Copyright 2012, Joanna Szyda Nonlinear regression BIOSTATISTICS
1.Binomial distribution - example 2.Transformations of binomial
data logit probit log-log 3.Logistic regression equation equation
parameter estimation example INTRODUCTION Copyright 2012, Joanna
Szyda BINOMIAL DISTRIBUTION Examples ??? Copyright 2012, Joanna
Szyda DATA SAMPLE 1. 1.Testing the strength of joints in aircrafts
2.Various pressure forces tested Copyright 2012, Joanna Szyda
pressure Total number defect DATA SAMPLE 1. Copyright 2012, Joanna
Szyda sick k healthy n-k case212 control Case - a room filled with
cigarette smoke every hour for 12 hr/day 2.Control identical room
without smoke 3.Individuals killed after one year of experiment -
lung cancer DATA SAMPLE 2. Copyright 2012, Joanna Szyda 1.Data is
not continuous 2.Data originate from a binomial distribution 3.Y {
sick, healthy } 4.Probability of cancer health status [y] group [x]
10= case = cont DATA SAMPLE 2. Copyright 2012, Joanna Szyda DATA
TRANSFORMATIONS DATA TRANSFORMATION 0 probability 1 - function of
probability + transformation Copyright 2012, Joanna Szyda
1.Logistic transformation p0 logit(p)- p1 logit(p)+ p=0.5
logit(p)=1 DATA TRANSFORMATION Copyright 2012, Joanna Szyda
1.Logistic transformation DATA TRANSFORMATION Copyright 2012,
Joanna Szyda nonlinear dependence linear dependence 2.Probit
transformation DATA TRANSFORMATION Copyright 2012, Joanna Szyda
3.Log-log transformation DATA TRANSFORMATION Copyright 2012, Joanna
Szyda 1.Logit transformation most common 2.Probit transformation
similar to logit, but more difficult to calculate 3.Log-log
transformation used when data modeling requires nonsymmetrical
distribution with respect to p=0.5 DATA TRANSFORMATION Copyright
2012, Joanna Szyda LOGISTIC REGRESSION EQUATION Copyright 2012,
Joanna Szyda PARAMETER ESTIMATION Iterative least squares method
Fisher's method of scoring Copyright 2012, Joanna Szyda EXAMPLES
EXAMPLE SAMPLE 1 1.Regression equation Copyright 2012, Joanna Szyda
2.E.g. Probability of damage by pressure = Probability of damage
increases with pressure EXAMPLE SAMPLE 1 Copyright 2012, Joanna
Szyda 1.Regression equation choroba k=0/1 n=1 grupa x=0/1 10=b =k
Probability of cancer in case group: 2.Probability of cancer is
lower in a control group 4.Probability of cancer in control group:
EXAMPLE SAMPLE 2 Copyright 2012, Joanna Szyda EXAMPLE Copyright
2012, Joanna Szyda NONLINEAR REGRESSION example datadata
transformation regression equation results interpretation
