Segmenting markets - Essay Example

? Discussion on Factor Analysis and Cluster Analysis [Supervisor’s Discussion on Factor Analysis and Cluster Analysis 1. Factor Analysis: Factor Analysis is a statistical tool that helps in understanding variables, or factors among the correlated and observed variables. It is mostly used to determine the variations in a larger number of groups by identifying the small number of factors within the large number of a particular group (Gorsuch, 1983). The first step is to select a method for factor analysis. There are two methods while conducting a factor analysis which are known as exploratory factor analysis and confirmatory factor analysis. Exploratory factor analysis is a technique for factor analysis which is often used for a larger set of variable. If the goal of a researcher is to identify the relationship with the measured variable then he should opt for the exploratory factor analysis. This method would help a researcher if no prior assumption or theory is made on the relation of the factors. However, in confirmatory factor analysis the variables are determined with the relation of prior assumptions or theory which aims to see if it meets the expectation as it was predicted. This method is selected when a social research is conducted. The simplification of a factor analysis is often interpreted by a method known as rotation which makes the output more understandable for the researcher. Rotation is the next step involved in factor analysis. The pattern of loadings in rotation works differently on each variable, the loading of each variable that has extracted factors are maximized while it minimizes the loading for other factors. There are five methods of rotation in which varimax, equamax and quartimax are orthogonal rotations whereas promax and direct oblimin are oblique rotations. The rotation of a particular variable mostly depends on a person if he thinks that the factors that are underlined should be related or not. If factors are considered to be independent then the author suggests that a person should use orthogonal rotation methods whereas if factors have chances to correlate then it is required to adopt direct oblimin which is an oblique rotation (Gorsuch, 1983). Labeling a factor is the next step which is an art of segmentation in which a factor is named which best describes the particular factor. The most common and appropriate technique is to name the highly ranked or the top one or two factors on the list. It is labeled on the basis of its characteristics, for example factor one can be labeled as price conscious whereas factor two can be labeled as quality conscious (Rummel, 1970). In the final step, interpretation is been made to assess the validity of factors outlines previously. In this step, four types of validity methods are used namely, content validity, concurrent validity, predictive validity, and construct validity. Content validity intends to measure the intended or the desired area which is associated with the theme of the research. Construct validity intends to assess the factors which involve the testing of hypothesis to which the researcher was trying to measure. Concurrent validity is the method in which scores are correlated with some other variables and then it is justified. In predictive validity method, a test is used to determine or justifying the theoretical outcomes which were expected. These steps are used for the purpose of finding a correlation between variables (Gorsuch, 1983). 2. Cluster Analysis: Cluster analysis is a statistical technique which helps in assorting of ‘mountain’ of information into neat files by forming a cluster or a group in which variables are similar to one another. It helps in creating subgroups which becomes more manageable than previously dealing with the individual variable. Similar to factor analysis, it is used to determine the relationship of variables between other variables. The first step involved in cluster analysis is the assigning of similar variables to their respective clusters (Stahl, Leese, Landau, & Everitt, 2011). Variables that have a similar patter or homogenous characteristics will be assigned to particular clusters. The cluster will determine that the variables that are inside a particular cluster will have similar characteristics. This process is also considered as a marketing strategy in which market segmentation is carried out that has similar needs and wants (Romesburg, 1984). In the next step, selection of cluster analysis is measured. A method which is involved in the cluster is hierarchical clustering. Hierarchical clustering is the process of finding the homogenous cluster which starts from many clusters each identified as a separate cluster (Sarstedt, 2011). These clusters are then combined and reducing the number of clusters and is left with just one cluster in the end. The aim is to convert clusters into a large cluster with the help of similarities between them. In the next step, distance is measured between clusters which can be accomplished by many ways. The distances are measured with the assistance of a ruler which is known as squared Euclidean distance. The Ward’s method is the other technique which uses the variance approach in order to find the distance between clusters. The other method is k-means clustering which is used in the situation when the information is unknown for the number of clusters and on what basis it has characterized (Romesburg, 1984). In the next step, the numbers of clusters in a particular data set which is selected by various methods such as the elbow method and the k-means algorithm. Determining the quantity of a cluster is the most common issue in cluster analysis which becomes the source of creating cluster problems. The elbow method is a way of determining the numbers of clusters which focuses on the percentage of variance present in a cluster. The cluster is chosen on the basis that if another cluster is added to a particular cluster. Firstly it would show more information but gradually it would decline and it would create a particular angle in the graph. The point would show the number of clusters that should be considered in a data set (Romesburg, 1984). In the next step, clusters are specified with a name on the basis of their characteristics or similarity of its variables. In the next step profiling of clusters are carried out. The set of a mean value is known as the profile of a cluster which is performed in two ways either by comparing the derived cluster means or comparing the derived means against a class. It is required to generate the mean of a cluster which defines cluster and then ANOVA test is performed to find out the difference between the clusters mean with other clusters. If tests are significant then it means that the groups differ. However, if tests are not significant, then it means that it still differ on the basis of individual variables which defines a cluster (Das, Abraham, & Konar, 2009). Finally in the last step, assessing of validity of clusters is determined. Significant groups are selected in a data set whose member have common characteristics or have a high degree of similarity. The purpose is to find clusters that fit with the data set. There are three approaches to cluster validity which are known as external criteria, internal criteria and relative criteria. In external criteria, the results are evaluated on the basis of the structure which was previously specified and reflects the intuition of a researcher. In internal criteria, results are evaluated on the grounds of vectors of the data set. In relative criteria, the evaluation of cluster structure is carried out by comparing it with the other clustering schemes but with different parameter values (Halkidi, Batistakis, & Vazirgiannis, 2001). 3. Conducting Factor Analysis In order to perform factor analysis the data needs to be quantitative and it should have a bivariate normal distribution for each pair of variables. The descriptive statistics of 10 attributes is provided in the following which indicates mean and standard deviation for each of variables included in the questionnaire. The difference in N for each attribute is due to missing values for responses collected. Descriptive Statistics N Mean Std. Deviation Walking distance 1074 2.9218 1.07822 Parking 1077 1.8774 .82357 Short waiting times 1100 1.6818 .75511 Modern facilities 1093 1.7823 .78690 Staff wont talk 1099 1.4049 .70181 Number of doctors work there 1091 2.1595 .90475 Small practice 1075 3.2912 .90615 Comfortable atmosphere 1099 1.7953 .67274 Bulk bill 1094 1.8382 .94514 Staff friendly 1097 1.5032 .58434 Valid N (listwise) 1000 First step that is performed for factor analysis is descriptives which results in the R-matrix and also indicates the significance level for each of the correlations in the R-matrix between variables selected for investigation. In this case, there are 10 attributes indicating the possible factors affecting decisions of patients to select medical centres/doctors' surgeries. The collinearity is tested out by selecting the Determinant of this matrix which is then compared with the value 0.00001. Furthermore, KMO and Barlett’s test of sphericity (KMO) which is then compared with the value 0.5 to suggest whether the same is adequate or not. The results from SPSS are provided in the following: Correlation Matrixa Walking distance Parking Short waiting times Modern facilities Staff wont talk Number of doctors work there Small practice Comfortable atmosphere Bulk bill Staff friendly Correlation Walking distance 1.000 .258 .162 .195 .069 .137 .165 .233 .270 .181 Parking .258 1.000 .314 .268 .232 .239 .021 .289 .162 .258 Short waiting times .162 .314 1.000 .369 .293 .153 .030 .275 .268 .328 Modern facilities .195 .268 .369 1.000 .297 .368 -.082 .322 .182 .285 Staff wont talk .069 .232 .293 .297 1.000 .206 -.015 .334 .149 .365 Number of doctors work there .137 .239 .153 .368 .206 1.000 -.336 .185 .077 .209 Small practice .165 .021 .030 -.082 -.015 -.336 1.000 .046 .118 .004 Comfortable atmosphere .233 .289 .275 .322 .334 .185 .046 1.000 .225 .515 Bulk bill .270 .162 .268 .182 .149 .077 .118 .225 1.000 .322 Staff friendly .181 .258 .328 .285 .365 .209 .004 .515 .322 1.000 Sig. (1-tailed) Walking distance .000 .000 .000 .012 .000 .000 .000 .000 .000 Parking .000 .000 .000 .000 .000 .246 .000 .000 .000 Short waiting times .000 .000 .000 .000 .000 .163 .000 .000 .000 Modern facilities .000 .000 .000 .000 .000 .004 .000 .000 .000 Staff wont talk .012 .000 .000 .000 .000 .310 .000 .000 .000 Number of doctors work there .000 .000 .000 .000 .000 .000 .000 .006 .000 Small practice .000 .246 .163 .004 .310 .000 .067 .000 .446 Comfortable atmosphere .000 .000 .000 .000 .000 .000 .067 .000 .000 Bulk bill .000 .000 .000 .000 .000 .006 .000 .000 .000 Staff friendly .000 .000 .000 .000 .000 .000 .446 .000 .000 a. Determinant = .175 In the above table, the upper half indicates values of the Pearson correlation coefficient between all selected attributes and the lower half indicates the one-tailed significant of these correlation coefficients. The attribute of ‘small practice’ has majority of significance values greater than 0.05. The value of determinant is .175 which is greater than 0.00001 as indicated above implying that the multicollinearity of data is not a problem. Moreover, by examining the coefficients in the above table it could be stated that none of correlation coefficients are greater than 0.9 which implies that the analysis does not require elimination of any attributes at this stage. The KMO statistics results are presented in the following which indicate adequacy of the sampling as the value of KMO is .779 is between 0.7 and 0.8 which is considered as good level for appropriateness of the data (Kaiser, 1974). Furthermore, Barlett’s test of sphericity indicates significance value p less than 0.001 which also confirms the appropriateness of the factor analysis. KMO and Bartlett's Test Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .779 Bartlett's Test of Sphericity Approx. Chi-Square 1820.331 df 45 Sig. .000 The table below derived indicates Eigenvalues before and after extraction and rotation. Before extraction the results show 10 linear components (factors). Factor 1 explains 30.504% of total variance. After extraction factors are extracted for which eigenvalues are greater than 1 and the remaining factors are discarded. Moreover, after the rotation which is aimed at optimizing the factor structure the percentage of variance associated with Factor 1 has reduced and that of Factor 2 has increased. Total Variance Explained Component Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative % 1 3.050 30.504 30.504 3.050 30.504 30.504 2.993 29.926 29.926 2 1.416 14.165 44.669 1.416 14.165 44.669 1.474 14.743 44.669 3 .999 9.988 54.657 4 .846 8.460 63.116 5 .808 8.078 71.194 6 .704 7.044 78.238 7 .652 6.517 84.755 8 .573 5.730 90.485 9 .507 5.065 95.550 10 .445 4.450 100.000 Extraction Method: Principal Component Analysis. The next table indicates commonalities before and after extraction. Since the principal component analysis assumes initial variances to be equal for all data therefore all commonalities have a value of 1 in the table (Field, 2005). The column Extraction indicates the common variance which is found in the data collected. The highest variation is associated with ‘Small practice’ i.e. 67% and next is that associated with ‘Number of doctors work there’ i.e. .60.2%. The average of commonalities is .4476 (4.476/10). Communalities Initial Extraction Walking distance 1.000 .320 Parking 1.000 .331 Short waiting times 1.000 .390 Modern facilities 1.000 .472 Staff wont talk 1.000 .345 Number of doctors work there 1.000 .602 Small practice 1.000 .670 Comfortable atmosphere 1.000 .471 Bulk bill 1.000 .375 Staff friendly 1.000 .491 Extraction Method: Principal Component Analysis. The following tables show the component matrix before rotation which suppresses the loadings having value less than 0.1. The results show some of the factors are discarded including ‘Parking’, ‘Short waiting times’ and ‘Staff friendly’ which implies that the variance in each variable are explained by the remaining factors. Component Matrixa Component 1 2 Walking distance .435 .362 Parking .575 Short waiting times .621 Modern facilities .643 -.242 Staff wont talk .578 -.104 Number of doctors work there .468 -.619 Small practice .819 Comfortable atmosphere .679 .103 Bulk bill .484 .376 Staff friendly .696 Extraction Method: Principal Component Analysis. a. 2 components extracted. Rotated Component Matrixa Component 1 2 Walking distance .495 -.273 Parking .568 Short waiting times .623 Modern facilities .586 .359 Staff wont talk .548 .211 Number of doctors work there .343 .696 Small practice .142 -.806 Comfortable atmosphere .686 Bulk bill .546 -.278 Staff friendly .699 Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 3 iterations. At the end of the above stage, there are two factors which have been extracted. This is not appropriate as per Kaiser (1974) who suggested minimum of 4 components however it is not possible because there are very few variables. Furthermore, the point of inflexion on the curve is indicated in the following. This also suggests that the scree plot tails off after 3 factors therefore retention of 3 components seems sufficient. 4. Conducting Cluster Analysis The first step in the cluster analysis is to decide upon the number of clusters based on the principal component scores obtained and updated after the completion of the factor analysis. For this purpose, the hierarchal cluster has been used for determining the number of cases to be selected for cluster analysis. By applying Ward’s method the following results are achieved from hierarchal cluster is obtained. Some of the extracts of the agglomeration schedule are provided in the following. From the agglomeration schedule t can be observed that biggest in the distance coefficient is at 997. The total number of cases is 1000 and using step of elbow of 997 the number of cases can be obtained as 1000-997=3 cases. Case Processing Summarya,b Cases Valid Missing Total N Percent N Percent N Percent 1000 90.6 104 9.4 1104 100.0 a. Squared Euclidean Distance used b. Ward Linkage Ward Linkage Agglomeration Schedule Stage Cluster Combined Coefficients Stage Cluster First Appears Next Stage Cluster 1 Cluster 2 Cluster 1 Cluster 2 1 903 1104 .000 0 0 42 2 198 1102 .000 0 0 447 3 603 1100 .000 0 0 101 4 1082 1092 .000 0 0 249 5 856 1087 .000 0 0 50 6 1024 1086 .000 0 0 18 ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. ……….. 990 8 42 344.359 982 969 994 991 5 105 372.474 977 974 993 992 2 11 426.874 980 987 998 993 5 10 483.203 991 988 996 994 8 17 559.753 990 989 997 995 1 4 642.361 985 981 997 996 5 6 764.340 993 986 998 997 1 8 1004.342 995 994 999 998 2 5 1354.833 992 996 999 999 1 2 1959.501 997 998 0 After deciding the number of clusters the next step in the cluster analysis is to specify names for the clusters on the basis of their characteristics. This is done by examining the component matrix obtained from the factor analysis and examining the values. Cluster#1: Likes Short Waiting Times Cluster#2: Likes Small Practice and Cluster#3: Likes Modern Facilities. Repeating the cluster analysis using K-means method and defining the number of clusters as 3 the following results are obtained. Initial Cluster Centers Cluster 1 2 3 gender 1 1 0 age 2.00 4.00 1.00 education 3.00 1.00 1.00 Aboriginal or TSI .00 .00 .00 Income 2.00 1.00 3.00 Adult males 1.00 .00 3.00 Adult females 1.00 .00 2.00 Children 6.00 .00 .00 Do you take other members of your household to visit a GP 1.00 .00 .00 Health status 2.00 1.00 5.00 Iteration Historya Iteration Change in Cluster Centers 1 2 3 1 3.063 2.575 2.988 2 .470 .298 .487 3 .153 .162 .286 4 .083 .265 .310 5 .080 .108 .080 6 .072 .033 .043 7 .068 .041 .025 8 .018 .031 .032 9 .014 .031 .030 10 .000 .007 .008 a. Iterations stopped because the maximum number of iterations was performed. Iterations failed to converge. The maximum absolute coordinate change for any center is .005. The current iteration is 10. The minimum distance between initial centers is 6.557. Final Cluster Centers Cluster 1 2 3 gender 1 1 1 age 1.88 2.41 2.85 education 1.97 2.09 1.39 Aboriginal or TSI .04 .00 .02 Income 2.28 2.25 1.71 Adult males 1.02 .98 .95 Adult females 1.03 1.07 .97 Children 2.65 .23 .15 Do you take other members of your household to visit a GP .92 .50 .47 Health status 2.36 1.78 3.69 And finally the following table indicates the number of cases in each of the 3 clusters. Number of Cases in each Cluster Cluster 1 232.000 2 397.000 3 364.000 Valid 993.000 Missing 111.000 From the ANOVA table provided the variations observed within clusters and between groups have been indicated. Furthermore from the table below it can be indicated that Gender, Income and Health appear to have a significant impact on the decision of individuals to select their surgeries/doctor clinics. ANOVA Sum of Squares df Mean Square F Sig. gender Between Groups 2.223 2 1.111 4.706 .009 Within Groups 233.580 989 .236 Total 235.802 991 age Between Groups 1.967 2 .984 1.332 .264 Within Groups 733.433 993 .739 Total 735.401 995 education Between Groups 5.324 2 2.662 3.141 .044 Within Groups 834.769 985 .847 Total 840.092 987 Aboriginal or TSI Between Groups .042 2 .021 .639 .528 Within Groups 32.422 984 .033 Total 32.464 986 Income Between Groups 18.532 2 9.266 17.989 .000 Within Groups 492.428 956 .515 Total 510.959 958 Adult males Between Groups .762 2 .381 1.180 .308 Within Groups 322.013 997 .323 Total 322.775 999 Adult females Between Groups .396 2 .198 .710 .492 Within Groups 278.483 997 .279 Total 278.879 999 Children Between Groups .216 2 .108 .074 .929 Within Groups 1453.423 997 1.458 Total 1453.639 999 Do you take other members of your household to visit a GP Between Groups 1.392 2 .696 2.905 .055 Within Groups 233.846 976 .240 Total 235.238 978 Health status Between Groups 28.255 2 14.128 10.551 .000 Within Groups 1326.941 991 1.339 Total 1355.196 993 Reference List Das, S., Abraham, A., & Konar, A. (2009). Metaheuristic Clustering. Heidelberg: Springer. Field, A. (2005). Factor Analysis Using SPSS. Retrieved September 13, 2012, from Statistic Shell: http://www.statisticshell.com/docs/factor.pdf Gorsuch, R. (1983). Factor Analysis. New Jersey: Routledge. Halkidi, M., Batistakis, Y., & Vazirgiannis, M. (2001). On Clustering Validation Techniques. Journal of Intelligent Information System , 107-145. Kaiser, H. F. (1974). Image Analysis. In C. W. Harris, Problems in Measuring Change. Madison: University of Winconsin. Romesburg, C. (1984). Cluster Analysis For Researchers. North Carolina: Lulu.com. Rummel, R. (1970). Applied Factor Analysis. New York: Northwestern University Press. Sarstedt, M. (2011). A Concise Guide to Market Research: The Process, Data, and Methods Using IBM. Heidelberg: Springer. Stahl, D., Leese, M., Landau, S., & Everitt, B. (2011). Cluster Analysis. London: John Wiley & Sons. Reference List Das, S., Abraham, A., & Konar, A. (2009). Metaheuristic Clustering. Heidelberg: Springer. Gorsuch, R. (1983). Factor Analysis. New Jersey: Routledge. Halkidi, M., Batistakis, Y., & Vazirgiannis, M. (2001). On Clustering Validation Techniques. Journal of Intelligent Information System , 107-145. Romesburg, C. (1984). Cluster Analysis For Researchers. North Carolina: Lulu.com. Rummel, R. (1970). Applied Factor Analysis. New York: Northwestern University Press. Sarstedt, M. (2011). A Concise Guide to Market Research: The Process, Data, and Methods Using IBM. Heidelberg: Springer. Stahl, D., Leese, M., Landau, S., & Everitt, B. (2011). Cluster Analysis. London: John Wiley & Sons. Read More