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    Non Linear Regression

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    Prasad Tp
    This document discusses linear and non-linear regression analysis. It explains that linear regression assumes a linear relationship between variables, while non-linear regression is needed when the relationship is curved. Some common non-linear models include exponential, logistic, and asymptotic curves. The document demonstrates how to check if a relationship is linear by examining residual plots, and how to transform data or split it into segments to apply multiple regression models if needed to better fit non-linear data.

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    Non Linear Regression

    Uploaded by

    Prasad Tp
    75 views20 pages
    This document discusses linear and non-linear regression analysis. It explains that linear regression assumes a linear relationship between variables, while non-linear regression is needed when the relationship is curved. Some common non-linear models include exponential, logistic, and asymptotic curves. The document demonstrates how to check if a relationship is linear by examining residual plots, and how to transform data or split it into segments to apply multiple regression models if needed to better fit non-linear data.

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    This document discusses linear and non-linear regression analysis. It explains that linear regression assumes a linear relationship between variables, while non-linear regression is needed when the relationship is curved. Some common non-linear models include exponential, logistic, and asymptotic curves. The document demonstrates how to check if a relationship is linear by examining residual plots, and how to transform data or split it into segments to apply multiple regression models if needed to better fit non-linear data.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    75 views20 pages

    Non Linear Regression

    Uploaded by

    Prasad Tp
    This document discusses linear and non-linear regression analysis. It explains that linear regression assumes a linear relationship between variables, while non-linear regression is needed when the relationship is curved. Some common non-linear models include exponential, logistic, and asymptotic curves. The document demonstrates how to check if a relationship is linear by examining residual plots, and how to transform data or split it into segments to apply multiple regression models if needed to better fit non-linear data.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 20

    Non-Linear Regression

    Analysis
    By Chanaka Kaluarachchi

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Presentation outline

    Linear regression

    Checking linear Assumptions

    Linear vs non-linear

    Non linear regression analysis

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Linear regression (reminder)
    Linear regression is an approach for modelling dependent
    variable() and one or more explanatory variables ().

    = 0 + 1 +
    Assumptions:
    ~(0, 2 ) iid ( independently identically distributed)

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Checking linear Assumptions

    iid- residual plot ( ) can be inspect to check that


    assumptions are met.

    Constant variance- Scattering is a constant magnitude

    Normal data- few outliers, systematic spared above and


    below the axis

    Liner relationship- No curve in the residual plot

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Residual plot in SPSS

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Residual plots in SPSS

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Linear vs non linear

    Linear

    Linear scatter plot


    No curves in residual plot
    Correlation between variable is significant

    Non-linear

    Curves in scatter plot


    Curves in residual plot
    No significant correlation between variables

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Non linear regression

    Non linear regression arises when predictors and


    response follows particular function form.

    = , +

    Examples

    = 2 + - non linear = 2 + - linear


    1 1
    = + - non linear = + - linear

    = + - non linear = ln + - linear


    1
    = + - non linear
    1+

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Transformation
    Some nonlinear regression problems can be moved to a linear
    domain by a suitable transformation of the model formulation.

    Four common transformations to induce linearity are:


    logarithmic transformation, square root transformation, inverse
    transformation and the square transformation

    Examples

    = ln = if 0

    1 1
    = 1 = if 0
    1+

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Curve Estimation
    Curve fitting is the process of constructing a curve, or mathematical
    function, that has the best fit to a series of data points.

    Example Viral growth model

    An internet service provider (ISP) is determining the effects of a


    virus on its networks. As part of this effort, they have tracked the
    (approximate) percentage of e-mail traffic on its networks over time,
    from the moment of discovery until the threat was contained.

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Curve Estimation- Cont.

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Output

    Scatter plot
    P value< 0.05
    means model is
    significant
    Higher the
    2 better
    the model fit

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Segmentation
    We can split the graph in to segments and fit a segmented
    model.
    Example Viral growth model

    We can fit a logistic equation for the first 19 hours and an


    asymptotic regression for the remaining hours should provide
    a good fit and interpretability over the entire time period.

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Logistic model and choosing starting values
    1
    =
    1 + 2 3

    Starting values

    1 - upper value of growth (0.65)

    2 - ratio upper value and lowest


    value (0.65/0.13=5)

    3 - estimated slop between


    points in plot.
    (0.6-0.12/19-3)=0.03

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Asymptotic regression model

    = 1 + 2 3

    Starting values

    1 - lowest value (0)

    2 - difference upper value and


    lowest value (0.6)

    3 - estimated slop between


    points in plot.
    (0.6-0.1/20-40)=-0.025

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago
    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago
    Output

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Output

    Research in Pharmacoepidemiology (RIPE) @ National School of Pharmacy, University of Otago


    Thanks for listening

    Research in Pharmacoepidemiology
    Research (RIPE) @ National
    in Pharmacoepidemiology School@
    (RIPE) of Pharmacy,
    National University
    School of of Pharmacy,
    Otago University of Otago

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