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The Variability of Pseudo R2s in Logistic Regression Models
-- Wade Rose and Inder Jit Singh Mann
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.
© 2011 IUP. All Rights Reserved.
A New Multi-Step Fixed Newton's Method
for Solving Large-Scale Systems
of Nonlinear Equations
-- Mohammed Waziri Yusuf, Ibrahim Saidu and Aisha Haliru
The simplest modification to overcome the widely known shortcomings of classical Newton's method
is fixed Newton's method. However, the numerical convergence of fixed Newton's method is too
slow, which results in high consumption of CPU time and large number of iterations as the system's
dimension increases. This paper designs and implements a simple new approach via multi-step method for
solving large systems of nonlinear equations. Practical insights into the effectiveness and reliability of the
proposed method are presented through numerical comparison of well-known benchmark nonlinear systems
with Newton's method and its variant.
© 2011 IUP. All Rights Reserved.
A New 3-Dimensional Polynomial Interpolation Method: an Algorithmic Approach
--
Amitava Chatterjee and Rupak Bhattacharyya
A new 3-dimensional interpolation method is introduced in this paper. Corresponding to the method
a novel interpolation operator has been constructed and used to obtain results. The main objective is
to develop a mechanical way of interpolation that does not require very high degree of knowledge
of mathematical analysis, but only elementary mathematics. The properties of the operator have
been discussed in detail. Unlike other methods, the number of nodes required in the proposed
interpolation method is much less. A numerical example is also furnished in support of the formula obtained.
© 2011 IUP. All Rights Reserved.
Prices Expansion in the Wishart Model
-- Pierre Gauthier and Dylan Possamaï
Using probability change techniques introduced by Drimus for Heston model, the paper derives a nth order expansion formula of Wishart option price in terms of Black-Scholes price and
Black-Scholes Greeks. Numerical results are given for the second-order case. Due to this new approximation, the
smile implied by the Wishart model can be better understood. The sensitivity of Delta and Vega to the
volatility (Vanna and Volga respectively) indeed appears explicitly in this formula. En route to this formula,
the paper presents a number of new results on Laplace transforms and moments of the integrated
Wishart processes.
© 2011 IUP. All Rights Reserved.
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March'11
