Conjugate Analysis What and Why?

Conjoint analysis is a statistical technique used in market research to determine how people value different features that make up an individual product or service.

The objective of conjoint analysis is to determine what combination of a limited number of attributes is most influential on respondent choice or decision making.

Total utility = Sum of all partial utilities

Conjoint analysis can also be used through many softwares that are available like Sawtooth software.

Conjoint Analysis is perfect for answering these types of questions:

· What is the optimal feature set for my product?

· What price level maximizes its profitability?

· What services are consumers willing to pay more for in the product?

· Which of these changes will increase our market share?

· What impact will this have on my current suite of products/cannibalization?

As Conjoint analysis is very beautifully explained by Saurabh with golf ball example. So I am not getting into what is conjoint analysis but focus more on its applications.

Uses for Conjoint Analysis

Conjoint analysis is appropriate when a researcher wants to measure preference for a product or service, the source of that preference, or the impact on preference caused by product design changes. While there are a wide number of uses for conjoint analysis, four of the most common will be discussed below.

· Product Design

· Research Market Segmentation

· Research Brand Equity

· Research Price Sensitivity Research

Product Design Research

Product design research is the most common use of conjoint analysis among marketing researchers today. By knowing buyers’ preference for various product features, as well as the design and production costs associated with those features, products can be designed that produce the strongest preference among buyers while still being profitable for the seller.

Market Segmentation Research

Generally buyers’ utilities were not identical. It is more likely that there will be groups of buyers that exhibit similar preference structures, but that not everyone will agree. Market segmentation research is a name applied to the process of identifying and explaining the meaningful differences between groups of buyers.

Conjoint analysis can be used two ways in segmentation research. First, results can be compared across segments that already exist, or a priori segments. Alternatively, the market segments can be identified from the data collected in the study itself.

Brand Equity Research

conjoint analysis can be used to better understand the market’s preference for specific brands. While there are many ideas about exactly what brand equity is, the discussions tend to revolve around a) economic value that b) biases consumer choice. Simply stated, brand equity is the power of certain brands to:

• Charge more money than their competitors and still be purchased, or

• Realize incremental market share while maintaining competitive pricing.

Price Sensitivity Research

Similarly, conjoint methods can be used to measure the market’s price sensitivity towards a brand. Price sensitivity is most frequently measured with price elasticity of demand. Price elasticity is defined as the percent change in demand divided by the percent change in price. Price elasticities are generally negative. Elasticities between 0 and -1 are termed inelastic and represent markets that are not price sensitive. Elasticities less than -1 indicate price sensitive, or elastic, markets.

Refrences

http://en.wikipedia.org/wiki/Conjoint_analysis_(marketing)

http://www.sawtoothsoftware.com/conjoint-analysis-software

Author Aakash Bavariya (13001)

Operations Group 2

FACTOR ANALYSIS

Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance observed in a much larger number of manifest variables. Factor analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for subsequent analysis (for example, to identify collinearity prior to performing a linear regression analysis).

A few points to be kept in mind while using Factor Analysis:

Data - The variables should be quantitative at the interval or ratio level. Categorical data (such as religion or country of origin) are not suitable for factor analysis. Data for which Pearson correlation coefficients can sensibly be calculated should be suitable for factor analysis.

Assumptions - The data should have a bivariate normal distribution for each pair of variables, and observations should be independent.

Uses Of Factor Analysis

Interdependency and pattern delineation. If a scientist has a table of data--say, UN votes, personality characteristics, or answers to a questionnaire--and if he suspects that these data are interrelated in a complex fashion, then factor analysis may be used to untangle the linear relationships into their separate patterns. Each pattern will appear as a factor delineating a distinct cluster of interrelated data.

Data reduction. Factor analysis can be useful for reducing a mass of information to an economical description. For example, data on fifty characteristics for 300 nations are unwieldy to handle, descriptively or analytically. The management, analysis, and understanding of such data are facilitated by reducing them to their common factor patterns. These factors concentrate and index the dispersed information in the original data and can therefore replace the fifty characteristics without much loss of information. Nations can be more easily discussed and compared on economic development, size, and politics dimensions, for example, than on the hundreds of characteristics each dimension involves.

Structure. Factor analysis may be employed to discover the basic structure of a domain. As a case in point, a scientist may want to uncover the primary independent lines or dimensions--such as size, leadership, and age--of variation in group characteristics and behavior. Data collected on a large sample of groups and factor analyzed can help disclose this structure.

Classification or description. Factor analysis is a tool for developing an empirical typology. It can be used to group interdependent variables into descriptive categories, such as ideology, revolution, liberal voting, and authoritarianism. It can be used to classify nation profiles into types with similar characteristics or behavior. Or it can be used on data matrices of a transaction type or a social-choice type to show how individuals, social groups, or nations cluster on their transactions with or choices of each other.

Scaling. A scientist often wishes to develop a scale on which individuals, groups, or nations can be rated and compared. The scale may refer to such phenomena as political participation, voting behavior, or conflict. A problem in developing a scale is to weight the characteristics being combined. Factor analysis offers a solution by dividing the characteristics into independent sources of variation (factors). Each factor then represents a scale based on the empirical relationships among the characteristics. As additional findings, the factor analysis will give the weights to employ for each characteristic when combining them into the scales. The factor score results are actually such scales, developed by summing characteristics times these weights.

Hypothesis testing. Hypotheses abound regarding dimensions of attitude, personality, group, social behavior, voting, and conflict. Since the meaning usually associated with "dimension" is that of a cluster or group of highly intercorrelated characteristics or behavior, factor analysis may be used to test for their empirical existence. Which characteristics or behavior should, by theory, be related to which dimensions can be postulated in advance and statistical tests of significance can be applied to the factor analysis results.

Besides those relating to dimensions, there are other kinds of hypotheses that may be tested. To illustrate: if the concern is with a relationship between economic development and instability, holding other things constant, a factor analysis can be done of economic and instability variables along with other variables that may affect (hide, mediate, depress) their relationship. The resulting factors can be so defined (rotated) that the first several factors involve the mediating measures (to the maximum allowed by the empirical relationships). A remaining independent factor can be calculated to best define the postulated relationships between the economic and instability measures. The magnitude of involvement of both variables in this pattern enables the scientist to see whether an economic development-instability pattern actually exists when other things are held constant.

Author:- Dipankar Patir

Group:- Operation 3

WHY DO WE USE FACTOR ANALYSIS……..?

This blog will outline factor analysis applications relevant to various scientific and policy concerns:

Interdependency and pattern delineation. If a scientist has a table of data--say, UN votes, personality characteristics, or answers to a questionnaire--and if he suspects that these data are interrelated in a complex fashion, then, factor analysis may be used to untangle the linear relationships into their separate patterns. Each pattern will appear as a factor delineating a distinct cluster of interrelated data.

Parsimony or data reduction. Factor analysis can be useful for reducing a mass of information to an economical description. For example, data on fifty characteristics for 300 nations are unwieldy to handle, descriptively or analytically. The management, analysis, and understanding of such data are facilitated by reducing them to their common factor patterns. These factors concentrate and index the dispersed information in the original data and can therefore replace the fifty characteristics without much loss of information. Nations can be more easily discussed and compared on economic development, size, and politics dimensions, for example, than on the hundreds of characteristics each dimension involves.

Structure. Factor analysis may be employed to discover the basic structure of a domain. As a case in point, a scientist may want to uncover the primary independent lines or dimensions--such as size, leadership, and age--of variation in group characteristics and behavior. Data collected on a large sample of groups and factor analyzed can help disclose this structure.

Classification or description. Factor analysis is a tool for developing an empirical typology. It can be used to group interdependent variables into descriptive categories, such as ideology, revolution, liberal voting, and authoritarianism. It can be used to classify nation profiles into types with similar characteristics or behavior. Or it can be used on data matrices of a transaction type or a social-choice type to show how individuals, social groups, or nations cluster on their transactions with or choices of each other.

Scaling. A scientist often wishes to develop a scale on which individuals, groups, or nations can be rated and compared. The scale may refer to such phenomena as political participation, voting behavior, or conflict. A problem in developing a scale is to weight the characteristics being combined. Factor analysis offers a solution by dividing the characteristics into independent sources of variation (factors). Each factor then represents a scale based on the empirical relationships among the characteristics. As additional findings, the factor analysis will give the weights to employ for each characteristic when combining them into the scales.

Hypothesis testing. Hypotheses abound regarding dimensions of attitude, personality, group, social behavior, voting, and conflict. Since the meaning usually associated with "dimension" is that of a cluster or group of highly inter-correlated characteristics or behavior, factor analysis may be used to test for their empirical existence. Which characteristics or behavior should, by theory, be related to which dimensions can be postulated in advance and statistical tests of significance can be applied to the factor analysis results.

Besides those relating to dimensions, there are other kinds of hypotheses that may be tested. To illustrate: if the concern is with a relationship between economic development and instability, holding other things constant, a factor analysis can be done of economic and instability variables along with other variables that may affect (hide, mediate, depress) their relationship. The resulting factors can be so defined (rotated) that the first several factors involve the mediating measures (to the maximum allowed by the empirical relationships). A remaining independent factor can be calculated to best define the postulated relationships between the economic and instability measures. The magnitude of involvement of both variables in this pattern enables the scientist to see whether an economic development-instability pattern actually exists when other things are held constant.

Author- Sahil Singhal

Finance Group 3

Factor Analysis........!

Factor analysis is a method for investigating whether a number of variables of interest Y1, Y2, ........Yl, are linearly related to a smaller number of unobservable factors F1, F2, ....Fk i.e.; it is a means by which the regularity and order in phenomena can be discerned. As phenomena co-occur in space or in time, they are patterned; as these co-occurring phenomena are independent of each other, there are a number of distinct patterns. Patterned phenomena are the essence of workaday concepts such as "table," "chair," and "house," and--at a less trivial level--patterns structure our scientific theories and hypotheses. We associate a pattern of attitudes, for example, with businessmen and another pattern with farmers.

Factor analysis takes thousands and potentially millions of measurements and qualitative observations and resolves them into distinct patterns of occurrence. It makes explicit and more precise the building of fact-linkages going on continuously in the human mind.

Types of factor analysis:

1. Confirmatory Factor Analysis

CFA allows the researcher to test the hypothesis that a relationship between the observed variables and their underlying latent construct(s) exists. The researcher uses knowledge of the theory, empirical research, or both, postulates the relationship pattern a priori and then tests the hypothesis statistically.

The use of CFA could be impacted by the research hypothesis being tested, the requirement of sufficient sample size (e.g., 5-20 cases per parameter estimate), measurement instruments, multivariate normality, parameter identification, outliers, missing data, interpretation of model fit indices etc.

A suggested approach to CFA proceeds through the following process:

· Review the relevant theory and research literature to support model specification

· Specify a model (e.g., diagram, equations)

· Determine model identification (e.g., if unique values can be found for parameter estimation; the number of degrees of freedom, df, for model testing is positive)

· Collect data

· Conduct preliminary descriptive statistical analysis (e.g., scaling, missing data, co linearity issues, outlier detection)

· Estimate parameters in the model

· Assess model fit

· Present and interpret the results.

1. Exploratory Factor Analysis

It is a variable reduction technique which identifies the number of latent constructs and the underlying factor. It involves the following:

· Hypothesizes an underlying construct, a variable not measured directly.

· Estimates factors which influence responses on observed variables.

· Allows us to describe and identify the number of latent constructs (factors).

· Includes unique factors, error due to unreliability in measurement.

· Traditionally, it has been used to explore the possible underlying factor structure of a set of measured variables.

Assumptions underlying EFA are

· Interval or ratio level of measurement

· Random sampling

· Relationship between observed variables is linear

· A normal distribution (each observed variable)

· A bi-variate normal distribution (each pair of observed variables)

· Multivariate normality

SUGI 31 Statistics and Data Analysis

Practical applications in HR:

HRM practices are analyzed on the basis of recruitment, performance management, reward systems, and retention functions. The HR managers are usually asked to respond to statements such as “Our performance appraisal system is based on results?”,“In determining salaries, offering salaries that are competitive in the job market is more important to our organization than maintaining internal equity,” and “For high level positions the organization prefers to promote personnel from within rather than recruiting personnel from outside the organization.” The items that make up the HRM practices scale are selected from a long list of items, which is done using exploratory factor analysis.

Group- HR1

Author- Tage Otung

Factor Analysis........!

Factor analysis is a method for investigating whether a number of variables of interest Y1, Y2, ........Yl, are linearly related to a smaller number of unobservable factors F1, F2, ....Fk i.e.; it is a means by which the regularity and order in phenomena can be discerned. As phenomena co-occur in space or in time, they are patterned; as these co-occurring phenomena are independent of each other, there are a number of distinct patterns. Patterned phenomena are the essence of workaday concepts such as "table," "chair," and "house," and--at a less trivial level--patterns structure our scientific theories and hypotheses. We associate a pattern of attitudes, for example, with businessmen and another pattern with farmers.

Factor analysis takes thousands and potentially millions of measurements and qualitative observations and resolves them into distinct patterns of occurrence. It makes explicit and more precise the building of fact-linkages going on continuously in the human mind.

Types of factor analysis:

1. Confirmatory Factor Analysis

CFA allows the researcher to test the hypothesis that a relationship between the observed variables and their underlying latent construct(s) exists. The researcher uses knowledge of the theory, empirical research, or both, postulates the relationship pattern a priori and then tests the hypothesis statistically.

The use of CFA could be impacted by the research hypothesis being tested, the requirement of sufficient sample size (e.g., 5-20 cases per parameter estimate), measurement instruments, multivariate normality, parameter identification, outliers, missing data, interpretation of model fit indices etc.

A suggested approach to CFA proceeds through the following process:

· Review the relevant theory and research literature to support model specification

· Specify a model (e.g., diagram, equations)

· Determine model identification (e.g., if unique values can be found for parameter estimation; the number of degrees of freedom, df, for model testing is positive)

· Collect data

· Conduct preliminary descriptive statistical analysis (e.g., scaling, missing data, co linearity issues, outlier detection)

· Estimate parameters in the model

· Assess model fit

· Present and interpret the results.

1. Exploratory Factor Analysis

It is a variable reduction technique which identifies the number of latent constructs and the underlying factor. It involves the following:

· Hypothesizes an underlying construct, a variable not measured directly.

· Estimates factors which influence responses on observed variables.

· Allows us to describe and identify the number of latent constructs (factors).

· Includes unique factors, error due to unreliability in measurement.

· Traditionally, it has been used to explore the possible underlying factor structure of a set of measured variables.

Assumptions underlying EFA are

· Interval or ratio level of measurement

· Random sampling

· Relationship between observed variables is linear

· A normal distribution (each observed variable)

· A bi-variate normal distribution (each pair of observed variables)

· Multivariate normality

SUGI 31 Statistics and Data Analysis

Practical applications in HR:

HRM practices are analyzed on the basis of recruitment, performance management, reward systems, and retention functions. The HR managers are usually asked to respond to statements such as “Our performance appraisal system is based on results?”,“In determining salaries, offering salaries that are competitive in the job market is more important to our organization than maintaining internal equity,” and “For high level positions the organization prefers to promote personnel from within rather than recruiting personnel from outside the organization.” The items that make up the HRM practices scale are selected from a long list of items, which is done using exploratory factor analysis.

Group- HR1

Author- Tage Otung

Exploratory factor analysis Vs Confirmatory factor analysis

Exploratory factor analysis (EFA) could be described as orderly simplification of interrelated measures.  EFA, traditionally, has been used to explore the possible underlying factor structure of a set of observed variables without imposing a preconceived structure on the outcome. By performing EFA, the underlying factor structure is identified.  

Confirmatory factor analysis (CFA) is a statistical technique used to verify the factor structure of a set of observed variables. CFA allows the researcher to test the hypothesis that a relationship between observed variables and their underlying latent constructs exists. The researcher uses knowledge of the theory, empirical research, or both, postulates the relationship pattern and then tests the hypothesis statistically. 

CFA and EFA are powerful statistical techniques. An example of application of CFA and EFA may be the development of measurement instruments, e.g. a satisfaction scale, attitudes toward health, customer service questionnaire etc.

A blueprint is first developed, questions written, a scale determined, the instrument pilot tested, data collected, and CFA applied. The blueprint identifies the factor structure or what we think it is. However, some questions may not measure what we thought they should. If the factor structure is not confirmed, EFA is the next step. EFA helps us determine what the factor structure looks like according to how participant responses. Exploratory factor analysis is essential to determine underlying constructs for a set of measured variables.

The use of CFA could be impacted by 

·         ƒ the research hypothesis being tested

·         ƒ the requirement of sufficient sample size (e.g., 5-20 cases per parameter estimate)

·         ƒ measurement instruments

·         ƒ multivariate normality

·         ƒ parameter identification

·         ƒ outliers

·         ƒ missing data

·         ƒ Interpretation of model fit indices 

A suggested approach to CFA proceeds through the following process: 

·         review the relevant theory and research literature to support model specification

·          specify a model (e.g., diagram, equations)

·         determine model identification (e.g., if unique values can be found for parameter estimation; the number of degrees of freedom for model testing  is positive) 

·         collect data 

·         conduct preliminary descriptive statistical analysis (e.g., scaling, missing data, collinearity issues, outlier detection)

·          estimate parameters in the model

·          assess model fit

·          present and interpret the results

Characteristics of EFA

·         ƒIt is a variable reduction technique which identifies the number of latent constructs and the underlying factor structure of a set of variables

·         ƒ hypothesizes an underlying construct, a variable not measured directly

·         ƒ estimates factors which influence responses on observed variables

·         ƒ allows you to describe and identify the number of latent constructs (factors)

·         ƒ includes unique factors, error due to unreliability in measurement

·         ƒ traditionally has been used to explore the possible underlying factor structure of a set of measured variables without imposing any preconceived structure on the outcome

Assumptions underlying EFA are

·         Interval or ratio level of measurement

·         Random sampling

·         Relationship between observed variables is linear

·         A normal distribution (each observed variable)

·         A bi-variate normal distribution (each pair of observed variables)

·         Multivariate normality

Limitations of EFA are 

·         The correlations, the basis of factor analysis, describe relationships.  No causal inferences can be made from correlations alone.

·         the reliability of the measurement instrument (avoid an instrument with low reliability)

·         sample size ( larger sample à larger correlation)

Ø  Minimal number of cases for reliable results is more than 100 observations and 5 times the number of items

Ø  Since some subjects may not answer every item, a larger sample is desirable. For example, 30 items would require at least 150 cases (5*30), a sample of 200 subjects would allow for missing data

·         sample selection

Ø  Should be representative of population

Ø  Do not pool populations

·         variables could be sample specific, e.g., a unique quality possessed by a group does not generalize to the population 

·         Can’t process non-normal distribution of data

Written By Nirupam Mandal (13025)

OPS Group 1