Modeling Continuous Non-Linear Data with Lagged Fractional Polynomial Regression

Kazeem Kehinde Adesanya, Abass Ishola Taiwo, Adebayo Funmi Adedodun, Timothy Olabisi Olatayo

Abstract


Fractional Polynomial regression is a form of regression analysis in which the relationship between the independent variable and the dependent variable is modelled as a 1/nth degree polynomial. Thus, this work is used to propose an extension of Fractional Polynomial Regression (FPR) term Lagged Fractional Polynomial Regression (LFPR) which is an alternative method to traditional techniques of analysing the pattern and degree of relationship between two or more continuous non-linear data. The coefficients of the proposed method were estimate using Maximum Likelihood Estimation method. From the results, the LFPR model indicated that for a unit increase in Evaporation, Humidity and Temperature there will be an increase in the millimeter of rainfall series on yearly basis. The value of coefficient of variation (R2) for the LFPR and FPR were 99% and 77%. While the value of adjusted Coefficient of Variation (R2) for LFPR and FPR were 96% and 75% respectively. Hence, the proposed method outperformed and adequately explained the variation in the dependent variable better than Fractional Polynomial Regression based on the values (R2) and adjusted (R2).


Keywords


Continuous data, Fractional Polynomial, Lagged, Regression, Maximum Likelihood Estimation

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References


Gasparrini, A. and Leone, M. “Attributable risk from distributed lag models.” BMC Medical Research

Methodology vol. 14, pp. 55 - 60.

Hubert G. “Statistical Analysis of Management Data” Second Edition. New York: Springer Publication, 2010.

Royston, P. and Altman, D.G. “Regression using Fractional Polynomials of Continuous Covariates:

Parsimonious Parametric Modelling”. Applied Statistics; vol. 43, pp. 429-467, 1994.

Jansen, J.P. “Network Meta-Analysis of Survival Data with Fractional Polynomials”. BMC Medical Research

Methodology. vol. 11, no 61, pp. 11-61, 2011.

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. “On the practice of dichotomization of

quantitative variables”. Psychological Methods, vol. 7, 19–40, 2002.

Royston, P, Altman, D. G. and Sauerbrei, W.” Dichotomizing continuous predictors in multiple regression:

A bad idea”. Statistics in Medicine, vol. 25, no 1, pp.127-141, 2006.

Royston, P. and Sauerbrei, W. “Multivariable Model-building: A Pragmatic Approach to Regression Analysis

Based on Fractional Polynomials for Modelling Continuous Variables”. Wiley; Chichesters, 2008.

Hutcheson, G. D., Pampaka, M. and Williams. J. Enrolment, Achievement and Retention on Traditional’

and ‘Use of Mathematics’ Pre-university Courses.” Research in Mathematics Education vol. 13 no 2, pp. 147–168, 2011.

Wainer, H. “14 Conversations about Three Things”. Journal of Educational and Behavioral Statistics, vol. 35 no 1,

pp. 5–25, 2010.

Gasparrini A, Scheipl F., Armstrong B., and Kenward M.G. “A Penalized Framework for Distributed Lag

Non-Linear Models”. Biometrics vol. 73, pp. 938–94, 2017.

Royston, P., and Sauerbrei. W. “A new measure of prognostic separation in survival

data”. Statistics in Medicine vol. 23, pp. 723–748, 2004.

National Bureau of Statistics Annual Publication Published Reports (2016).




DOI: https://doi.org/10.24203/ajas.v6i5.5492

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