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The IUP Journal of Computational Mathematics
The Variability of Pseudo R2s in Logistic Regression Models
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Over the past few decades, the use of logistic regression has increased in social and medical sciences research involving binary response variables. With respect to logistic regression, there is at present no widely accepted measure of explained variation with which one could judge the fit of a given model. A number of pseudo R2s have been proposed for the purpose. A number of studies carried out to compare and contrast their strengths, weaknesses and applicability indicate that these pseudo R2s vary considerably in terms of interpretability and range. This paper brings out the propensity of the various pseudo R2s to have different absolute values, different percentages of change from one model to another, and in some cases even vary in terms of their direction of change (i.e., increase versus decrease). This paper contributes to the literature by highlighting the variability of pseudo R2 and the importance of knowing which pseudo R2 is being utilized and its particular characteristics.

 
 
 

The utilization of logistic regression modeling has increased over the past couple of decades as its use spread from epidemiological research to a number of other research fields, including business management (Hosmer and Lemeshow, 2000). In parallel, considerable effort has been spent toward researching the various statistical aspects of this modeling process. Hosmer and Lemeshow have commented on "more than 1,000 citations that have appeared in the 10 years since the first edition of this book was published" (2000, p. ix).

Logistic regression has facilitated quantitative research in various aspects of business management, including marketing, strategy, decision theory, and organizational behavior. Whether it is used in business research, or in another field, the goal of using this model development technique is the same; to develop a model that best describes the relationship between a dependent variable and a set of independent variables. The choice to use logistic regression versus linear regression is a function of the dependent variable. If the dependent variable has a binary outcome, logistic regression is a good choice.

The pseudo R2 in logistic regression (in contrast to R2 in linear regression) is useful when trying to determine the relative fit of various models, each using different combinations of independent variables. Pseudo R2s are also valuable in determining the absolute fit of logistic regression models in cases where large sample sizes are utilized as input to the models.

 
 
 

Computational Mathematics Journal, Logistic Regression Models, Business Management, Decision Theory, Logistic Regression Programs, SPSS Nonlinear Program, Proportional Reductions, Statistical Aanalysis Software Package, Statistical Software SPSS, Squared Pearson Correlation .