Joseph Retzer - Academia.edu (original) (raw)

Papers by Joseph Retzer

Research paper thumbnail of Non-Normal Simultaneous Regression Models for Customer Linkage Analysis

Social Science Research Network, 2007

Simultaneous systems of equations with non-normal errors are developed to study the relationship ... more Simultaneous systems of equations with non-normal errors are developed to study the relationship between customer and employee satisfaction. Customers interact with many employees, and employees serve many customers, such that a one-to-one mapping between customers and employees is not possible. Analysis proceeds by relating, or linking, distribution percentiles among variables. Such analysis is commonly encountered in marketing when data are from independently collected samples. We demonstrate our model in the context of retail banking, where drivers of customer and employee satisfaction are shown to be percentile-dependent.

Research paper thumbnail of Information Importance of Models and Relative Importance of Predictors: Concept, Measures, Bayes Inference, and Applications

Comparison of relative importance of predictors is a subject of discussion of research findings i... more Comparison of relative importance of predictors is a subject of discussion of research findings in many disci- plines, as well as being input for decision-making in business practice. Relative importance methodologists have proposed measures for specific problems such as normal linear regression and logit. Some attempts have been made to set requirements for relative importance of predictors, given a measure of "importance", without characterizing the notion of "importance" itself. The main objective of this paper is to fill this gap by providing a notion of importance of predictors suciently general so as to be applicable to various models and data types, yet to admit a unique interpretation. The importance of predictors is characterized by the ex- tent to which their use reduces uncertainty about predicting the response variable, namely their information importance. Uncertainty associated with a probability distribution is a concave function of the density such...

Research paper thumbnail of Measuring The Information Content Of Regressors In The Linear Model Using Proc Reg

This paper begins by describing an implementation of Kruskal's relative importance analysis u... more This paper begins by describing an implementation of Kruskal's relative importance analysis using SAS STAT and SAS IML. While Kruskal's weights lend insight into the relative importance of each regressor, they are non-additive in nature and therefore limit potential interpretation. In order to overcome the non-additivity drawback, an information theoretic measure (as suggested by Theil and Chung in \Information-theoretic measures of t for univariate and multivariate linear regressions", The American Statistician 1988) is implemented. In addition, the impact of regressor variable collinearity is examined using simulated data. This paper is targeted toward experienced SAS users familiar with PROC REG in SAS STAT. Additional background knowledge of statistical concepts, particularly with respect to partial correlations and regression analysis is also recommended. 1 Measuring Importance Numerous methods for measuring importance in multiattribute value models have been prese...

Research paper thumbnail of The Century of Bayes

International Journal of Market Research, 2006

Research paper thumbnail of The Century of Bayes

Research paper thumbnail of Implementing weighted average cost of capital in place of return on equity to characterize firm performance /

Research paper thumbnail of Non-normal simultaneous regression models for customer linkage analysis

Quantitative Marketing and Economics, 2008

Simultaneous systems of equations with non-normal errors are developed to study the relationship ... more Simultaneous systems of equations with non-normal errors are developed to study the relationship between customer and employee satisfaction. Customers interact with many employees, and employees serve many customers, such that a one-to-one mapping between customers and employees is not possible. Analysis proceeds by relating, or linking, distribution percentiles among variables. Such analysis is commonly encountered in marketing when data are from independently collected samples. We demonstrate our model in the context of retail banking, where drivers of customer and employee satisfaction are shown to be percentile-dependent.

Research paper thumbnail of A Simultaneous Quantile Regression Model for Customer Linkage Analysis

Research paper thumbnail of Information indices: unification and applications

Journal of Econometrics, 2002

ABSTRACT

Research paper thumbnail of Adjustment of importance weights in multiattribute value models by minimum discrimination information

European Journal of Operational Research, 1992

ABSTRACT

Research paper thumbnail of A Framework for Measuring the Importance of Variables with Applications to Management Research and Decision Models

Decision Sciences, 2000

In many disciplines, including various management science fields, researchers have shown interest... more In many disciplines, including various management science fields, researchers have shown interest in assigning relative importance weights to a set of explanatory variables in multivariable statistical analysis. This paper provides a synthesis of the relative importance measures scattered in the statistics, psychometrics, and management science literature. These measures are computed by averaging the partial contributions of each variable over all orderings of the explanatory variables. We define an Analysis of Importance (ANIMP) framework that reflects two desirable properties for the relative importance measures discussed in the literature: additive separability and order independence. We also provide a formal justification and generalization of the "averaging over all orderings" procedure based on the Maximum Entropy Principle. We then examine the question of relative importance in management research within the framework of the "contingency theory of organizational design" and provide an example of the use of relative importance measures in an actual management decision situation. Contrasts are drawn between the consequences of use of statistical significance, which is an inappropriate indicator of relative importance and the results of the appropriate ANIMP measures.

Research paper thumbnail of Information importance of predictors: Concept, measures, Bayesian inference, and applications

Computational Statistics & Data Analysis, 2009

The importance of predictors is characterized by the extent to which their use reduces uncertaint... more The importance of predictors is characterized by the extent to which their use reduces uncertainty about predicting the response variable, namely their information importance. The uncertainty associated with a probability distribution is a concave function of the density such that its global maximum is a uniform distribution reflecting the most difficult prediction situation. Shannon entropy is used to operationalize the concept. For nonstochastic predictors, maximum entropy characterization of probability distributions provides measures of information importance. For stochastic predictors, the expected entropy difference gives measures of information importance, which are invariant under one-to-one transformations of the variables. Applications to various data types lead to familiar statistical quantities for various models, yet with the unified interpretation of uncertainty reduction. Bayesian inference procedures for the importance and relative importance of predictors are developed. Three examples show applications to normal regression, contingency table, and logit analyses.

Research paper thumbnail of A New way of Assigning Relative Attribute Importance1

Importance should indicate the degree to which the attribute is associated with the dependent var... more Importance should indicate the degree to which the attribute is associated with the dependent variable. The first measure, statistical significance, instead only tells us the level of confidence we have in accurately measuring a coefficient of association (i.e. correlation, regression, etc.). Specifically, as sample size increases, statistical significance rises. This reflects the fact that as we add more and more observations, our ability to accurately measure the coefficient attached to the attribute (important or otherwise) increases. The remaining two techniques estimate importance as some portion of variation in a dependent variable explained by an attribute (this common variation is also referred to as “shared information”). Usually when two or more variables are considered for their explanatory power, a certain amount of overlap occurs in that some common portion of the variation in the dependent variable is explained by more than one attribute. This information overlap is illustrated in Chart 1 where the circle labeled “Overall Satisfaction” represents the total variation in the dependent variable. The “Quality” and “Image” circles reflect corresponding quantities for two independent attributes. The regions labeled A, B and C represent portions of shared information between the attributes and dependent variable, “Overall Satisfaction” (the sum, A + B + C, is the total amount of shared information between the attributes and dependent variable). The regions can be described in terms of explained variation as: A. The variation in “Overall Satisfaction” uniquely explained by “Quality”. B. The variation in “Overall Satisfaction” explained by both “Quality and “Image”. C. The variation in “Overall Satisfaction” uniquely explained by “Image”.

Research paper thumbnail of Non-Normal Simultaneous Regression Models for Customer Linkage Analysis

Social Science Research Network, 2007

Simultaneous systems of equations with non-normal errors are developed to study the relationship ... more Simultaneous systems of equations with non-normal errors are developed to study the relationship between customer and employee satisfaction. Customers interact with many employees, and employees serve many customers, such that a one-to-one mapping between customers and employees is not possible. Analysis proceeds by relating, or linking, distribution percentiles among variables. Such analysis is commonly encountered in marketing when data are from independently collected samples. We demonstrate our model in the context of retail banking, where drivers of customer and employee satisfaction are shown to be percentile-dependent.

Research paper thumbnail of Information Importance of Models and Relative Importance of Predictors: Concept, Measures, Bayes Inference, and Applications

Comparison of relative importance of predictors is a subject of discussion of research findings i... more Comparison of relative importance of predictors is a subject of discussion of research findings in many disci- plines, as well as being input for decision-making in business practice. Relative importance methodologists have proposed measures for specific problems such as normal linear regression and logit. Some attempts have been made to set requirements for relative importance of predictors, given a measure of "importance", without characterizing the notion of "importance" itself. The main objective of this paper is to fill this gap by providing a notion of importance of predictors suciently general so as to be applicable to various models and data types, yet to admit a unique interpretation. The importance of predictors is characterized by the ex- tent to which their use reduces uncertainty about predicting the response variable, namely their information importance. Uncertainty associated with a probability distribution is a concave function of the density such...

Research paper thumbnail of Measuring The Information Content Of Regressors In The Linear Model Using Proc Reg

This paper begins by describing an implementation of Kruskal's relative importance analysis u... more This paper begins by describing an implementation of Kruskal's relative importance analysis using SAS STAT and SAS IML. While Kruskal's weights lend insight into the relative importance of each regressor, they are non-additive in nature and therefore limit potential interpretation. In order to overcome the non-additivity drawback, an information theoretic measure (as suggested by Theil and Chung in \Information-theoretic measures of t for univariate and multivariate linear regressions", The American Statistician 1988) is implemented. In addition, the impact of regressor variable collinearity is examined using simulated data. This paper is targeted toward experienced SAS users familiar with PROC REG in SAS STAT. Additional background knowledge of statistical concepts, particularly with respect to partial correlations and regression analysis is also recommended. 1 Measuring Importance Numerous methods for measuring importance in multiattribute value models have been prese...

Research paper thumbnail of The Century of Bayes

International Journal of Market Research, 2006

Research paper thumbnail of The Century of Bayes

Research paper thumbnail of Implementing weighted average cost of capital in place of return on equity to characterize firm performance /

Research paper thumbnail of Non-normal simultaneous regression models for customer linkage analysis

Quantitative Marketing and Economics, 2008

Simultaneous systems of equations with non-normal errors are developed to study the relationship ... more Simultaneous systems of equations with non-normal errors are developed to study the relationship between customer and employee satisfaction. Customers interact with many employees, and employees serve many customers, such that a one-to-one mapping between customers and employees is not possible. Analysis proceeds by relating, or linking, distribution percentiles among variables. Such analysis is commonly encountered in marketing when data are from independently collected samples. We demonstrate our model in the context of retail banking, where drivers of customer and employee satisfaction are shown to be percentile-dependent.

Research paper thumbnail of A Simultaneous Quantile Regression Model for Customer Linkage Analysis

Research paper thumbnail of Information indices: unification and applications

Journal of Econometrics, 2002

ABSTRACT

Research paper thumbnail of Adjustment of importance weights in multiattribute value models by minimum discrimination information

European Journal of Operational Research, 1992

ABSTRACT

Research paper thumbnail of A Framework for Measuring the Importance of Variables with Applications to Management Research and Decision Models

Decision Sciences, 2000

In many disciplines, including various management science fields, researchers have shown interest... more In many disciplines, including various management science fields, researchers have shown interest in assigning relative importance weights to a set of explanatory variables in multivariable statistical analysis. This paper provides a synthesis of the relative importance measures scattered in the statistics, psychometrics, and management science literature. These measures are computed by averaging the partial contributions of each variable over all orderings of the explanatory variables. We define an Analysis of Importance (ANIMP) framework that reflects two desirable properties for the relative importance measures discussed in the literature: additive separability and order independence. We also provide a formal justification and generalization of the "averaging over all orderings" procedure based on the Maximum Entropy Principle. We then examine the question of relative importance in management research within the framework of the "contingency theory of organizational design" and provide an example of the use of relative importance measures in an actual management decision situation. Contrasts are drawn between the consequences of use of statistical significance, which is an inappropriate indicator of relative importance and the results of the appropriate ANIMP measures.

Research paper thumbnail of Information importance of predictors: Concept, measures, Bayesian inference, and applications

Computational Statistics & Data Analysis, 2009

The importance of predictors is characterized by the extent to which their use reduces uncertaint... more The importance of predictors is characterized by the extent to which their use reduces uncertainty about predicting the response variable, namely their information importance. The uncertainty associated with a probability distribution is a concave function of the density such that its global maximum is a uniform distribution reflecting the most difficult prediction situation. Shannon entropy is used to operationalize the concept. For nonstochastic predictors, maximum entropy characterization of probability distributions provides measures of information importance. For stochastic predictors, the expected entropy difference gives measures of information importance, which are invariant under one-to-one transformations of the variables. Applications to various data types lead to familiar statistical quantities for various models, yet with the unified interpretation of uncertainty reduction. Bayesian inference procedures for the importance and relative importance of predictors are developed. Three examples show applications to normal regression, contingency table, and logit analyses.

Research paper thumbnail of A New way of Assigning Relative Attribute Importance1

Importance should indicate the degree to which the attribute is associated with the dependent var... more Importance should indicate the degree to which the attribute is associated with the dependent variable. The first measure, statistical significance, instead only tells us the level of confidence we have in accurately measuring a coefficient of association (i.e. correlation, regression, etc.). Specifically, as sample size increases, statistical significance rises. This reflects the fact that as we add more and more observations, our ability to accurately measure the coefficient attached to the attribute (important or otherwise) increases. The remaining two techniques estimate importance as some portion of variation in a dependent variable explained by an attribute (this common variation is also referred to as “shared information”). Usually when two or more variables are considered for their explanatory power, a certain amount of overlap occurs in that some common portion of the variation in the dependent variable is explained by more than one attribute. This information overlap is illustrated in Chart 1 where the circle labeled “Overall Satisfaction” represents the total variation in the dependent variable. The “Quality” and “Image” circles reflect corresponding quantities for two independent attributes. The regions labeled A, B and C represent portions of shared information between the attributes and dependent variable, “Overall Satisfaction” (the sum, A + B + C, is the total amount of shared information between the attributes and dependent variable). The regions can be described in terms of explained variation as: A. The variation in “Overall Satisfaction” uniquely explained by “Quality”. B. The variation in “Overall Satisfaction” explained by both “Quality and “Image”. C. The variation in “Overall Satisfaction” uniquely explained by “Image”.