Data Analysis for the Consumer Model
6.4 Consumer Questionnaire Inferential Analysis .1 Mann-Whitney U Test .1 Mann-Whitney U Test
6.4.3.1 Factor Analysis Test for All the Home Preference Variables Test Question Test Question
What is the highest consumer preference factor in the consumer questionnaire?
The Reliability
In Table 6.18, Cronbach’s alpha coefficient is above .7 for all the factors, which indicates that our sample is reliable (Field, 2013).
Table 6-18 Component reliability coefficients
The location and specification details factor 13 - .898
The external design factor 8 - .857
The internal design factor 11 - .890
The district and street lot 6 - .880
The Kaiser-Meyer-Olkin Value
In Table 6.19, the KMO is above .6 for the questionnaire, which indicates that our sample reached the required standard (Field, 2013).
Table 6-19 KMO and Bartlett's Test
In Table 6.20, each component is set according to a series of correlations between different preferences. Thus, it shows how correlated a preference could be to other factors. The first column shows initial eigenvalues related to eigenvalue of the correlation matrix and indicates which components of the table remain in analysis. To carry out the factor analysis, only components with eigenvalues of more than 1 are selected and those with eigenvalues of less
Kaiser-Meyer-Olkin Measure of Sampling Adequacy for consumer questionnaire
.958 Values of 0.5 are acceptable.
Values between 0.5 and 0.7 are good. Values between 0.7 and 0.8 are great. Values above 0.8 are superb.
157 than 1 are excluded. The initial and rotated eigenvalues are used to confirm the variation explained by each preference’s components. Lower values indicate that the contribution to the explanation of the variances in the set of the preferences survey attributes is minimal.
Table 6-20 Total variance explained
Component Initial Eigenvalues Rotation Sums of Squared
Loadings
Total % of
Variance
Cumulativ e %
Total % of Variance
Cumulativ e %
1 15.302 40.269 40.269 5.469 14.391 14.391
2 2.893 7.613 47.882 4.965 13.065 27.457
3 1.897 4.992 52.875 4.641 12.212 39.669
4 1.473 3.876 56.751 2.321 6.108 45.777
5 1.243 3.271 60.023 1.983 5.219 50.996
6 1.101 2.897 62.920 1.935 5.092 56.089
For example, the initial eigenvalue of the first financial preference in Table 6.20 is 15.302.
Hence, the proportion of the total test variance accounted for by the first factor is 40.2% (the figure given in % in the variance column). In this analysis for the Principal Component Analysis of occurrence, just six components carry eigenvalues of 1 and more, and account for 62.5% of the variance, as shown in the cumulative % column. This means that the selected six components present 62.5% of the whole variance. Therefore, the six components can be considered as representative of all consumer preferences. Another way of presenting the most important factors of a study is through a scree plot of data, shown here in Figure 6.9.
Figure 6-9 Scree plot for all the home preference variables
158 The purpose of a scree plot is to provide a graphical picture of the eigenvalue for each component extracted in SPSS. As the figure shows, the slope of the scree is levelling off, while moving towards components with eigenvalue less than 1. The point of interest is defined between components 3 and 2, where the figure curve connects to the points, starting to flatten out and become horizontal.
From principal component analysis, six components that have an eigenvalue of more than 1 are selected. The next phase is the extraction of a rotated component matrix in order to find out which consumer preferences are contributing the highest level of influence, as shown in Table 6.21. The matrix loading score presented shows the degree of influence of each consumer preference in the survey. This factor loading tells us about the relative contribution that a variable makes to a factor. Most variables have high loadings on the most important factors, and fewer loadings on other factors. It is recommended to interpret factor loadings with an absolute value greater than 0.3. From Table 6.21, it can be seen that the preference Safety of the neighbourhood (LF3 .800) has a greater influence on component 1 compared to other components, whereas the preference Quality of the building (SPF1 .771) has more influence on component 2 in relation to other components, and Lot size (EXF4 .715) has more influence on component 3 in relation to other components.
159 Table 6-21 Rotated factor matrixa
The variables Components
1 2 3 4 5 6
Safety of the neighbourhood LF3 Quality of the neighbourhood LF2 Cleanliness of the neighbourhood LF4 Fresh air in location LF12
Soil of land LF13 Materials used in the building SPF4 Cold and hot system SPF6
Number of building storeys EXF8 Bigger home even if it is far from a city EXF6
Garden EXF3 Aesthetics EXF1
Number of parking spaces EXF7
.715 Near to public transport LF7
Service in the neighbourhood LF6 The environmentally friendly nature of the building SPF3 reduced list of preferences, which is highly manageable without losing a large amount of data.
By applying factor analysis and data reduction in this survey, the 38 consumer preferences in the questionnaire were reduced to six components, as shown in Table 6.22. It identifies consumer preferences, which are groupings of preferences from the 38 initially identified.
Factor analysis occurs whereby financial consumer preference components with eigenvalues in excess of 1 are extracted, leaving a total of six. The table below reports both the variance
160 explained by these retained factors from the total variance of all 38 consumer preference factors and the factor loadings (and their variances) following varimax rotation (an orthogonal rotation method) in which the variance of each of the factors is maximised.
Table 6-22 New group of variables
Component Rotated Component Matrixa Code Extracted
eigenvalue Fresh air in location LF12
Soil of land LF13
Design of and details in home (DHD)
Quality of the building SPF1 Materials used in the building SPF4 Cold and hot system SPF6
Number of building storeys EXF8 Bigger home even if it is far from a city EXF6
Garden EXF3 Aesthetics EXF1
Number of parking spaces EXF7
EDP1 of the building and services in the neighbourhood (ESN)
Near to public transport LF7 Services in the neighbourhood LF6 The environmentally friendly nature of the building SPF3
ESN1 ESN2 ESN3
1.101 5.092
Component 1 (Neighbourhoods Quality and Needs NQN)
This component has an eigenvalue of 15.302. This component covered 10 different preferences; the Safety of the neighbourhood (NQN1) (.800) got the highest score. Name of district (NQN10) was lowest (.388).
161 Component 2 (Design and Homes Details DHD)
This component has an eigenvalue of 2.893. This component covered nine different preferences; Quality of the building (DHD1) (.771) got the highest score. Privacy (DHD9) was lowest (.399).
Component 3 (External Design Preferences EDP)
This component has an eigenvalue of 1.897. This component covered seven different preferences; Lot size (EDP1) (.715) got the highest score. Number of parking spaces (EDP2) was lowest (.510).
Component 4 (Extra Rooms and Internal Design Preferences EIP)
This component has an eigenvalue of 1.473. This component covered three different preferences; Size of windows (EIP1) (.585) got the highest score. Facility room (EIP3) was lowest (.459).
Component 5 (Spaciousness and Number of Rooms SNR)
This component has an eigenvalue of 1.243. This component covered four different preferences; Number of bedrooms (SNR1) (.635) got the highest score, whilst the Space for family (SNR4) was lowest (.391).
Component 6 (Environmentally friendly nature of the building and Services in the Neighbourhood ESN)
This component has an eigenvalue of 1.101. This component covered three different preferences; Near to public transport (ESN1) (.663) got the highest score, whilst the environmentally friendly nature of the building (ESN3) was lowest (.440).
162 6.4.3.1.1 Consumer Questionnaire Model with all the Variables Together (Model A) This study identified and ranked the indicators of consumer preferences according to their level of significance, based on consumers’ views. In Table 6.23, each component is set according to a series of correlations between different preferences.
Table 6-23 The new group of variables based on consumers’ views Components Initial Eigenvalues
% of Variance
Extraction Sums of Squared Loadings % of Variance
Rotation Sums of Squared Loadings % of Variance
1 40.269 39.243 14.391
2 7.613 6.553 13.065
3 4.992 3.876 12.212
4 3.876 2.697 6.108
5 3.271 2.015 5.219
6 2.897 1.704 5.092
The above table shows that the components after the factor analysis for the 38 variables are in six different groups. The consumer model shows the regrouping of all the variables after the factor analysis was conducted. It also shows the different components with the weight of each group. After the reduction of the variables, the model shows the priority stage for buyers. This factor loading tells us about the relative contribution that a variable makes to a factor. Most variables have high loadings on the most important factors, and fewer loadings on other factors.
It is recommended to interpret factor loadings with an absolute value greater than 0.3 (Field, 2013).
From Table 6.24 it is apparent that the preference variable Safety of the neighbourhood (NQN1 .800) has greater influence on component 1 compared to other components, whereas the preference Quality of the building (DHD1 .771) has more influence on component 2 in relation to other components, and Lot size (EDP1 .715) has more influence on component 3 in relation to other components.
163 Table 6-24 The new groups of components based on consumers’ views
Component Rotated Component Matrixa Code Factor loading Materials used in the building Cold and hot system The sustainability of the building
ESN1
Moreover, Figure 6.10 shows the model and the component codes with circles showing the size of each one.
164
Coding Components sizes Figure 6-10 The components and coding
165 Model (A) in Figure 6.11 shows the consumer priorities split into groups, starting with Neighbourhood quality and needs (NQN), which includes nine variables. The second priority is Design and home details (DHD), which also includes nine variables. The third priority is External design preferences (EDP), which includes six variables. Fourth is the Extra rooms and internal design preferences (EIP), which includes three variables, whilst the fifth priority is Spaciousness and number of bedrooms (SNR), which includes three variables. The final priority is environmentally friendly nature of the building and services in the neighbourhood (ESN), which includes three variables.
Figure 6-11 Model shows all the variables group of variables from the consumer questionnaire
166 6.4.3.2 Factor Analysis Test for Each Home Preference Variable
Test Question
What are the highest consumer preferences for each factor in the consumer questionnaire?
The Reliability
In Table 6.25, Cronbach’s alpha coefficient is above .7 for each factor, Location, Eternal design, Internal design and Home specification details.
Table 6-25 Reliability Statistics
The Kaiser-Meyer-Olkin Value
In Table 6.26, the KMO is above .6 for all the factors, which indicates that our sample has a great result (Field, 2013).
Table 6-26 KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy for the Location .923
Recommends
Kaiser-Meyer-Olkin Measure of Sampling Adequacy for the External design
Kaiser-Meyer-Olkin Measure of Sampling Adequacy for the Internal design
Kaiser-Meyer-Olkin Measure of Sampling Adequacy for home specification details
Component Cronbach's Alpha N of Items Deleted items When the alpha is 0.7 or higher, it means
167 6.4.3.2.1 Location factor
In Table 6.27, each component is set according to a series of correlations between different preferences. Thus, it shows how correlated a preference could be to other factors. The first column, Initial Eigenvalues, relates to eigenvalue of the correlation matrix and indicates which components of the table remain in analysis. To carry out the factor analysis, only components with eigenvalues of more than 1 are selected and those with eigenvalues of less than 1 are excluded. The initial and rotated eigenvalues are used to confirm the variation explained by each preference’s components. Lower values indicate that the contribution to the explanation of the variances in the set of the preferences survey attributes is minimal.
Table 6-27 Total variance explained
Components Initial Eigenvalues Rotation Sums of Squared Loadings Total % of
Variance
Cumulative
%
Total % of Variance
Cumulative
%
1 6.448 49.602 49.602 3.735 28.732 28.732
2 1.237 9.513 59.115 2.021 15.547 44.279
3 1.088 8.371 67.486 1.793 13.792 58.071
For example, in Table 6.27 the initial eigenvalue of the first location preference is 6.448. Hence, the proportion of the total test variance accounted for by the first factor is 49.6% (the figure given in % of variance column). In this analysis, just three components carry eigenvalues of 1 and more, and account for 65.4% of the variance, as shown in the cumulative % column.
Therefore, the three components can be considered as representative of 13 consumer preferences. The following scree plot of data is another way of presenting the most important factors of the study.
168 Figure 6-12 Scree plot for the location factor
As Figure 6.12 shows, the slope of the scree is levelling off, while moving towards components with an eigenvalue of less than 1. The point of interest is defined between components 1 and 2, where the figure curve connects to the points, starting to flatten out and become horizontal.
From principal component analysis, three components that have an eigenvalue of more than 1 are selected. The next phase is the extraction of a rotated component matrix for finding out which consumer location preferences are contributing the highest level of influence, as shown in Table 6.28. The matrix loading score presented shows the degree of influence of each consumer location preference in the survey. This factor loading tells us about the relative contribution that a variable makes to a factor. From Table 6.28 below, it can be seen that Safety of the neighbourhood (LF3; 0.894) has greater influence on component 1 compared to other components, whereas the preference Design of district (LF11; 0.713) has more influence on component 2 in relation to other components, and Near to public transport (LF7; 0.645) has more influence on component 3 in relation to other components.
169 Table 6-28 Rotated factor matrixa
The variables Components
1 2 3
Safety of the neighbourhood LF3 Cleanliness of the neighbourhood LF4 Quality of the neighbourhood LF2 Fresh air in location LF12 Soil of land LF13 Near to public transport LF7
Service in the neighbourhood LF6 Closeness to school LF5 reduced list of preferences, which is highly manageable without losing a large amount of data.
By applying factor analysis and data reduction in this survey, the 13 consumer location preferences in the questionnaire were reduced to three components, as shown in Table 6.29. It identifies consumer location preferences, which are groupings of preferences from the 13 initially identified. Factor analysis for consumer location preference components with eigenvalues in excess of 1 are extracted, leaving a total of three. The table reports both the variance explained by these retained factors from the total variance of all 13 location factors as well as the factor loadings (and their variances) following varimax rotation in which the variance of each of the factors is maximised.
Table 6-29 New group of variables
Components Rotated Component Matrixa Code Extracted eigenvalue Quality of the neighbourhood LF2 Fresh air in location LF12 Soil of land LF13 Service in the neighbourhood LF6 Closeness to school LF5
LNLS1 LNLS2 LNLS3
1.088 13.792
170 Component 1: The Neighbourhood Quality and Accessibility (LNQA)
This component has an eigenvalue of 6.448. This component covered six different preferences;
Safety of the neighbourhood (LNQA1) (.894) got the highest score, whilst the Accessibility of location (LNQA6) was lowest (.580).