Understanding of factor analysis describes us a method for investigating whether a number of variables of interest are linearly related to a smaller number of unobservable factors. It determines the strength of relationship between each factor and each observed measure. By the exercises to comprehend factor analysis we derive that it is a statistical tool to account for variability in a set of measured items in terms of a smaller numbers factors. There are several ways to conduct factor analysis and the choice of method depends on many things. We have the options pertaining to the retention of factors. The choice of either selexting factors with eigen values greater than a user- specified value or retaining a fixed number of factors. By looking at the scree plot and the Eigen values over 1 will lead us to retain the same number of factors then continue with analysis.
The objective of the factor analysis is to objectively detect natural groupings of variables. It also aims to extract quantitative information from large matrices using objective statistical criteria. It reduces the redundant data in the list.
The software uses the sample size from which communalities after extraction should probably be above 0.5. The system then finds a factor solution to a set of variables. When the first factor solution does not reveal the hypothesized structure of the loadings, it is customary to apply rotation in an effort to find another set of loadings that fit the observations equally well but can be more easily interpreted. The most widely used of these is the varimax criterion. It seeks the rotated loadings that maximize the variance of the squared loadings for each factor; the goal is to make some of these loadings as large as possible, and the rest as small as absolute value. It encourages the detection of factors each of which is related to few variables. It discourages the detection of factors influencing all variables.
The interpretability of factors can be improved through rotation. Rotation maximizes the loading of each variable on one of the extracted factors whilst minimizing the loading on all other factors. Rotation works through changing the absolute values of the variables whilst keeping their differential values constant.
The scores factor allows one to save factor scores for each subject in the data editor. It reates new column for each factor extracted and then places the factor score for each subject within that column. These scores can then be used for further analysis, or simply to identify groups of subjects who score highly on particular factors. Another feature provided by SPSS is options which helps use to list variables by size.
To analysis the output in SPSS software, the R matrix shows the Pearson correlation coefficient between all pairs of questions whereas the bottom half contains the one tailed significance of these coefficients. We can use this matrix to check the pattern of relations. The significance values details provides the confidence level or the reliability of the data. If any data of significance value more than 0.9 is found, then one should be aware that a problem could arise because of singularity in the data which demands for the check of determinants of the correlation matrix and if necessary eliminate one of the two variables causing the problem. Generally, the data is considered based on the null hypothesis proven right or wrong. Based on the acceptance or rejection of null hypothesis, further analysis is done on the information obtained.
SPSS lists the Eigen values associated with each linear component before extraction, after extraction and after rotation. The eigen values associated with each factor represent the variance explained by that particular linear component and it also displays the eigen values in terms of the percentage of variance explained.
Another output table displays the communalities before and after extraction. The principal component analysis works on the initial assumption that all variance are common, therefore before extraction he communalities are 1. Another way to look at these is in terms of the proportion of variance explained by the underlying factors. The output also explains the component matrix before rotation. This matrix contains loadings of each variable onto each factor.
Another important output is the rotated component matrix which provides with loads of information. It is the matrix that contains same information as the component matrix except that it is calculated after rotation. Before rotation most variables loaded highly onto first factor and the remaining factors didn’t really get a look in.
Therefore, the detailed analysis report explains that SPSS as a tool is every exploratory and is it should be used to guide the researcher to make various decisions. The conclusions derived out of the SPSS analysis can help the leaders to take strategic decisions and build strategies to achieve them.
Regards,
Nisha
Live...let live!
27.1.11
Applications of Multivariate Analysis (CLUSTER Analysis) in International Tourism Research: The Marketing Strategy Perspective of NTOs
Source - Applications of Multivariate Analysis in International Tourism Research: The Marketing Strategy Perspective of NTOs by Satish Chandra & Dennis Menezes
• In recent times International tourism has increased exponentially. With this growth the industry has become significantly more competitive, and the marketing role of National Tourism Organizations (NTOs) has taken on added significance. Correspondingly, research related to the marketing aspects of international tourism has increased.
• The paper focuses on:
– 1. identifying and describing the key components of marketing strategy that must be addressed by NTOs, and
– 2. identifying and describing the multivariate statistical techniques most relevant to research that relates to enhancing the marketing strategies of NTOs along with citing some of the recent related research.
Multivariate Techniques used for achieving the Marketing Strategies.
Refer Above Diagram. Prior to addressing these tasks, a SWOT analysis should be completed.
• Cluster Analysis (In Baseline/Post Hoc Segmentation): In Baseline/Post Hoc Segmentation tourists are classified into clusters on the basis of their appropriate attribute similarities.
• Baseline segmentation involves analyzing a large cross sectional sample of tourists where data has been collected on a variety of variables, such as psychological, life style, demographic, and other variables of interest. The preferred mode of analyzing this large set of data is Cluster analysis. In the baseline segmentation approach using Cluster analysis, the segments are produced analytically.
• Cluster analysis classifies the subjects into clusters, so that each subject is very similar to other subjects in that cluster with respect to selected criterion variables. The clusters formed exhibit high within cluster homogeneity and high between cluster heterogeneity. Thus, when good classification is achieved, subjects within clusters will be close together when plotted geometrically, but different clusters will be far apart. (Refer Figure 3 above).
• In the context of segmenting tourism markets, Cluster analysis can be used to identify different clusters of tourists that exist within a larger group or market of tourists. As a result, Cluster analysis may be used to develop a taxonomy of different types of tourist segments and thereby gain a better understanding of the composition of the larger population of tourists. The within cluster similarity of the tourists is typically determined using an inter subject Euclidean distance measured on two variables.
Conclusion
• International tourist arrivals increased from approximately 25 million in 1950 to 625 million in 1998, an increase of 2,500 percent. A WTO survey of NTOs and leading experts in tourism envision the following :
– (1) international tourism arrivals by 2020 to be 1.6 billion, with spending in excess of 2 trillion U.S. dollars,
– (2) the percent of the traveling population involved in international travel increasing from 3.5 percent in 1998 to 7 percent by 2020,
– (3), Europe continuing to be the largest international tourism region, although by 2020 its market share being significantly eroded,
– (4) by 2020 China being the largest receiver of international tourists,
– (5) among the various international tourism market segments, eco-tourism, cultural tourism, theme based tourism, adventure tourism, and the cruise market growing in importance, and
– (6) tourism as a sector growing at a faster rate than the global economy.
• These predictions by the WTO suggest that the international tourism market will continue to expand at a rapid rate and become increasingly competitive. In this environment, the use of effective and efficient marketing strategies (based on appropriate usage of Multivariate Techniques) by NTOs as well as other international tourism organizations will therefore become increasingly important.
Submitted by;
Sumit Acharya
Roll - 12108
Finance Batch
SIBM Bangalore
Introduction to Logistic Regression
As we could not discuss the logistic regression in the class, below is some information about the same.
Meaning:
Logistic Regression is a type of predictive model that can be used when the target variable is a categorical variable with two categories – for example live/die, has disease/doesn’t have disease, purchases product/doesn’t purchase, wins race/doesn’t win, etc.
A logistic regression model does not involve decision trees and is more similar to nonlinear regression such as fitting a polynomial to a set of data values.
Logistic regression can be used only with two types of target variables:
1. A categorical target variable that has exactly two categories (i.e., a binary or dichotomous variable).
2. A continuous target variable that has values in the range 0.0 to 1.0 representing probability values or proportions.
As an example of logistic regression, consider a study whose goal is to model the response to a drug as a function of the dose of the drug administered. The target (dependent) variable, Response, has a value 1 if the patient is successfully treated by the drug and 0 if the treatment is not successful. Thus the general form of the model is:
Response = f(dose)
The input data for Response will have the value 1 if the drug is effective and 0 if the drug is not effective. The value of Response predicted by the model represents the probability of achieving an effective outcome, P(Response=1|Dose). As with all probability values, it is in the range 0.0 to 1.0.
One obvious question is “Why not simply use linear regression?” In fact, many studies have done just that, but there are two significant problems:
1. There are no limits on the values predicted by a linear regression, so the predicted response might be less than 0 or greater than 1 – clearly nonsensical as a response probability.
2. The response usually is not a linear function of the dosage. If a minute amount of the drug is administered, no patients will respond. Doubling the dose to a larger but still minute amount will not yield any positive response. But as the dosage is increases a threshold will be reached where the drug begins to become effective. Incremental increases in the dosage above the threshold usually will elicit an increasingly positive effect. However, eventually a saturation level is reached, and beyond that point increasing the dosage does not increase the response.
Measuring the performance of MFIs: An application of factor analysis
(1) To reduce the number of variables.
(2) To detect structure in the relationships between variables, that is to classify variables.
Therefore, factor analysis is applied as a data reduction or structure detection.
Measuring the performance of microfinance institutions (MFIs) is not a small task. Indeed, looking at the financials of an MFI only gives its performance. As many MFIs primarily exist in order to help the poorest people, one also has to include aspects which influence their performance. Hence, MFIs' performance can be termed multidimensional.
This article which I’m sharing here, talks about how “Factor Analysis” as a statistical tools can offer new insights in the context of MFIs' performance evaluation. Factor analysis is used in a first step to construct performance indices based on several possible associations of variables without posing too many a prior restrictions.
Then the base variables are thus combined to produce different factors, each one representing a distinct dimension of performance. We then use the individual scores attributed to each MFI on each factor as the dependent variables of a simultaneous-equations model and present new evidence on the determinants of MFIs' performance.
Variables can be of different types which, according to me, can be classified as qualitative variables and quantitative as the two broad groups initially.
Qualitative variables like –
(i) Type of investors (are they PE investors or social investors)
ii) Motive of Investors (Highly Profit motive or Social Motive)
iii) Who Is investing
iv) Type of security accepted
v) Purpose of taking loan
etc. are the variables.
Qualitative variables like-
i. Profit on Every account
ii. Interest charged
iii. Amount of loan
Etc
Such Qualitative and Quantitative variables are then grouped into components on the basis of similarities. Such similar groups can be
1. investors 2. Security 3. Margins 4. Safety 5. Liquidity etc.
The correlation & variance within groups and across groups is then taken to know which are the variables are of same features and tackled in a same way. And also which are the most important and most influential ones.
Cluster of groups and their behaviour towards performance of MFIs will help the policymakers to solve the problems related to performance of MFIs.
In fact factor analysis is used for measuring the performances of various financial institutions and also for assessment of risks of banks & institutions.
Submitted By
Akhil Parekh
12066
A NOTE ON CLUSTER ANALYSIS:
It is a multivariate technique used to determine group membership for cases or variables. In cluster analysis, the number of groups and the members of the groups are unknown. A cluster analysis of variables is like a factor analysis. A cluster analysis of cases is like a discriminant analysis. SPSS provides hierarchical cluster analysis and k-means cluster analysis. The hierarchical cluster analysis is for either cases or variables.
The k-means cluster analysis is for cases only when we have a large number (n >= 200) of cases. By using a distance measure the hierarchical algorithm combines closest pair of cases or variables to form a cluster. This technique continues to join pairs of cases (or variables) or cluster until the final step where all cases (or variables) are joined to form one cluster. Once two cases (or variables) are joined in earlier step, they remain together throughout the process. When some variables have large values or different scales of measurement, they should be standardized before using them in cluster analysis. Data for cluster analysis could be interval, count or binary. There are different distance measures depending on the type of data. Hierarchical cluster analysis provides way to automatically standardize the variables but one has to do standardization prior to using k-means cluster analysis.
This technique is common for reducing dimensionality among cases (case dimension reduction) or among variables (variable dimension reduction). Researchers usually take one step further by trying to make a meaningful interpretation of the common properties for each cluster, and by combining each cluster into a new single variable or a case, which are then used in other analyses.
A few important considerations for a successful cluster analysis:
Different measurement scales among different variables have dramatic influence on the clusters. It is important to make some kind of standardization of the measurement scales.
Outlying cases often dominate some clusters. It is important to take care of outliers.
Cluster analysis depends on the distance measures used for clustering. It is important to identify proper distance measure for the problem of interest. SPSS has a set of defaults. If you do not know what would be appropriate, the default options are usually the more commonly used.
The determination of the final number of clusters may differ from different criteria. It is a good idea to use several selection criteria to help you to choose the final number of clusters.
The context behind the problem of study is an important consideration in the choice of clustering techniques and the criteria for selecting the number of clusters.
METHODS OF CLUSTER ANALYSIS:
Two Step Cluster Analysis: This is an exploratory data analysis to determine clusters within a data set. This procedure works with both continuous and categorical variables. Cases are clustered based on the variables which could be continuous or categorical. To obtain a Two Step cluster analysis, go to Analyze, Classify, Two Step Cluster. This opens the main dialog box of Two Step Cluster Analysis. Select the distance measure, number of clusters and clustering criterion. The submenus are:
Options- This is where you select standardized variables and those to be standardized.
Plots- Enables you to select plots.
Output- Enables you to export final model.
K-Means Cluster Analysis: This is used to cluster cases when you have a large number of cases. The analysis requires one to specify the number of clusters. To run k-means cluster analysis, go to Analyze, Classify, k-Means Cluster. Select the variables and the classification method. There are three submenus:
Iterate- Allows you to select options for the iteration algorithm.
Save- Allows you to save results from the analysis.
Options- Allows you to select some results for display.
Hierarchical Cluster Analysis: This is used to cluster variables (or cases). One can analyze raw variables or use a variety of standardization to transform the variables. To run a Hierarchical Cluster Analysis, go to Analyze, Classify, Hierarchical Cluster. Select the variables for the analysis. Select cases or variables to cluster. By default, statistics and plots will be displayed. The main dialog box has the following submenus:
Statistics- Agglomeration schedule shows the cases or clusters combined at each state. Proximity matrix shows the distances/similarities between items. You can also display cluster membership by requesting a single solution or a range of solutions.
Plots- You can request dendrogram. By default, icicle of all clusters is displayed. You can turn this off. You can also select an orientation pattern.
Method- Here, one selects the cluster method, select the type of measure, choose whether to transform data values. Transform measures allows you to transform the distance measure values that are generated.
Save- Allows you to save cluster membership. This can be saved as a single solution or a range of solutions.
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