement that keep on lingering in
the minds of the consumer while purchase decision. The consumers’
attach importance good condition of roads, effortless riding, finally, the
price, the third sub dimension of attributes dimension, has a regression
weight of 0.08. The price of the product is not given importance by the
153
consumers towards purchase inclination. This attitude stems out of the
higher needs such as flexible credit, serviceability, family compulsions.
The serviceability is given more importance than other two sub
dimensions such as price and features fuel consumption in the sample
study area.
Advertising media has a regression weight of 0.13, which is less
significant yet significant considering the other dimensions such as
features, needs and price. Advertising, as empirically proved a priori,
has considerable impact on making purchase decisions. The
newspapers, radio and television has a wide reach among the
consumers. Internet advertising is yet to gain its place in the study area.
After sales support has a regression weight of 0.13, which is again
significant considering other dimensions mentioned above. Service
quality is the first and foremost requirement of the consumers as
empirically proven by Parasuraman et al. As often, the motorcycles
need maintenance, spare availability and its price influence the purchase
behavior of the consumers in the study area.
While the needs has a regression weight of 0.01, features has 0.03, Sales
Support has 0.09, advertising media has 0.03, credit facility has 0.03
and finally the infrastructure, price have regression weights of 0.01
154
respectively. It is evident from the SEM-CPD (WOM) model, that the
individual sub-dimensions except infrastructure have lesser or no
significant impact on the consumer purchase behavior. While the
individual sub-dimensions when mediated through the mediating factor
referral has a regression weight of 0.66, which is considered as strong
and sustainable impact.
Cross validations of dimensions in the SQM-HEI mediated model
Needs and Features had correlated 0.19 (Table 4.18). It reveals that
needs and features are having a significant role in changing the
consumers’ perceptions. Similarly, Features and Sales Support had
correlated 0.59, which is quite significant. Features and Support Service
have together a crucial role in molding purchase attitudes. Another
interesting correlation is between AdMedia and Price, which is 0.59.
Together, they have significant influence on the purchase decisions.
Infrastructure and maintenance needs of the consumers are highly
correlated with sales support with a positive correlation of 0.56. All the
sub-dimensions have significant correlation or degree of association
with purchase decision except the needs expressed by the consumers.
The above correlation results show that the Support Service,
Infrastructure availability along with higher level of advertising reach is
155
considered essential for a successful selling of motorcycles. Availability
of credit decides the purchase by almost 50%, it is the advertising and
price that have higher correlation among them and purchase decisions.
Therefore, the infrastructure and maintenance requirements are the most
crucial factors to be considered before launching a motorcycle for sale.
Evaluation of SQM-HEI Mediated Model
The following table, table 4.9 gives the summary of the various
measures of goodness of fit statistics and other values corresponding to
the SQM-HEI mediated structural equation model. Also the last column
in the table provides the acceptable level for the various measures of
goodness of fit statistics and other values.
TABLE 4.16: SUMMARY OF THE VARIOUS GOODNESS OF
FIT STATISTICS AND OTHER VALUES CORRESPONDING
TO THE SEM-CPD (WOM) MEDIATED STRUCTURAL
EQUATION MODEL
S.NO Measures of fit Output of
SQM-HEI
model
Acceptable
level for good
fit
1. Chi-square ( 2) at p 0.01 2.679 Highly
Significant
2. Degree of freedom (df) 1 -
3. Goodness-of-fit index (GFI) 0.934 >0.90
4. Adjusted Goodness of Fit
Index (AGFI) 0.921 >0.90
156
5. Parsimony Goodness of Fit
Index ( PGFI) 0.923 >0.90
6. Comparative fit index (CFI) 0.999 >0.90
7.
Bentler –Bonett Index or
Normed Fit Index ( NFI)
0.999 >0.90
8.
Tucker Lewis Index (TLI) or
Non-Normed Fit Index (
NNFI)
0.968 >0.90
9. Comparative fit Index ( CFI)
0.999 >0.90
10. Root mean squared error of
approximation (RMSEA)
0.050
<0.05
reasonable fit
=0.050 perfect
fit
11. Standardized Root Mean
Square Error Residual
( SRMR)
0.057 Smaller the
better
12. Non Centrality Parameter
(NCP) 1.679
Lower the
better <2
13. Non Centrality Parameter,
Lower boundary(NCPLO) 1.000 -
14. Non Centrality Parameter,
Upper boundary (NCPHI) 10.769 -
15. Parsimony adjusted NFI
(PNFI) 0.028 -
16. Parsimony adjusted CFI
(PCFI) 0.028 -
17. Minimum value of
Discrepancy ( FMIN) 0.004
Lower the
closeness of
157
Fit
18. Lower Limit of FMIN (LO90) 0.000 -
19. Upper limit of FMIN (HI90) 0.016 -
20. Browne-Cudeck Criterion
(BCC) 110.283 -
21. Akaike Information Criterion
(AIC) 108.679 -
22. ECVI 0.162
Lower the
closeness of
Fit
23. LO90 0.159 -
24. HI90 0.176 -
25. MECVI 0.164 -
26. HOELTER .05 963 <= 75 poor fit
27. HOELTER .01 1662 At least 200
Source: AMOS 15.0 output
From the above table it is revealed that all the criterions of goodness of
fit statistics and other measures of statistics are acceptable for the SEM-
CPD mediated structural equation model.
158
TABLE 4.17: Correlation Matrix of Dimensions of SEM-CPD
(WOM) Model
Needs Features Support Ad
Media Price Credit Faci
Service Infra Referral
Pur Decision
Needs 1 0.19** 0.16** 0.20** 0.21** 0.18** 0.14** 0.14** 0.14**
Features .0 1 0.59** 0.45** 0.38** 0.38** 0.43** 0.31** 0.48**
Support 0 0 1 0.45** 0.44** 0.43** 0.56** 0.26** 0.53**
AdMedia 0 0 0 1 0.59** 0.34** 0.39** 0.29** 0.48**
Price 0 0 0 0 1 0.30** 0.38** 0.24** 0.43**
CreditFaci 0 0 0 0 0 1 0.55** 0.26** 0.49**
ServiceInfra 0 0 0 0 0 0 1 0.25** 0.62**
Referral 0 0 0 0 0 0 0 1 0.40**
PurDecision 0 0 0 0 0 0 0 0 1
** Correlation is significant at the 0.01 level (2-tailed).
4.3.1 BAYESIAN ESTIMATION AND TESTING OF SQM-HEI
MEDIATED STRUCTURAL EQUATION MODEL
The table 4.10 shows the Bayesian convergence distribution of the
SQM-HEI mediated structural equation model. In this research the
researcher has adopted for the procedure of assessing convergence of
MCMC (Markov Chain Monte Carlo) algorithm of maximum
likelihood.
159
TABLE 4.18: BAYESIAN CONVERGENCE DISTRIBUTION FOR
SEM-CPD (WOM) MODEL
Mean S.E. S.D. C.S. Median
95%
Lower
bound
95%
Upper
bound
Skewn
ess
Kurtos
is Min Max Name
Regression
weights
Referral<--
ServiceInfra 0.011 0.000 0.015 1.000 0.010 -0.019 0.040 0.005 -0.015 -0.052 0.070 W1
Referral<--
CreditFaci 0.031 0.000 0.013 1.000 0.031 0.005 0.058 0.003 0.041 -0.023 0.090 W2
Referral<--
Price 0.012 0.000 0.015 1.000 0.012 -0.019 0.042 0.006 -0.004 -0.047 0.076 W3
Referral<--
AdMedia 0.034 0.000 0.011 1.000 0.034 0.013 0.055 0.037 0.059 -0.009 0.084 W4
Referral<--
Support 0.009 0.000 0.012 1.000 0.009 -0.015 0.033 0.015 -0.034 -0.046 0.063 W5
Referral<--
Features 0.026 0.000 0.009 1.000 0.026 0.009 0.043 -0.033 0.014 -0.011 0.060 W6
Referral<--
Needs 0.004 0.000 0.006 1.000 0.004 -0.007 0.016 -0.004 -0.023 -0.020 0.029 W7
Purchase
Decision<--
Referral
0.668 0.001 0.106 1.000 0.669 0.456 0.874 -0.054 0.012 0.218 1.122 W8
Purchase
Decision<--
ServiceInfra
0.384 0.000 0.042 1.000 0.384 0.301 0.465 -0.043 0.022 0.210 0.549 W9
Purchase
Decision<--
CreditFaci
0.127 0.000 0.036 1.000 0.127 0.057 0.199 0.023 -0.045 -0.006 0.292 W10
Purchase
Decision<--
Price
0.082 0.001 0.042 1.000 0.082 -0.001 0.163 -0.006 0.054 -0.093 0.265 W11
Purchase
Decision<--
AdMedia
0.135 0.000 0.029 1.000 0.135 0.077 0.192 -0.015 0.003 0.023 0.264 W12
Purchase
Decision<--
Support
0.130 0.000 0.033 1.000 0.130 0.065 0.196 0.001 -0.002 -0.005 0.269 W13
Purchase
Decisions<--
Features
0.011 0.000 0.024 1.000 0.011 -0.035 0.057 0.014 0.039 -0.077 0.120 W14
Means
160
Needs 42.011 0.007 0.443 1.000 42.012 41.142 42.875 -0.012 -0.003 40.220 43.819 M1
Features 58.394 0.006 0.379 1.000 58.394 57.641 59.136 -0.025 0.033 56.515 60.017 M2
Support 39.104 0.004 0.286 1.000 39.106 38.541 39.658 -0.027 0.025 38.042 40.395 M3
AdMedia 31.559 0.004 0.274 1.000 31.558 31.022 32.103 0.010 0.015 30.504 32.609 M4
Price 18.974 0.003 0.178 1.000 18.975 18.623 19.320 -0.016 0.002 18.172 19.677 M5
CreditFaci 21.771 0.003 0.225 1.000 21.770 21.331 22.215 0.023 0.010 20.898 22.689 M6
ServiceInfra 21.361 0.003 0.214 1.000 21.361 20.944 21.779 0.018 0.008 20.577 22.264 M7
Intercepts
Referral 1.012 0.005 0.438 1.000 1.016 0.154 1.862 -0.022 0.046 -0.869 2.707 I1
BuyingAtt 1.568 0.018 1.156 1.000 1.575 -0.712 3.837 -0.001 -0.027 -3.429 5.988 I2
Covariances
CreditFaci<-
>ServiceInfra 17.572 0.020 1.424 1.000 17.537 14.874 20.493 0.177 0.103 12.383 24.643 C1
CreditFaci<-
>Price 6.749 0.016 1.088 1.000 6.727 4.668 8.961 0.130 0.076 2.429 11.852 C2
Price<-
>AdMedia 13.547 0.021 1.394 1.000 13.510 10.921 16.361 0.141 0.022 8.686 19.719 C3
AdMedia<-
>Support 24.472 0.028 2.271 1.000 24.389 20.237 29.115 0.169 0.037 16.003 34.197 C4
Support<-
>Features 46.362 0.043 3.406 1.000 46.208 40.031 53.413 0.222 0.080 33.722 62.334 C5
Features<-
>Needs 32.636 0.075 4.550 1.000 32.563 23.996 41.793 0.119 0.027 15.779 52.701 C6
ServiceInfra<-
>Needs 8.141 0.038 2.468 1.000 8.108 3.362 13.044 0.059 0.116 -3.255 18.807 C7
ServiceInfra<-
>Features 23.477 0.032 2.306 1.000 23.421 19.160 28.199 0.183 0.097 15.137 33.595 C8
ServiceInfra<-
>Support 22.961 0.020 1.842 1.000 22.918 19.499 26.724 0.172 0.055 15.604 31.457 C9
ServiceInfra<-
>AdMedia 15.334 0.021 1.639 1.000 15.304 12.190 18.679 0.128 0.079 9.026 23.078 C10
ServiceInfra<-
>Price 8.279 0.015 1.054 1.000 8.255 6.273 10.439 0.147 0.047 4.842 12.831 C11
CreditFaci<-
>Needs 10.816 0.039 2.600 1.000 10.801 5.797 15.968 0.054 0.078 -0.084 21.184 C12
CreditFaci<-
>Features
23.056
0.034
2.397
1.000
22.991
18.537
27.880
0.179
0.140
12.978
33.878
C13
CreditFaci<-
>Support 18.791 0.029 1.840 1.000 18.759 15.283 22.563 0.138 0.068 12.439 26.723 C14
CreditFaci<-
>AdMedia 13.981 0.026 1.713 1.000 13.934 10.746 17.440 0.137 0.012 6.503 22.372 C15
Price<-
>Needs 10.405 0.024 2.103 1.000 10.379 6.335 14.589 0.077 0.090 1.652 21.312 C16
161
Price<-
>Features 13.780 0.023 1.873 1.000 13.725 10.242 17.606 0.152 0.061 5.742 22.360 C17
Price<-
>Support 12.987 0.022 1.430 1.000 12.941 10.298 15.880 0.152 0.057 7.435 19.431 C18
AdMedia<-
>Needs 16.940 0.039 3.247 1.000 16.886 10.762 23.487 0.118 0.079 4.652 30.629 C19
AdMedia<-
>Features 32.058 0.039 3.035 1.000 31.950 26.425 38.325 0.211 0.080 20.246 46.086 C20
Support<-
>Needs 13.443 0.049 3.326 1.000 13.386 7.140 20.081 0.099 0.065 -1.107 26.974 C21
Variances
Needs 130.186 0.097 7.213 1.000 129.929 116.854 145.046 0.213 0.107 104.29
2 162.154 V1
Features 97.399 0.081 5.417 1.000 97.215 87.424 108.660 0.236 0.032 79.729 120.272 V2
Support 55.365 0.037 3.067 1.000 55.268 49.702 61.694 0.232 0.072 44.434 68.878 V3
AdMedia 51.062 0.040 2.772 1.000 50.964 45.906 56.783 0.225 0.078 41.049 64.192 V4
Price 21.572 0.014 1.184 1.000 21.517 19.397 24.043 0.250 0.141 17.420 26.770 V5
CreditFaci 33.707 0.022 1.851 1.000 33.654 30.270 37.540 0.205 0.111 26.472 43.130 V6
ServiceInfra 30.145 0.017 1.682 1.000 30.083 27.015 33.548 0.210 0.104 24.100 38.971 V7
e1 2.576 0.002 0.141 1.000 2.569 2.317 2.870 0.261 0.143 2.031 3.359 V8
e2 19.071 0.015 1.058 1.000 19.043 17.094 21.251 0.186 0.040 15.217 23.836 V9
To estimate the MCMC convergence the researcher has adopted two
methods namely, convergence in distribution, convergence of posterior
summaries. The values of posterior mean accurately estimate the SQM-
HEI mediated SEM model. From the above table the highest value of
Convergence Statistics (C.S) is 1.001 which is less than the 1.002
conservative measure (Gelman et al. 2004).
162
4.3.1.1 POSTERIOR DIAGNOSTIC PLOTS OF SEM-CPD
(WOM) MEDIATED MODEL
To check the convergence of the Bayesian MCMC method the posterior
diagnostic plots are analyzed. The following figures (figure 4.27 to
4.34) shows the posterior frequency polygon of the distribution of the
parameters across the 60000 samples. The Bayesian MCMC diagnostic
plots reveals that for all the figures the normality is achieved, so the
structural equation model fit is accurately estimated.
Figure 4.27: Posterior frequency polygon distribution of the
mediating factor Referral and Service Infrastructure (W1)
163
Figure 4.28: Posterior frequency polygon distribution of the
mediating factor Referral and Credit Facility (W2)
Figure 4.29: Posterior frequency polygon distribution of the
mediating factor Referral and Price (W3)
164
Figure 4.30: Posterior frequency polygon distribution of the
mediating factor Referral and AdMedia (W4)
Figure 4.31: Posterior frequency polygon distribution of the
mediating factor Referral and Support Service (W5)
165
Figure 4.32: Posterior frequency polygon distribution of the
mediating factor Referral and Features (W6)
Figure 4.33: Posterior frequency polygon distribution of the
mediating factor Referral and Needs (W7)
166
Figure 4.34: Posterior frequency polygon distribution of the
mediating factor Referral and Purchase Decision (BuyingAtt) (W8)
To ensure that Amos has converged to the posterior distribution is a
simultaneous display of two estimates of the distribution, one obtained
from the first third of the accumulated samples and another obtained
from the last third. The following figures ( Figure 4.35 to Figure 4.37)
shows the simultaneous display of two estimates of the distribution for
the mediated factor referral with the other dimensions across 70 000
samples. From the three figures it is observed that the distributions of
the first and last thirds of the analysis samples are almost identical,
which suggests that Amos has successfully identified the important
features of the posterior distribution of the relationship between the
mediated factor referral and other quality dimensions.
167
Figure 4.35 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Service Infrastructure
168
Figure 4.36 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Credit Facility
Figure 4.37 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Price
169
Figure 4.38 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and AdMedia
Figure 4.39 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Support Service
170
Figure 4.40 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Features
Figure 4.41 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Needs
171
Figure 4.42 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Purchase Decision
The trace plot also called as time-series plot shows the sampled values
of a parameter over time. This plot helps to judge how quickly the
MCMC procedure converges in distribution. The following figures
(figure 4.54 – figure 4.61) show the trace plot of the SEM-CPD (WOM)
model for the mediated factor referral with other dimensions across
60000 samples. All the three figures exhibit rapid up-and-down
variation with no long-term trends or drifts. If we mentally break up this
plot into a few horizontal sections, the trace within any section would
not look much different from the trace in any other section. This
indicates that the convergence in distribution takes place rapidly. Hence
172
the SEM-CPD (WOM) MCMC procedure very quickly forget its
starting values.
Figure 4.43 Posterior trace plot of the SEM-CPD regression model
for the mediated factor Referral and Service Infrastructure
173
Figure 4.44 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Credit Facility
Figure 4.45 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Price
174
Figure 4.46 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and AdMedia
Figure 4.47 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Support Service
175
Figure 4.48 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Features
Figure 4.49 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Needs
176
Figure 4.50 Posterior frequency polygon distributions of the first and
last third of the samples of the SEM-CPD regression model for the
mediating factor Referral and Purchase Decision (BuyingAtt)
To determine how long it takes for the correlations among the samples
to die down, autocorrelation plot which is the estimated correlation
between the sampled value at any iteration and the sampled value k
iterations later for k = 1, 2, 3,…. is analyzed for the SEM-CPD
regression model. The figures (figure 4.16 to figure 4.18) shows the
correlation plot of the SEM-CPD model for the mediated factor Referral
with other dimensions across 60,000 samples. The three figures
exhibits that at lag 90 and beyond, the correlation is effectively 0. This
indicates that by 90 iterations, the MCMC procedure has essentially
177
forgotten its starting position. Forgetting the starting position is
equivalent to convergence in distribution. Hence, it is ensured that
convergence in distribution was attained, and that the analysis samples
are indeed samples from the true posterior distribution.
Figure 4.51 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and Service Infrastructure
178
Figure 4.52 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and Credit Facility
Figure 4.53 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and Price
179
Figure 4.54 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and AdMedia
Figure 4.55 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and Support Service
180
Figure 4.56 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and Features
Figure 4.57 Posterior correlation plot of the SEM-CPD regression
model for the mediated factor Referral and Needs
181
Even though marginal posterior distributions are very important, they do
not reveal relationships that may exist among the two parameters. The
summary table given in table 4.8 and the frequency polygons given in
the figure 4.3 to figure 4.9 describe only the marginal posterior
distributions of the parameters. Hence to visualize the relationships
among pairs of Parameters in three dimensional the following figures
(figure 4.70 to figure 4.75) provide bivariate marginal posterior plots of
the SEM-CPD model for the mediated factor Referral with other
dimensions across 60000 samples. From the three figures it reveals that
the three dimensional surface plots also signifies the interrelationship
between the mediating variable Referral with the other dimensions
Needs, Features, Support, Price, Infrastructure, AdMedia, Credit
Facility.
182
Figure 4.58: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor Referral with the Service
Infrastructure & Credit Facility
Figure 4.59: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor Referral with the Price & Credit
Facility
183
Figure 4.60: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor Referral with the Price &
AdMedia
Figure 4.61: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor Referral with the AdMedia &
Support Service
184
Figure 4.62: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor Referral with the Support
Service Infrastructure & Features
Figure 4.63: Three-dimensional surface plot of the marginal posterior
distributions of the mediating factor Referral with the Feature &
Needs
185
Figure 4.64 : Three-dimensional surface plot of the marginal
posterior distributions of the mediating factor Referral with the Needs
& Purchase Decision (Buying Attitude)
The following figures (figure 4.77 to figure 4.83) displays the two-
dimensional plot of the bivariate posterior density across 60000
samples. Ranging from dark to light, the three shades of gray represent
50%, 90%, and 95% credible regions, respectively. From the three
figures, it reveals that the sample respondent’s responses are normally
distributed.
186
Figure 4.65: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Service Infrastructure and
Credit Facility
Figure 4.66: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Price and Credit Facility
187
Figure 4.67: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Price and AdMedia
Figure 4.68: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Support Service and AdMedia
188
Figure 4.69: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Support Service and Features
Figure 4.70: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Features and Needs
189
Figure 4.71: Two-dimensional plot of the bivariate posterior density
for the regression weights Referral to Needs and Purchase Decision
(Buying Attitude)
4.4 CONCLUSION
The researcher has empirically analyzed the objectives with the help of
hypotheses and statistical tools for the study. The study reveals that the
conceptual research models are empirically proved. These findings are
interpreted in the final chapter for future research and suggestions for
gauging consumer purchase behavior to the benefit of both the
consumers and companies.
top related